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Dissertations / Theses on the topic 'Geometric learning'
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Sturz, Bradley R. Katz Jeffrey S. "Geometric rule learning by pigeons." Auburn, Ala., 2007. http://repo.lib.auburn.edu/2006%20Fall/Dissertations/STURZ_BRADLEY_52.pdf.
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Saive, Yannick. "DirCNN: Rotation Invariant Geometric Deep Learning." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252573.
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Recently geometric deep learning introduced a new way for machine learning algorithms to tackle point cloud data in its raw form. Pioneers like PointNet and many architectures building on top of its success realize the importance of invariance to initial data transformations. These include shifting, scaling and rotating the point cloud in 3D space. Similarly to our desire for image classifying machine learning models to classify an upside down dog as a dog, we wish geometric deep learning models to succeed on transformed data. As such, many models employ an initial data transform in their models which is learned as part of a neural network, to transform the point cloud into a global canonical space. I see weaknesses in this approach as they are not guaranteed to perform completely invariant to input data transformations, but rather approximately. To combat this I propose to use local deterministic transformations which do not need to be learned. The novelty layer of this project builds upon Edge Convolutions and is thus dubbed DirEdgeConv, with the directional invariance in mind. This layer is slightly altered to introduce another layer by the name of DirSplineConv. These layers are assembled in a variety of models which are then benchmarked against the same tasks as its predecessor to invite a fair comparison. The results are not quite as good as state of the art results, however are still respectable. It is also my belief that the results can be improved by improving the learning rate and its scheduling. Another experiment in which ablation is performed on the novel layers shows that the layers main concept indeed improves the overall results.Nyligen har ämnet geometrisk deep learning presenterat ett nytt sätt för maskininlärningsalgoritmer att arbeta med punktmolnsdata i dess råa form.Banbrytande arkitekturer som PointNet och många andra som byggt på dennes framgång framhåller vikten av invarians under inledande datatransformationer. Sådana transformationer inkluderar skiftning, skalning och rotation av punktmoln i ett tredimensionellt rum. Precis som vi önskar att klassifierande maskininlärningsalgoritmer lyckas identifiera en uppochnedvänd hund som en hund vill vi att våra geometriska deep learning-modeller framgångsrikt ska kunna hantera transformerade punktmoln. Därför använder många modeller en inledande datatransformation som tränas som en del av ett neuralt nätverk för att transformera punktmoln till ett globalt kanoniskt rum. Jag ser tillkortakommanden i detta tillgångavägssätt eftersom invariansen är inte fullständigt garanterad, den är snarare approximativ. För att motverka detta föreslår jag en lokal deterministisk transformation som inte måste läras från datan. Det nya lagret i det här projektet bygger på Edge Convolutions och döps därför till DirEdgeConv, namnet tar den riktningsmässiga invariansen i åtanke. Lagret ändras en aning för att introducera ett nytt lager vid namn DirSplineConv. Dessa lager sätts ihop i olika modeller som sedan jämförs med sina efterföljare på samma uppgifter för att ge en rättvis grund för att jämföra dem. Resultaten är inte lika bra som toppmoderna resultat men de är ändå tillfredsställande. Jag tror även resultaten kan förbättas genom att förbättra inlärningshastigheten och dess schemaläggning. I ett experiment där ablation genomförs på de nya lagren ser vi att lagrens huvudkoncept förbättrar resultaten överlag.
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Lamma, Tommaso. "A mathematical introduction to geometric deep learning." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23886/.
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Lo scopo del geometric deep learning è quello di estendere l'algoritmo di deep learning sviluppato per la classificazione di immagini a domini non euclidei come grafi e complessi simpliciali.In questa tesi ci proponiamo di dare una definizione matematica dei concetti cardine utilizzati nel geometric deep learning quali equivarianza e convoluzione sui grafi. Vedremo inoltre come definire una rete convoluzionale invariante rispetto all'azione di gruppi.
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Hold-Geoffroy, Yannick. "Learning geometric and lighting priors from natural images." Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/31264.
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Comprendre les images est d’une importance cruciale pour une pléthore de tâches, de la composition numérique au ré-éclairage d’une image, en passant par la reconstruction 3D d’objets. Ces tâches permettent aux artistes visuels de réaliser des chef-d’oeuvres ou d’aider des opérateurs à prendre des décisions de façon sécuritaire en fonction de stimulis visuels. Pour beaucoup de ces tâches, les modèles physiques et géométriques que la communauté scientifique a développés donnent lieu à des problèmes mal posés possédant plusieurs solutions, dont généralement une seule est raisonnable. Pour résoudre ces indéterminations, le raisonnement sur le contexte visuel et sémantique d’une scène est habituellement relayé à un artiste ou un expert qui emploie son expérience pour réaliser son travail. Ceci est dû au fait qu’il est généralement nécessaire de raisonner sur la scène de façon globale afin d’obtenir des résultats plausibles et appréciables. Serait-il possible de modéliser l’expérience à partir de données visuelles et d’automatiser en partie ou en totalité ces tâches ? Le sujet de cette thèse est celui-ci : la modélisation d’a priori par apprentissage automatique profond pour permettre la résolution de problèmes typiquement mal posés. Plus spécifiquement, nous couvrirons trois axes de recherche, soient : 1) la reconstruction de surface par photométrie, 2) l’estimation d’illumination extérieure à partir d’une seule image et 3) l’estimation de calibration de caméra à partir d’une seule image avec un contenu générique. Ces trois sujets seront abordés avec une perspective axée sur les données. Chacun de ces axes comporte des analyses de performance approfondies et, malgré la réputation d’opacité des algorithmes d’apprentissage machine profonds, nous proposons des études sur les indices visuels captés par nos méthodes.Understanding images is needed for a plethora of tasks, from compositing to image relighting, including 3D object reconstruction. These tasks allow artists to realize masterpieces or help operators to safely make decisions based on visual stimuli. For many of these tasks, the physical and geometric models that the scientific community has developed give rise to ill-posed problems with several solutions, only one of which is generally reasonable. To resolve these indeterminations, the reasoning about the visual and semantic context of a scene is usually relayed to an artist or an expert who uses his experience to carry out his work. This is because humans are able to reason globally on the scene in order to obtain plausible and appreciable results. Would it be possible to model this experience from visual data and partly or totally automate tasks? This is the topic of this thesis: modeling priors using deep machine learning to solve typically ill-posed problems. More specifically, we will cover three research axes: 1) surface reconstruction using photometric cues, 2) outdoor illumination estimation from a single image and 3) camera calibration estimation from a single image with generic content. These three topics will be addressed from a data-driven perspective. Each of these axes includes in-depth performance analyses and, despite the reputation of opacity of deep machine learning algorithms, we offer studies on the visual cues captured by our methods.
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Xia, Baiqiang. "Learning 3D geometric features for soft-biometrics recognition." Thesis, Lille 1, 2014. http://www.theses.fr/2014LIL10132/document.
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La reconnaissance des biomètries douces (genre, âge, etc.)trouve ses applications dans plusieurs domaines. Les approches proposéesse basent sur l’analyse de l’apparence (images 2D), très sensiblesaux changements de la pose et à l’illumination, et surtout pauvre en descriptionsmorphologiques. Dans cette thèse, nous proposons d’exploiterla forme 3D du visage. Basée sur une approche Riemannienne d’analysede formes 3D, nous introduisons quatre descriptions denses à savoir: lasymétrie bilatérale, la moyenneté, la configuration spatiale et les variationslocales de sa forme. Les évaluations faites sur la base FRGCv2 montrentque l’approche proposée est capable de reconnaître des biomètries douces.A notre connaissance, c’est la première étude menée sur l’estimation del’âge, et c’est aussi la première étude qui propose d’explorer les corrélationsentre les attributs faciaux, à partir de formes 3DSoft-Biometric (gender, age, etc.) recognition has shown growingapplications in different domains. Previous 2D face based studies aresensitive to illumination and pose changes, and insufficient to representthe facial morphology. To overcome these problems, this thesis employsthe 3D face in Soft-Biometric recognition. Based on a Riemannian shapeanalysis of facial radial curves, four types of Dense Scalar Field (DSF) featuresare proposed, which represent the Averageness, the Symmetry, theglobal Spatiality and the local Gradient of 3D face. Experiments with RandomForest on the 3D FRGCv2 dataset demonstrate the effectiveness ofthe proposed features in Soft-Biometric recognition. Furtherly, we demonstratethe correlations of Soft-Biometrics are useful in the recognition. Tothe best of our knowledge, this is the first work which studies age estimation,and the correlations of Soft-Biometrics, using 3D face
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Liberatore, Lorenzo. "Introduction to geometric deep learning and graph neural networks." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25339/.
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This thesis proposes an introduction to the fundamental concepts of supervised deep learning. Starting from Rosemblatt's Perceptron we will discuss the architectures that, in recent years, have revolutioned the world of deep learning: graph neural networks, which led to the formulation of geometric deep learning. We will then give a simple example of graph neural network, discussing the code that composes it and then test our
architecture on the MNISTSuperpixels dataset, which is a variation of the benchmark dataset MNIST.
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Araya, Valdivia Ernesto. "Kernel spectral learning and inference in random geometric graphs." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM020.
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Cette thèse comporte deux objectifs. Un premier objectif concerne l’étude des propriétés de concentration des matrices à noyau, qui sont fondamentales dans l’ensemble des méthodes à noyau. Le deuxième objectif repose quant à lui sur l’étude des problèmes d’inférence statistique dans le modèle des graphes aléatoires géométriques. Ces deux objectifs sont liés entre eux par le formalisme du graphon, qui permet représenter un graphe par un noyau. Nous rappelons les rudiments du modèle du graphon dans le premier chapitre. Le chapitre 2 présente des bornes précises pour les valeurs propres individuelles d’une matrice à noyau, où notre principale contribution est d’obtenir des inégalités à l’échelle de la valeur propre en considération. Ceci donne des vitesses de convergence qui sont meilleures que la vitesse paramétrique et, en occasions, exponentielles. Jusqu’ici cela n’avait été établi qu’avec des hypothèses contraignantes dans le contexte des graphes. Nous spécialisons les résultats au cas de noyaux de produit scalaire, en soulignant sa relation avec le modèle des graphes géométriques. Le chapitre 3 étudie le problème d’estimation des distances latentes pour le modèle des graphes aléatoires géométriques dans la sphère Euclidienne. Nous proposons un algorithme spectral efficace qui utilise la matrice d’adjacence pour construire un estimateur de la matrice des distances latentes, et des garanties théoriques pour l’erreur d’estimation, ainsi que la vitesse de convergence, sont montrées. Le chapitre 4 étend les méthodes développées dans le chapitre précédent au cas des graphes aléatoires géométriques dans la boule Euclidienne, un modèle qui, en dépit des similarités formelles avec le cas sphérique, est plus flexible en termes de modélisation. En particulier, nous montrons que pour certains choix des paramètres le profil des dégrées est distribué selon une loi de puissance, ce qui a été vérifié empiriquement dans plusieurs réseaux réels. Tous les résultats théoriques des deux derniers chapitres sont confirmés par des expériences numériquesThis thesis has two main objectives. The first is to investigate the concentration properties of random kernel matrices, which are central in the study of kernel methods. The second objective is to study statistical inference problems on random geometric graphs. Both objectives are connected by the graphon formalism, which allows to represent a graph by a kernel function. We briefly recall the basics of the graphon model in the first chapter. In chapter two, we present a set of accurate concentration inequalities for individual eigenvalues of the kernel matrix, where our main contribution is to obtain inequalities that scale with the eigenvalue in consideration, implying convergence rates that are faster than parametric and often exponential, which hitherto has only been establish under assumptions which are too restrictive for graph applications. We specialized our results to the case of dot products kernels, highlighting its relation with the random geometric graph model. In chapter three, we study the problem of latent distances estimation on random geometric graphs on the Euclidean sphere. We propose an efficient spectral algorithm that use the adjacency matrix to construct an estimator for the latent distances, and prove finite sample guaranties for the estimation error, establishing its convergence rate. In chapter four, we extend the method developed in the previous chapter to the case of random geometric graphs on the Euclidean ball, a model that despite its formal similarities with the spherical case it is more flexible for modelling purposes. In particular, we prove that for certain parameter choices its degree profile is power law distributed, which has been observed in many real life networks. All the theoretical findings of the last two chapters are verified and complemented by numerical experiments
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Masters, Jennifer Ellen. "Investigations in geometric thinking : young children learning with technology." Thesis, Queensland University of Technology, 1997. https://eprints.qut.edu.au/36544/1/36544_Masters_1997.pdf.
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While it is usually assumed that the implementation of computers in the
classroom will enhance teaching and learning, research has suggested that
too often the use of computers does not meet this assumption.
This thesis investigated the implementation of a technology-based
mathematics curriculum unit that was characterised by tasks designed to
promote exploration and investigation of geometric concepts. In particular
it focused on the children's application of prior mathematical knowledge
while they worked in pairs on computer -based tasks.
The study found that children could often apply prior mathematical
knowledge to solve problems in a new context, however, on other occasions
they were unable to do so or they choose to apply less sophisticated
mathematical strategies (such as visual approximation). Other evidence
suggested that at times the children appeared to be constructing new
mathematical ideas or at least, implementing concepts not formally
presented in a school context.
A further observation of this study was that the results of this type of
technological project seemed to be highly dependent on dynamic group
structures and teacher support mechanisms such as scaffolding.
Consequently it was recommended that further research wa
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Peng, Liz Shihching. "p5.Polar - Programming For Geometric Patterns." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-theses/1353.
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Traditional teaching methods are often passive and do not interactively engage students, and this is even more challenging when teaching programming to beginners. In recent years, tech companies such as Google, and academic institutions like MIT, have introduced online learning environments to schools for teaching programming. Most of these learning environments are web-based, interactive, and provide visual feedback. Our project follows these trends and builds on p5.js, a JavaScript library that provides software sketching features and rapid visual feedback to reduce the barrier for learning programming languages. We designed and implemented a new library for drawing geometric patterns using polar coordinate systems, p5.Polar. We then developed a game that incrementally teaches our library to players, and evaluated it with an online user study.
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Batt, Kathleen J. "The Implementation of kinesthetic learning activities to identify geometric shapes with preschool students." Defiance College / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=def1281535832.
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Winer, Michael Loyd. "Students' Reasoning with Geometric Proofs that use Triangle Congruence Postulates." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037701968622.
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García, López Javier. "Geometric computer vision meets deep learning for autonomous driving applications." Doctoral thesis, TDX (Tesis Doctorals en Xarxa), 2021. http://hdl.handle.net/10803/672708.
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This dissertation intends to provide theoretical and practical contributions on the development of deep learning algorithms for
autonomous driving applications. The research is motivated by the need of deep neural networks (DNNs) to get a full
understanding of the surrounding area and to be executed on real driving scenarios with real vehicles equipped with specific
hardware, such as memory constrained (DSP or GPU platforms) or multiple optical sensors, which constraints the algorithm's
development forcing the designed deep networks to be accurate, with minimum number of operations and low memory
consumption.
The main objective of this thesis is, on one hand, the research in the actual limitations of DL-based algorithms that prevent them
of being integrated in nowadays' ADAS (Autonomous Driving System) functionalities, and on the other hand, the design and
implementation of deep learning algorithms able to overcome such constraints to be applied on real autonomous driving
scenarios, enabling their integration in low memory hardware platforms and avoiding sensor redundancy. Deep learning (DL)
applications have been widely exploited over the last years but have some weak points that need to be faced and overcame in
order to fully integrate DL into the development process of big manufacturers or automotive companies, like the time needed to
design, train and validate and optimal network for a specific application or the vast knowledge from the required experts to tune
hyperparameters of predefined networks in order to make them executable in the target platform and to obtain the biggest
advantage of the hardware resources. During this thesis, we have addressed these topics and focused on the implementations
of breakthroughs that would help in the industrial integration of DL-based applications in the automobile industry.
This work has been done as part of the "Doctorat Industrial" program, at the company FICOSA ADAS, and it is because of the
possibilities that developing this research at the company's facilities have brought to the author, that a direct impact of the
achieved algorithms could be tested on real scenarios to proof their validity. Moreover, in this work, the author investigates deep
in the automatic design of deep neural networks (DNN) based on state-of-the-art deep learning frameworks like NAS (neural
architecture search). As stated in this work, one of the identified barriers of deep learning technology in nowadays automobile
companies is the difficulty of developing light and accurate networks that could be integrated in small system on chips (SoC) or
DSP. To overcome this constraint, the author proposes a framework named E-DNAS for the automatic design, training and
validation of deep neural networks to perform image classification tasks and run on resource-limited hardware platforms. This
apporach have been validated on a real system on chip by the company Texas Instrumets (tda2x) provided by the company,
whose results are published within this thesis. As an extension of the mentioned E-DNAS, in the last chapter of this work the
author presents a framework based on NAS valid for detecting objects whose main contribution is a learnable and fast way of
finding object proposals on images that, on a second step, will be classified into one of the labeled classes.Esta disertación tiene como objetivo principal proporcionar contribuciones teóricas y prácticas sobre el desarrollo de algoritmos de aprendizaje profundo para aplicaciones de conducción autónoma. La investigación está motivada por la necesidad de redes neuronales profundas (DNN) para obtener una comprensión completa del entorno y para ejecutarse en escenarios de conducción reales con vehículos reales equipados con hardware específico, los cuales tienen memoria limitada (plataformas DSP o GPU) o utilizan múltiples sensores ópticos Esto limita el desarrollo del algoritmo obligando a las redes profundas diseñadas a ser precisas, con un número mínimo de operaciones y bajo consumo de memoria y energía. El objetivo principal de esta tesis es, por un lado, investigar las limitaciones reales de los algoritmos basados en DL que impiden que se integren en las funcionalidades ADAS (Autonomous Driving System) actuales, y por otro, el diseño e implementación de algoritmos de aprendizaje profundo capaces de superar tales limitaciones para ser aplicados en escenarios reales de conducción autónoma, permitiendo su integración en plataformas de hardware de baja memoria y evitando la redundancia de sensores. Las aplicaciones de aprendizaje profundo (DL) se han explotado ampliamente en los últimos años, pero tienen algunos puntos débiles que deben enfrentarse y superarse para integrar completamente la DL en el proceso de desarrollo de los grandes fabricantes o empresas automobilísticas, como el tiempo necesario para diseñar, entrenar y validar una red óptima para una aplicación específica o el vasto conocimiento de los expertos requeridos para tunear hiperparámetros de redes predefinidas con el fin de hacerlas ejecutables en una plataforma concreta y obtener la mayor ventaja de los recursos de hardware. Durante esta tesis, hemos abordado estos temas y nos hemos centrado en las implementaciones de avances que ayudarían en la integración industrial de aplicaciones basadas en DL en la industria del automóvil. Este trabajo se ha realizado en el marco del programa "Doctorat Industrial", en la empresa FICOSA ADAS, y es por las posibilidades que la empresa ha ofrecido que se ha podido demostrar un impacto rápido y directo de los algoritmos conseguidos en escenarios de test reales para probar su validez. Además, en este trabajo, se investiga en profundidad el diseño automático de redes neuronales profundas (DNN) basadas en frameworks de deep learning de última generación como NAS (neural architecture search). Como se afirma en esta tesis, una de las barreras identificadas de la tecnología de aprendizaje profundo en las empresas automotrices de hoy en día es la dificultad de desarrollar redes ligeras y precisas que puedan integrarse en pequeños systems on chip(SoC) o DSP. Para superar esta restricción, se propone un framework llamado E-DNAS para el diseño automático, entrenamiento y validación de redes neuronales profundas para realizar tareas de clasificación de imágenes y ejecutarse en plataformas de hardware con recursos limitados. Este apporach ha sido validado en un system on chip real de la empresa Texas Instrumets (tda2x) facilitado por FICOSA ADAS, cuyos resultados se publican dentro de esta tesis. Como extensión del mencionado E-DNAS, en el último capítulo de este trabajo se presenta un framework basado en NAS válido para la detección de objetos cuya principal contribución es una forma fácil y rápida de encontrar propuestas de objetos en imágenes que, en un segundo paso, se clasificará en una de las clases etiquetadas.
Automàtica, robòtica i visió
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Jiang, Yiming. "Automated Generation of CAD Big Data for Geometric Machine Learning." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1576329384392725.
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Zhu, Yitan. "Learning Statistical and Geometric Models from Microarray Gene Expression Data." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/28924.
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In this dissertation, we propose and develop innovative data modeling and analysis methods for extracting meaningful and specific information about disease mechanisms from microarray gene expression data.
To provide a high-level overview of gene expression data for easy and insightful understanding of data structure, we propose a novel statistical data clustering and visualization algorithm that is comprehensively effective for multiple clustering tasks and that overcomes some major limitations of existing clustering methods. The proposed clustering and visualization algorithm performs progressive, divisive hierarchical clustering and visualization, supported by hierarchical statistical modeling, supervised/unsupervised informative gene/feature selection, supervised/unsupervised data visualization, and user/prior knowledge guidance through human-data interactions, to discover cluster structure within complex, high-dimensional gene expression data.
For the purpose of selecting suitable clustering algorithm(s) for gene expression data analysis, we design an objective and reliable clustering evaluation scheme to assess the performance of clustering algorithms by comparing their sample clustering outcome to phenotype categories. Using the proposed evaluation scheme, we compared the performance of our newly developed clustering algorithm with those of several benchmark clustering methods, and demonstrated the superior and stable performance of the proposed clustering algorithm.
To identify the underlying active biological processes that jointly form the observed biological event, we propose a latent linear mixture model that quantitatively describes how the observed gene expressions are generated by a process of mixing the latent active biological processes. We prove a series of theorems to show the identifiability of the noise-free model. Based on relevant geometric concepts, convex analysis and optimization, gene clustering, and model stability analysis, we develop a robust blind source separation method that fits the model to the gene expression data and subsequently identify the underlying biological processes and their activity levels under different biological conditions.
Based on the experimental results obtained on cancer, muscle regeneration, and muscular dystrophy gene expression data, we believe that the research work presented in this dissertation not only contributes to the engineering research areas of machine learning and pattern recognition, but also provides novel and effective solutions to potentially solve many biomedical research problems, for improving the understanding about disease mechanisms.Ph. D.
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Ajam, Gard Nima. "Human Contour Detection and Tracking: A Geometric Deep Learning Approach." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1565803754784589.
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Arvidsson, Simon, and Marcus Gullstrand. "Predicting forest strata from point clouds using geometric deep learning." Thesis, Jönköping University, JTH, Avdelningen för datavetenskap, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-54155.
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Introduction: Number of strata (NoS) is an informative descriptor of forest structure and is therefore useful in forest management. Collection of NoS as well as other forest properties is performed by fieldworkers and could benefit from automation. Objectives: This study investigates automated prediction of NoS from airborne laser scanned point clouds over Swedish forest plots.Methods: A previously suggested approach of using vertical gap probability is compared through experimentation against the geometric neural network PointNet++ configured for ordinal prediction. For both approaches, the mean accuracy is measured for three datasets: coniferous forest, deciduous forest, and a combination of all forests. Results: PointNet++ displayed a better point performance for two out of three datasets, attaining a top mean accuracy of 46.2%. However only the coniferous subset displayed a statistically significant superiority for PointNet++. Conclusion: This study demonstrates the potential of geometric neural networks for data mining of forest properties. The results show that impediments in the data may need to be addressed for further improvements.
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Strack, Robert. "Geometric Approach to Support Vector Machines Learning for Large Datasets." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3124.
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The dissertation introduces Sphere Support Vector Machines (SphereSVM) and Minimal Norm Support Vector Machines (MNSVM) as the new fast classification algorithms that use geometrical properties of the underlying classification problems to efficiently obtain models describing training data. SphereSVM is based on combining minimal enclosing ball approach, state of the art nearest point problem solvers and probabilistic techniques. The blending of the three speeds up the training phase of SVMs significantly and reaches similar (i.e., practically the same) accuracy as the other classification models over several big and large real data sets within the strict validation frame of a double (nested) cross-validation (CV). MNSVM is further simplification of SphereSVM algorithm. Here, relatively complex classification task was converted into one of the simplest geometrical problems -- minimal norm problem. This resulted in additional speedup compared to SphereSVM. The results shown are promoting both SphereSVM and MNSVM as outstanding alternatives for handling large and ultra-large datasets in a reasonable time without switching to various parallelization schemes for SVMs algorithms proposed recently. The variants of both algorithms, which work without explicit bias term, are also presented. In addition, other techniques aiming to improve the time efficiency are discussed (such as over-relaxation and improved support vector selection scheme). Finally, the accuracy and performance of all these modifications are carefully analyzed and results based on nested cross-validation procedure are shown.
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Kodipaka, Santhosh. "A novel conic section classifier with tractable geometric learning algorithms." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024624.
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Zhou, Bingxin. "Geometric Signal Processing with Graph Neural Networks." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/28617.
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One of the most predominant techniques that have achieved phenomenal success in many modern applications is deep learning. The obsession with massive data analysis in image recognition, speech processing, and text understanding spawns remarkable advances in deep learning of diverse research areas. The alliance of deep learning technologies yields mighty graph neural networks (GNNs), an emerging type of deep neural networks that encodes internal structural relationships of inputs. The mainstream of GNNs finds an adequate numerical representation of graphs, which is vital to the prediction performance of machine learning models. Graph representation learning has many real-world applications, such as drug repurposing, protein classification, epidemic spread controlling, and social networks analysis. The rapid development of GNNs in the last five years has witnessed a couple of design flaws, such as over-smoothing, vulnerability to perturbation, lack of expressivity, and missing explainability. Meanwhile, the persistent enthusiasm in this research area allows for cumulative experience in solving complicated problems, such as size-variant graph compression and time-variant graph dynamic capturing.
The ambition of this thesis is to shed some light of mathematics on a few outlined issues. The permutation-invariant design of graph compression is supported by manifold learning, the robust graph smoothing relies heavily on the principles of convex optimization, and the efficient dynamic graph embedding leverages global spectral transforms and power method singular value decomposition. The author believes that the effectiveness of deep learning designs should not be oriented solely by performance over particular datasets. Modifications on a black-box model should operate beyond fine-tuning tricks. The reliability of deep learning looks forward to designing models with rigorous mathematics so that the `computer science' becomes actual science one day.
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Leung, Hoi-cheung, and 梁海翔. "Enhancing students' ability and interest in geometry learning through geometric constructions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48367746.
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Students nowadays are relatively confident in directly applying geometrical theorems and theories. Nevertheless, it has been a common phenomenon that students are not confident in constructing geometric proofs. They lack the confidence and sufficient experience and knowledge in conducting deductive geometrical proofs. To some students, they treat proofs simply as another type of examination questions which they can tackle by repeated drillings.
Students make use of straightedges and compasses to construct different geometry figures in geometric constructions. Through geometric constructions, we can train our prediction and logical thinking skills when investigating the properties of geometric figures. Geometric constructions provide students with hands-on experience to geometry learning which requires students to have more in-depth thinking.
This is an empirical study on the implementation of geometric construction workshops among junior secondary students in Hong Kong. Results have shown that students enjoyed the construction tasks during the workshops. Analysis has implied that geometric constructions help improve students’ ability in constructing geometric proofs and to raise their interests in geometry learning.published_or_final_version
Education
Master
Master of Education
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Abbas, Ayman. "A modelling approach to individualised computer aided learning for geometric design." Thesis, University of Strathclyde, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324096.
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Duong, Nam duong. "Hybrid Machine Learning and Geometric Approaches for Single RGB Camera Relocalization." Thesis, CentraleSupélec, 2019. http://www.theses.fr/2019CSUP0008.
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Au cours des dernières années, la relocalisation de la caméra à base d'images est devenue un enjeu important de la vision par ordinateur appliquée à la réalité augmentée, à la robotique ainsi qu'aux véhicules autonomes. La relocalisation de la caméra fait référence à la problématique de l'estimation de la pose de la caméra incluant à la fois la translation 3D et la rotation 3D. Dans les systèmes de localisation, le composant de relocalisation de la caméra est nécessaire pour récupérer la pose de la caméra après le suivi perdu, plutôt que de redémarrer la localisation à partir de zéro.Cette thèse vise à améliorer les performances de la relocalisation de la caméra en termes de temps d'exécution et de précision ainsi qu'à relever les défis de la relocalisation des caméras dans des environnements dynamiques.Nous présentons l'estimation de la pose de la caméra basée sur la combinaison de la régression de pose multi-patch pour surmonter l'incertitude des méthodes d'apprentissage profond de bout en bout. Afin d'équilibrer la précision et le temps de calcul de la relocalisation de la caméra à partir d'une seule image RVB, nous proposons une méthode hybride à caractéristiques éparses. Une meilleure prédiction dans la partie d’apprentissage automatique de nos méthodes conduit à une inférence rapide de la pose de la caméra dans la partie géométrique. Pour relever le défi des environnements dynamiques, nous proposons une forêt de régression adaptative qui s'adapte en temps réel au modèle prédictif. Il évolue en partie au fil du temps sans qu'il soit nécessaire de ré-entrainer le modèle entier à partir de zéro. En appliquant cet algorithme à notre relocalisation de la caméra en temps réel et précise, nous pouvons faire face à des environnements dynamiques, en particulier des objets en mouvement. Les expériences prouvent l'efficacité des méthodes que nous proposons. Notre méthode permet d'obtenir des résultats aussi précis que les meilleures méthodes d’état de l’art. De plus, nous obtenons également une grande précision même sur des scènes dynamiquesIn the last few years, image-based camera relocalization becomes an important issue of computer vision applied to augmented reality, robotics as well as autonomous vehicles. Camera relocalization refers to the problematic of the camera pose estimation including both 3D translation and 3D rotation. In localization systems, camera relocalization component is necessary to retrieve camera pose after tracking lost, rather than restarting the localization from scratch.This thesis aims at improving the performance of camera relocalization in terms of both runtime and accuracy as well as handling challenges of camera relocalization in dynamic environments. We present camera pose estimation based on combining multi-patch pose regression to overcome the uncertainty of end-to-end deep learning methods. To balance between accuracy and computational time of camera relocalization from a single RGB image, we propose a sparse feature hybrid methods. A better prediction in the machine learning part of our methods leads to a rapid inference of camera pose in the geometric part. To tackle the challenge of dynamic environments, we propose an adaptive regression forest algorithm that adapts itself in real time to predictive model. It evolves by part over time without requirement of re-training the whole model from scratch. When applying this algorithm to our real-time and accurate camera relocalization, we can cope with dynamic environments, especially moving objects. The experiments proves the efficiency of our proposed methods. Our method achieves results as accurate as the best state-of-the-art methods on the rigid scenes dataset. Moreover, we also obtain high accuracy even on the dynamic scenes dataset
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Qiu, Xuchong. "2D and 3D Geometric Attributes Estimation in Images via deep learning." Thesis, Marne-la-vallée, ENPC, 2021. http://www.theses.fr/2021ENPC0005.
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La perception visuelle d'attributs géométriques (ex. la translation, la rotation, la taille, etc.) est très importante dans les applications robotiques. Elle permet à un système robotique d'acquérir des connaissances sur son environnement et peut fournir des entrées pour des tâches telles que la localisation d'objets, la compréhension de scènes et la planification de trajectoire. Le principal objectif de cette thèse est d'estimer la position et l'orientation d'objets d'intérêt pour des tâches de manipulation robotique. En particulier, nous nous intéressons à la tâche de bas niveau d'estimation de la relation d'occultation, afin de mieux pouvoir discriminer objets différents, et aux tâches de plus haut niveau de suivi visuel d'objets et d'estimation de leur position et orientation. Le premier axe d'étude est le suivi (tracking) d'un objet d'intérêt dans une vidéo, avec des locations et tailles correctes. Tout d'abord, nous étudions attentivement le cadre du suivi d'objet basé sur des filtres de corrélation discriminants et proposons d'exploiter des informations sémantiques à deux niveaux~: l'étape d'encodage des caractéristiques visuelles et l'étape de localisation de la cible. Nos expériences démontrent que l'usage de la sémantique améliore à la fois les performances de la localisation et de l'estimation de taille de l'objet suivi. Nous effectuons également des analyses pour comprendre les cas d'échec. Le second axe d'étude est l'utilisation d'informations sur la forme des objets pour améliorer la performance de l'estimation de la pose 6D des objets et de son raffinement. Nous proposons d'estimer avec un modèle profond les projections 2D de points 3D à la surface de l'objet, afin de pouvoir calculer la pose 6D de l'objet. Nos résultats montrent que la méthode que nous proposons bénéficie du grand nombre de correspondances de points 3D à 2D et permet d'obtenir une meilleure précision des estimations. Dans un deuxième temps, nous étudions les contraintes des méthodes existantes pour raffiner la pose d'objets et développons une méthode de raffinement des objets dans des contextes arbitraires. Nos expériences montrent que nos modèles, entraînés sur des données réelles ou des données synthétiques générées, peuvent raffiner avec succès les estimations de pose pour les objets dans des contextes quelconques. Le troisième axe de recherche est l'étude de l'occultation géométrique dans des images, dans le but de mieux pouvoir distinguer les objets dans la scène. Nous formalisons d'abord la définition de l'occultation géométrique et proposons une méthode pour générer automatiquement des annotations d'occultation de haute qualité. Ensuite, nous proposons une nouvelle formulation de la relation d'occultation (abbnom) et une méthode d'inférence correspondante. Nos expériences sur les jeux de tests pour l'estimation d'occultations montrent la supériorité de notre formulation et de notre méthode. Afin de déterminer des discontinuités de profondeur précises, nous proposons également une méthode de raffinement de cartes de profondeur et une méthode monoculaire d'estimation de la profondeur en une étape. En utilisant l'estimation de relations d'occultation comme guide, ces deux méthodes atteignent les performances de l'état de l'art. Toutes les méthodes que nous proposons s'appuient sur la polyvalence et la puissance de l'apprentissage profond. Cela devrait faciliter leur intégration dans le module de perception visuelle des systèmes robotiques modernes. Outre les avancées méthodologiques mentionnées ci-dessus, nous avons également rendu publiquement disponibles des logiciels (pour l'estimation de l'occlusion et de la pose) et des jeux de données (informations de haute qualité sur les relations d'occultation) afin de contribuer aux outils offerts à la communauté scientifiqueThe visual perception of 2D and 3D geometric attributes (e.g. translation, rotation, spatial size and etc.) is important in robotic applications. It helps robotic system build knowledge about its surrounding environment and can serve as the input for down-stream tasks such as motion planning and physical intersection with objects.The main goal of this thesis is to automatically detect positions and poses of interested objects for robotic manipulation tasks. In particular, we are interested in the low-level task of estimating occlusion relationship to discriminate different objects and the high-level tasks of object visual tracking and object pose estimation.The first focus is to track the object of interest with correct locations and sizes in a given video. We first study systematically the tracking framework based on discriminative correlation filter (DCF) and propose to leverage semantics information in two tracking stages: the visual feature encoding stage and the target localization stage. Our experiments demonstrate that the involvement of semantics improves the performance of both localization and size estimation in our DCF-based tracking framework. We also make an analysis for failure cases.The second focus is using object shape information to improve the performance of object 6D pose estimation and do object pose refinement. We propose to estimate the 2D projections of object 3D surface points with deep models to recover object 6D poses. Our results show that the proposed method benefits from the large number of 3D-to-2D point correspondences and achieves better performance. As a second part, we study the constraints of existing object pose refinement methods and develop a pose refinement method for objects in the wild. Our experiments demonstrate that our models trained on either real data or generated synthetic data can refine pose estimates for objects in the wild, even though these objects are not seen during training.The third focus is studying geometric occlusion in single images to better discriminate objects in the scene. We first formalize geometric occlusion definition and propose a method to automatically generate high-quality occlusion annotations. Then we propose a new occlusion relationship formulation (i.e. abbnom) and the corresponding inference method. Experiments on occlusion reasoning benchmarks demonstrate the superiority of the proposed formulation and method. To recover accurate depth discontinuities, we also propose a depth map refinement method and a single-stage monocular depth estimation method.All the methods that we propose leverage on the versatility and power of deep learning. This should facilitate their integration in the visual perception module of modern robotic systems.Besides the above methodological advances, we also made available software (for occlusion and pose estimation) and datasets (of high-quality occlusion information) as a contribution to the scientific community
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Luo, Simon Junming. "An Information Geometric Approach to Increase Representational Power in Unsupervised Learning." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25773.
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Machine learning models increase their representational power by increasing the number of parameters in the model. The number of parameters in the model can be increased by introducing hidden nodes, higher-order interaction effects or by introducing new features into the model. In this thesis we study different approaches to increase the representational power in unsupervised machine learning models. We investigate the use of incidence algebra and information geometry to develop novel machine learning models to include higher-order interactions effects into the model. Incidence algebra provides a natural formulation for combinatorics by expressing it as a generative function and information geometry provides many theoretical guarantees in the model by projecting the problem onto a dually flat Riemannian structure for optimization. Combining the two techniques together formulates the information geometric formulation of the binary log-linear model. We first use the information geometric formulation of the binary log-linear model to formulate the higher-order Boltzmann machine (HBM) to compare the different behaviours when using hidden nodes and higher-order feature interactions to increase the representational power of the model. We then apply the concepts learnt from this study to include higher-order interaction terms in Blind Source Separation (BSS) and to create an efficient approach to estimate higher order functions in Poisson process. Lastly, we explore the possibility to use Bayesian non-parametrics to automatically reduce the number of higher-order interactions effects included in the model.
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IQBAL, HAFSA. "Learning of Geometric-based Probabilistic Self-Awareness Model for Autonomous Agents." Doctoral thesis, Università degli studi di Genova, 2022. http://hdl.handle.net/11567/1081940.
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In the emerging domain of self-aware and autonomous systems, the causal representation of the variables and the learning of their dynamics to make inferences of the future state at multiple abstraction levels in successive temporal slices, are getting attention of the researchers. This work presents a novel data-driven approach to learn the causal representation of the dynamic probabilistic graphical model. The proposed method employed the geometric-based approach to define the set of clusters of similar Generalized State (GS) space as linear attractors. Clustering of data variables corresponding to the linear attractors defines a set of switching vocabulary, which provides the higher-level representation of the graphical model, i.e., discrete and continuous levels. The transitions between the switching vocabulary are represented with the transition matrix, estimated from the temporal data series in switching models based on GSs. Each learned representation of the dynamic probabilistic graphical model is stored in Autobiographical Memory (AM) layers. A Markov Jump Particle Filter (MJPF) is proposed to make inferences at multiple abstraction levels of graphs which facilitates the detection of anomalies. Anomalies indicate that the agent encounters new experiences which can be learned incrementally and evolve new layers of AM.
The proposed approach is extended for the learning of interactions between autonomous agents to make them self-aware. In Low dimensional case, data from the odometry trajectories and the control parameters, i.e., steering angle and rotors' velocity, is employed. However, data from the LiDAR, i.e., 3D point clouds, is used for the high-dimensional case. The deep learning approach, such as 3D Convolutional Encode-Decoder together with the transfer learning employed to extract the features from the LiDAR’s point clouds. A similar learning approach (mentioned above) is employed to detect anomalous situations. Three predictive models, i.e., piecewise nonlinear, piecewise linear, and nonlinear models, are proposed to analyse the multiple abstraction level anomalies, i.e., continuous level, discrete level, and voxel level. Concurrently, the public KITTI dataset from the complex/urban environment is employed to validate the proposed methodology. Qualitative and quantitative analysis of the proposed methodology is perform by employing the anomaly measurements and the ROC curves to estimate the accuracy, respectively.
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Tachibana, Kanta, Takeshi Furuhashi, Tomohiro Yoshikawa, Eckhard Hitzer, and MINH TUAN PHAM. "Clustering of Questionnaire Based on Feature Extracted by Geometric Algebra." 日本知能情報ファジィ学会, 2008. http://hdl.handle.net/2237/20676.
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Session ID: FR-G2-2Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, September 17-21, 2008, Nagoya University, Nagoya, Japan
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Zhang, Chao. "Learning non-rigid, 3D shape variations using statistical, physical and geometric models." Thesis, University of York, 2018. http://etheses.whiterose.ac.uk/22342/.
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3D shape modelling is a fundamental component in computer vision and computer graphics. Applications include shape interpolation and extrapolation, shape reconstruction, motion capture and mesh editing, etc. By "modelling" we mean the process of learning a parameter-driven model. This thesis focused on the scope of statistical modelling for 3D non-rigid shapes, such as human faces and bodies. The problem is challenging due to highly non-linear deformations, high dimensionality, and data sparsity. Several new algorithms are proposed for 3D shape modelling, 3D shape matching (computing dense correspondence) and applications. First, we propose a variant of Principal Component Analysis called "Shell PCA" which provides a physically-inspired statistical shape model. This is our first attempt to use a physically plausible metric (specifically, the discrete shell model) for statistical shape modelling. Second, we further develop this line of work into a fully Riemannian approach called "Shell PGA". We demonstrate how to perform Principal Geodesic Analysis in the space of discrete shells. To achieve this, we present an alternate formulation of PGA which avoids working in the tangent space and deals with shapes lying on the manifold directly. Unlike displacement-based methods, Shell PGA is invariant to rigid body motion, and therefore alignment preprocessing such as Procrustes analysis is not needed. Third, we propose a groupwise shape matching method using functional map representation. Targeting at near-isometric deformations, we consider groupwise optimisation of consistent functional maps over a product of Stiefel manifolds, and optimise over a minimal subset of the transformations for efficiency. Last, we show that our proposed shape model achieves state-of-the-art performance in two very challenging applications: handle-based mesh editing, and model fitting using motion capture data. We also contribute a new algorithm for human body shape estimation using clothed scan sequence, along with a new dataset "BUFF" for evaluation.
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Roux, Annalie. "Die invloed van taalvaardigheid op die meetkundedenke van graad 8 en 9 leerders / Annalie Roux." Thesis, North-West University, 2004. http://hdl.handle.net/10394/4482.
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Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels
(d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language.Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.
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Kale, Neslihan. "A Comparision Of Drama-based Learning And Cooperative Learning With Respect To Seventh Grade Students." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609108/index.pdf.
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This study aimed to determine the effects of drama based learning on seventh grade students&rsquoachievement (angles and polygons, circle and cylinder), attitudes and thinking levels in geometry compared to the cooperative learning. The study was conducted on four seventh grade classes from two public elementary schools in the same district in the 2006-2007 academic year, lasting seven and a half week (30 lesson hours). The data were collected through angles and polygons (APA)
and circle and cylinder achievement (CCA) tests, the van Hiele geometric thinking level test (POSTVHL), geometry attitude scale (PRE-POSTGAS). The quantitative analyses were carried out by using Multivariate Analysis of Variance (MANOVA). The results showed that drama based learning had a significant effect on students&rsquo
angles and polygons achievement, circle and cylinder achievement, van Hiele geometric thinking level compared to the cooperative learning. However, attitude findings regarding the attitudes revealed that there is not a significant difference according to the geometry attitudes of drama group and cooperative group after treatment. Both the two instructional methods supported active participation, created cooperative working environment, included daily life examples and gave the chance to classroom communication. On the other hand, drama group students&rsquo
significantly better performance was attributable to the make belief plays and improvisations of daily life examples included in drama activities.
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Qhibi, Agness Dulu. "Alignment between senior phase mathematics content standards and numeric and geometric patterns' workbook activities." Thesis, University of Limpopo, 2019. http://hdl.handle.net/10386/3147.
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Thesis (M.Ed. (Mathematics Education)) -- University of Limpopo, 2019Alignment between content standards, instruction, assessment and learning materials assists in achieving the intended content in the classroom. The purpose of this study was to explore the alignment between Senior Phase Mathematics Content Standards (SPMCS) and numeric and geometric patterns’ workbook activities. The problem was that teachers sometimes use the Department of Basic Education’s workbooks interchangeably with textbooks, while their purpose is to supplement textbooks and provide worksheets for the learners. The alignment status of the Department of Basic Education (DBE) senior phase mathematics’ workbooks could not be found in the literature. Mixed methods research and document analysis were employed to explore the status of alignment between SPMCS and DBE workbook activities on Numeric and Geometric Patterns (NGP). This was aimed at highlighting the status of alignment in terms of the content structure and the alignment indices through the use of alignment model of Webb (1997) and of Porter (2002). The findings of this study revealed that the alignment between SPMCS and DBE workbook activities on NGP in terms of the categorical concurrence, depth of knowledge consistency and range of knowledge correspondence ranges from ‘acceptable’ to ‘full’ level of agreement. However, content beyond the scope of the content standards was found in Grade 7 and Grade 8 DBE workbook activities on NGP. The computed alignment indices for Grade 7, Grade 8 and Grade 9 range from moderate to strong alignment. Besides, weak and strong discrepancies were identified, which need to be addressed to improve the content structure of the DBE workbooks. This study recommends two alignment models to explore the alignment between educational components for comprehensive results and complementation. In addition, studies such as this should be conducted to enhance the quality in developing assessments in future. KEY CONCEPTS Alignment; assessment; content standards; learning materials; workbooks; numeric patterns and geometric patterns.
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Anderson, Joseph T. "Geometric Methods for Robust Data Analysis in High Dimension." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488372786126891.
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GLIDER, PEGGY. "THE EMERGENCE OF CHILDREN'S SPATIAL ABILITIES: A QUESTION OF GEOMETRIC PRECISION." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183953.
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This research investigated the precision with which spatial information can be maintained in memory and reproduced as well as factors which may effect these emerging abilities. To study this, ten males and ten females in each of first, third, fifth, and seventh grades participated in three drawing tasks under two conditions (match and recall). The tasks involved the presentation of a 4" straight line or a 2" x 2" right angle drawn on an 8" white disc. Subjects were asked to draw a line exactly the same size and in the same place (static), after an imagined rotation, or after an imagined bending or unbending of the line (transformation) on an 1" white disc. Several mixed design analyses of variance with repeated measures on the task variables were run. First graders made significantly more errors than all other subjects. Third and fifth graders differed little and both performed significantly less accurately than seventh graders. Performance on the rotation task and the transformation task did not differ significantly with performance on both yielding more error than performance on the static task. The match condition generally proved easier than the recall condition, straight lines led to less error than bent lines, and orientation information was more accurately preserved than metric information. The requirements of the task, i.e., no change, change in position, or a change in form, interacted with both the stimulus type and the type of information preserved. Grade level also interacted significantly with task and stimulus type. When determining how spatial abilities emerge and the accuracy with which spatial information can be dealt, task demands, stimulus characteristics, and type of information being measured must be considered along with the developmental changes.
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Rodrigues, Camila Roberta Ferrão. "Potencialidades e possibilidades do ensino das transformações geométricas no Ensino Fundamental." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/61264.
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Este estudo tem como objetivo examinar as possibilidades e potencialidades do ensino das Transformações Geométricas no Ensino Fundamental, assunto este pouco abordado nos currículos deste nível de ensino. Realiza um resgate histórico sobre o ensino da Geometria e constata que a introdução do tema das transformações se dá a partir do Movimento da Matemática Moderna. Identifica os Parâmetros Curriculares Nacionais como incentivador deste estudo, a partir do momento em que, devido a essas orientações, autores de livros didáticos passam a tratar do tema em suas coleções, mesmo que, em alguns casos, de forma tímida. Para verificar as potencialidades do estudo das Transformações Geométricas foram elaborados dois conjuntos de atividades, sendo um desenvolvido com professoras atuantes nos Anos Iniciais do Ensino Fundamental e outro com uma turma de alunos do 6º ano desse nível de ensino, ambas em uma escola municipal da Rede Pública de Ensino da cidade de São Leopoldo, RS. Esta pesquisa de caráter qualitativo segue princípios da pesquisa-ação, adotando procedimentos de acompanhamento e controle da intervenção produzida. Da análise da aplicação da proposta, foi produzido um livro do tipo paradidático intitulado Matemática das Transformações, o qual trata o tema com aspectos lúdicos, de caráter artístico e que, pela linguagem nele utilizada, tem a pretensão de incentivar a leitura.This study intents to examine the possibilities and potential of Geometric Transformations in teaching Elementary School, a few discussed subject in the curriculum of this educational level. Performs a historical survey about the teaching of geometry and notes that the introduction of the theme of change is given from the Movement of Modern Mathematics. Identifies how the National Curriculum Parameters for this study, from the time when, due to these guidelines, authors of textbooks come to address the issue in their collections, even though in some cases, so shy. To verify the potential of the study of Geometric Transformations were prepared two sets of activities, one developed with teachers working in early years of elementary school and another with a group of students from the 6th year of this level of education, both in a municipal school of the Network public Schools in the city of São Leopoldo, RS. This qualitative study follows the principles of action-research, adopting procedures for monitoring and control of the intervention produced. An analysis of the implementation of the proposal, was produced a textbook titled Transformation’s Mathematics , which treats the subject with playful aspects of artistic character, and that the language used therein, intend to encourage reading.
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McManigle, John E. "Three-dimensional geometric image analysis for interventional electrophysiology." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:2f36fa8e-9c64-4807-97c0-25e63398da7e.
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Improving imaging hardware, computational power, and algorithmic design are driving advances in interventional medical imaging. We lay the groundwork here for more effective use of machine learning and image registration in clinical electrophysiology. To achieve identification of atrial fibrosis using image data, we registered the electroanatomic map (EAM) data of atrial fibrillation (AF) patients undergoing pulmonary vein isolation (PVI) with MR (n = 16) or CT (n = 18) images. The relationship between image features and bipolar voltage was evaluated using single-parameter regression and random forest models. Random forest performed significantly better than regression, identifying fibrosis with area under the receiver operating characteristic curve (AUC) 0.746 (MR) and 0.977 (CT). This is the first evaluation of voltage prediction using image data. Next, we compared the character of native atrial fibrosis with ablation scar in MR images. Fourteen AF patients undergoing repeat PVI were recruited. EAM data from their first PVI was registered to the MR images acquired before the first PVI (‘pre-operative’) and before the second PVI ('post-operative' with respect to the first PVI). Non-ablation map points had similar characteristics in the two images, while ablation points exhibited higher intensity and more heterogeneity in post-operative images. Ablation scar is more strongly enhancing and more heterogeneous than native fibrosis. Finally, we addressed myocardial measurement in 3-D echocardiograms. The circular Hough transform was modified with a feature asymmetry filter, epicardial edges, and a search constraint. Manual and Hough measurements were compared in 5641 slices from 3-D images. The enhanced Hough algorithm was more accurate than the unmodified version (Dice coefficient 0.77 vs. 0.58). This method promises utility in segmentation-assisted cross-modality registration. By improving the information that can be extracted from medical images and the ease with which that information can be accessed, this progress will contribute to the advancing integration of imaging in electrophysiology.
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Zisler, Matthias [Verfasser], and Christoph [Akademischer Betreuer] Schnörr. "Non-Convex and Geometric Methods for Tomography and Label Learning / Matthias Zisler ; Betreuer: Christoph Schnörr." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1218547111/34.
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Silva, Evandro Ortiz da. "PROBLEMAS NO ENSINO DE GEOMETRIA: UMA PROPOSTA E ANÁLISE DA GEOMETRIA COMO DISCIPLINA NO ENSINO FUNDAMENTAL ALIADA AO ENSINO DE DESENHO GEOMÉTRICO." Universidade Estadual de Ponta Grossa, 2017. http://tede2.uepg.br/jspui/handle/prefix/2401.
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O ensino de geometria ao longo do tempo passou por algumas modificações. Esse processo desencadeou problemas, e em alguns momentos no abandono do ensino de geometria e no distanciamento dos elementos do desenho geométrico do currículo escolar sendo esse quadro agravado pelo acúmulo de funções que foram depositados na escola e nos professores nesse período e nas políticas públicas adotadas pela influência da sociedade com a expansão da escola pública. O presente trabalho buscou investigar bibliograficamente problemas que interferem ou causam dificuldades na aprendizagem de geometria. Através de questionário aplicado e da análise de seus resultados, verificou-se que muitos alunos do ensino fundamental de uma escola pública acumulam dificuldades em assimilar a sequência de conteúdos de geometria, podendo comprometer seu desempenho em estudos posteriores. Certos dessas dificuldades e tendo consciência de que qualquer mudança no sistema de ensino necessita da apreciação dos profissionais envolvidos, desenvolveu-se uma pesquisa com professores do NRE de Guarapuava – PR para fortalecer a justificativa de implementação da proposta de inserção da disciplina de geometria atrelada aos conceitos e ferramentas do desenho geométrico na matriz curricular das escolas públicas do Estado do Paraná, mais precisamente no 9º ano. Proposta essa, pensada como ponto inicial para solução dos problemas apontados. Como resultados obtiveram-se, além da concordância da maioria dos docentes na análise dessa proposta e de sugestões para seu aprimoramento, um perfil dos profissionais, do ensino atual e da aprendizagem dos alunos em relação aos conteúdos de geometria.
The teaching of geometry over time has undergone some modifications. This process triggered problems and in some moments the abandonment of the teaching of geometry and the distancing of the elements of the geometric design in the school curriculum. This situation were aggravated by the accumulation of functions that has been deposited in the school and the teachers in that period as the public policies adopted by the influence of society with an expansion of the public school. The present work aimed to investigate in a bibliographically way problems which to arise from a process that interferes or causes difficulties in the learning of geometry. Through of the applied questionnaire and the analysis of their results it was verified that, the students of the public elementary schools accumulate difficulties in assimilating the sequence of geometry contents, compromising their performance in later studies. Conscious of these difficulties and that any changes in the education system requires the appreciation of the professionals involved, a research was applied with teachers of the NRE of Guarapuava (PR). The intent was to strengthen the proposal‗s implementation of the geometry‘s discipline insertion, tied to concepts and tools of the geometric design in the curricular matrix of the public schools of the State of Paraná, more precisely in the 9th grade. The proposal was studied as the initial point to solving detected problems. As results of the research, it was obtained the agreement of the majority of teachers in the analysis of this proposal as well suggestions for its improvement and in addition a profile of the professionals of the current teaching and the students' learning in relation to the geometry discipline.
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Zhao, Yongheng. "3D feature representations for visual perception and geometric shape understanding." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3424787.
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In this thesis, we first present a unified look to several well known 3D feature representations, ranging from hand-crafted design to learning based ones. Then, we propose three kinds of feature representations from both RGB-D data and point cloud, addressing different problems and aiming for different functionality.
With RGB-D data, we address the existing problems of 2D feature representation in visual perception by integrating with the 3D information. We propose an RGB-D data based feature representation which fuses object's statistical color model and depth information in a probabilistic manner. The depth information is able to not only enhance the discriminative power of the model toward clutters with a different range but also can be used as a constraint to properly update the model and reduce model drifting. The proposed representation is then evaluated in our proposed object tracking algorithm (named MS3D) on a public RGB-D object tracking dataset. It runs in real-time and produces the best results compared against the other state-of-the-art RGB-D trackers. Furthermore, we integrate MS3D tracker in an RGB-D camera network in order to handle long-term and full occlusion. The accuracy and robustness of our algorithm are evaluated in our presented dataset and the results suggest our algorithm is able to track multiple objects accurately and continuously in the long term.
For 3D point cloud, the current deep learning based feature representations often discard spatial arrangements in data, hence falling short of respecting the parts-to-whole relationship, which is critical to explain and describe 3D shapes. Addressing this problem, we propose 3D point-capsule networks, an autoencoder designed for unsupervised learning of feature representations from sparse 3D point clouds while preserving spatial arrangements of the input data into different feature attentions. 3D capsule networks arise as a direct consequence of our unified formulation of the common 3D autoencoders. The dynamic routing scheme and the peculiar 2D latent feature representation deployed by our capsule networks bring in improvements for several common point cloud-related tasks, such as object classification, object reconstruction and part segmentation as substantiated by our extensive evaluations. Moreover, it enables new applications such as part interpolation and replacement.
Finally, towards rotation equivariance of the 3D feature representation, we present a 3D capsule architecture for processing of point clouds that is equivariant with respect to the SO(3) rotation group, translation, and permutation of the unordered input sets. The network operates on a sparse set of local reference frames, computed from an input point cloud and establishes end-to-end equivariance through a novel 3D quaternion group capsule layer, including an equivariant dynamic routing procedure. The capsule layer enables us to disentangle geometry from the pose, paving the way for more informative descriptions and structured latent space. In the process, we theoretically connect the process of dynamic routing between capsules to the well-known Weiszfeld algorithm, a scheme for solving iterative re-weighted least squares (IRLS) problems with provable convergence properties, enabling robust pose estimation between capsule layers. Due to the sparse equivariant quaternion capsules, our architecture allows joint object classification and orientation estimation, which we validate empirically on common benchmark datasets.
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Hühnerbein, Ruben [Verfasser], and Christoph [Akademischer Betreuer] Schnörr. "Inference and Model Parameter Learning for Image Labeling by Geometric Assignment / Ruben Hühnerbein ; Betreuer: Christoph Schnörr." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1210170094/34.
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Fisher, Kelly R. "Exploring the Mechanisms of Guided Play in Preschoolers' Developing Geometric Shape Concepts." Diss., Temple University Libraries, 2010. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/92502.
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PsychologyPh.D.
This dissertation offers the first set of empirical studies to examine the differential impact of didactic instruction and playful learning practices on geometric shape knowledge. Previous research demonstrated that successful child-centered, guided play pedagogies are often characterized by two components: (a) dialogic inquiry, or exploratory talk with the teacher, and (b) physical engagement with the educational materials. Building on this conclusion, three studies examined how guided play promotes criterial learning of shapes. Experiment 1 examined whether guided play or didactic instruction techniques promote criterial learning of four geometric shapes compared to a control condition. Results suggested that children in both didactic and guided play conditions learn the criterial features; however, this equivalence was most evident for relatively easy, familiar shapes (e.g., circles). A trend suggested that guided play promoted superior criterial understanding when learning more complex, novel shapes (i.e., pentagons). Experiment 2 expands on the previous study by examining how exposure to enriched geometric curricular content (e.g., teaching with typical shape exemplars only vs. typical and atypical exemplars) augments shape learning in guided play. As hypothesized, children taught with a mix of typical and atypical exemplars showed superior criterial learning compared to those in taught with only typical exemplars. Experiment 3 further explores the factors that facilitate shape learning by comparing the effectiveness of guided play, enriched free-play, and didactic instruction on children's criterial learning of two familiar shapes (triangles, rectangles) and two unfamiliar, complex shapes (pentagons, hexagons). As hypothesized, those who learned via guided play outperformed those who learned in didactic instruction who, in turn, outperformed those in enriched free play. In both didactic instruction and guided play, children's shape concepts persisted over one week. The findings from these studies suggest (1) guided play promotes equal or better criterial learning than didactic instruction, (2) curricular content (shape experience) augments criterial learning in guided play and (3) dialogic inquiry may be a key mechanism underlying guided play. The current research not only has implications for enhancing the acquisition of abstract spatial concepts but also for understanding the mechanisms that foster playful learning.
Temple University--Theses
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Andrews, Brock Taylor. "Student understanding of sight distance in geometric design a beginning line of inquiry to characterize student understanding of transportation engineering /." Pullman, Wash. : Washington State University, 2009. http://www.dissertations.wsu.edu/Thesis/Fall2009/B_ANDREWS_111909.pdf.
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Thesis (M.S. in civil engineering)--Washington State University, December 2009.Title from PDF title page (viewed on Jan. 15, 2010). "Department of Civil and Environmental Engineering." Includes bibliographical references (p. 30-31).
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Carriere, Mathieu. "On Metric and Statistical Properties of Topological Descriptors for geometric Data." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS433/document.
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Dans le cadre de l'apprentissage automatique, l'utilisation de représentations alternatives, ou descripteurs, pour les données est un problème fondamental permettant d'améliorer sensiblement les résultats des algorithmes. Parmi eux, les descripteurs topologiques calculent et encodent l'information de nature topologique contenue dans les données géométriques. Ils ont pour avantage de bénéficier de nombreuses bonnes propriétés issues de la topologie, et désirables en pratique, comme par exemple leur invariance aux déformations continues des données. En revanche, la structure et les opérations nécessaires à de nombreuses méthodes d'apprentissage, comme les moyennes ou les produits scalaires, sont souvent absents de l'espace de ces descripteurs. Dans cette thèse, nous étudions en détail les propriétés métriques et statistiques des descripteurs topologiques les plus fréquents, à savoir les diagrammes de persistance et Mapper. En particulier, nous montrons que le Mapper, qui est empiriquement un descripteur instable, peut être stabilisé avec une métrique appropriée, que l'on utilise ensuite pour calculer des régions de confiance et pour régler automatiquement ses paramètres. En ce qui concerne les diagrammes de persistance, nous montrons que des produits scalaires peuvent être utilisés via des méthodes à noyaux, en définissant deux noyaux, ou plongements, dans des espaces de Hilbert en dimension finie et infinieIn the context of supervised Machine Learning, finding alternate representations, or descriptors, for data is of primary interest since it can greatly enhance the performance of algorithms. Among them, topological descriptors focus on and encode the topological information contained in geometric data. One advantage of using these descriptors is that they enjoy many good and desireable properties, due to their topological nature. For instance, they are invariant to continuous deformations of data. However, the main drawback of these descriptors is that they often lack the structure and operations required by most Machine Learning algorithms, such as a means or scalar products. In this thesis, we study the metric and statistical properties of the most common topological descriptors, the persistence diagrams and the Mappers. In particular, we show that the Mapper, which is empirically instable, can be stabilized with an appropriate metric, that we use later on to conpute confidence regions and automatic tuning of its parameters. Concerning persistence diagrams, we show that scalar products can be defined with kernel methods by defining two kernels, or embeddings, into finite and infinite dimensional Hilbert spaces
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Frazee, Leah M. "The Interaction of Geometric and Spatial Reasoning: Student Learning of 2D Isometries in a Special Dynamic Geometry Environment." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531862080144028.
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Lal, Mithun. "Synthetic environment for machine learning experiments." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/236035/2/Mithun%2BLal%2BThesis%282%29.pdf.
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This thesis addresses the problem of data scarcity in human deep-learning applications. Automated estimation of human shape and pose from an image is challenging. It is even more difficult to map the identified human pixels onto a 3D model. Existing deep-learning models learn to map manually labelled human pixels in 2D images onto human surface, which is prone to human error, and the sparsity of annotated data leads to sub-optimal results. We solve this problem by generating realistic artificial human video data to train 2D-3D human mapping models and show promising results when compared to models trained on real data.
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Nardi, Daniele. "The Relationship Between Geometric Shape and Slope for the Representation of a Goal Location in Pigeons (Columba livia)." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1219336725.
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Astolfi, Pietro. "Toward the "Deep Learning" of Brain White Matter Structures." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/337629.
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In the brain, neuronal cells located in different functional regions communicate through a dense structural network of axons known as the white matter (WM) tissue. Bundles of axons that share similar pathways characterize the WM anatomy, which can be investigated in-vivo thanks to the recent advances of magnetic resonance (MR) techniques. Diffusion MR imaging combined with tractography pipelines allows for a virtual reconstruction of the whole WM anatomy of in-vivo brains, namely the tractogram. It consists of millions of WM fibers as 3D polylines, each approximating thousands of axons. From the analysis of a tractogram, neuroanatomists can characterize well-known white matter structures and detect anatomically non-plausible fibers, which are artifacts of the tractography and often constitute a large portion of it. The accurate characterization of tractograms is pivotal for several clinical and neuroscientific applications. However, such characterization is a complex and time-consuming process that is difficult to be automatized as it requires properly encoding well-known anatomical priors. In this thesis, we propose to investigate the encoding of anatomical priors with a supervised deep learning framework. The ultimate goal is to reduce the presence of artifactual fibers to enable a more accurate automatic process of WM characterization. We devise the problem by distinguishing between volumetric and non-volumetric representations of white matter structures. In the first case, we learn the segmentation of the WM regions that represent relevant anatomical waypoints not yet classified by WM atlases. We investigate using Convolutional Neural Networks (CNNs) to exploit the volumetric representation of such priors. In the second case, the goal is to learn from the 3D polyline representation of fibers where the typical CNN models are not suitable. We introduce the novelty of using Geometric Deep Learning (GDL) models designed to process data having an irregular representation. The working assumption is that the geometrical properties of fibers are informative for the detection of tractogram artifacts. As a first contribution, we present StemSeg that extends the use of CNNs to detect the WM portion representing the waypoints of all the fibers for a specific bundle. This anatomical landmark, called stem, can be critical for extracting that bundle. We provide the results of an empirical analysis focused on the Inferior Fronto-Occipital Fasciculus (IFOF). The effective segmentation of the stem improves the final segmentation of the IFOF, outperforming with a significant gap the reference state of the art. As a second and major contribution, we present Verifyber, a supervised tractogram filtering approach based on GDL, distinguishing between anatomically plausible and non-plausible fibers. The proposed model is designed to learn anatomical features directly from the fiber represented as a 3D points sequence. The extended empirical analysis on healthy and clinical subjects reveals multiple benefits of Verifyber: high filtering accuracy, low inference time, flexibility to different plausibility definitions, and good generalization. Overall, this thesis constitutes a step toward characterizing white matter using deep learning. It provides effective ways of encoding anatomical priors and an original deep learning model designed for fiber.
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Petrov, Aleksandar. "Understanding the relationships between aesthetic properties of shapes and geometric quantities of free-form curves and surfaces using Machine Learning Techniques." Thesis, Paris, ENSAM, 2016. http://www.theses.fr/2016ENAM0007/document.
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Aujourd’hui, sur le marché, on peut trouver une vaste gamme de produits différents ou des formes variées d’un même produit et ce grand assortiment fatigue les clients. Il est clair que la décision des clients d’acheter un produit dépend de l'aspect esthétique de la forme du produit et de l’affection émotionnelle. Par conséquent, il est très important de comprendre les propriétés esthétiques et de les adopter dans la conception du produit, dès le début. L'objectif de cette thèse est de proposer un cadre générique pour la cartographie des propriétés esthétiques des formes gauches en 3D en façon d'être en mesure d’extraire des règles de classification esthétiques et des propriétés géométriques associées. L'élément clé du cadre proposé est l'application des méthodologies de l’Exploration des données (Data Mining) et des Techniques d’apprentissage automatiques (Machine Learning Techniques) dans la cartographie des propriétés esthétiques des formes. L'application du cadre est d'étudier s’il y a une opinion commune pour la planéité perçu de la part des concepteurs non-professionnels. Le but de ce cadre n'est pas seulement d’établir une structure pour repérer des propriétés esthétiques des formes gauches, mais aussi pour être utilisé comme un chemin guidé pour l’identification d’une cartographie entre les sémantiques et les formes gauches différentes. L'objectif à long terme de ce travail est de définir une méthodologie pour intégrer efficacement le concept de l’Ingénierie affective (c.à.d. Affective Engineering) dans le design industrielToday on the market we can find a large variety of different products and differentshapes of the same product and this great choice overwhelms the customers. It is evident that the aesthetic appearance of the product shape and its emotional affection will lead the customers to the decision for buying the product. Therefore, it is very important to understand the aesthetic proper-ties and to adopt them in the early product design phases. The objective of this thesis is to propose a generic framework for mapping aesthetic properties to 3D freeform shapes, so as to be able to extract aesthetic classification rules and associated geometric properties. The key element of the proposed framework is the application of the Data Mining (DM) methodology and Machine Learning Techniques (MLTs) in the mapping of aesthetic properties to the shapes. The application of the framework is to investigate whether there is a common judgment for the flatness perceived from non-professional designers. The aim of the framework is not only to establish a structure for mapping aesthetic properties to free-form shapes, but also to be used as a guided path for identifying a mapping between different semantics and free-form shapes. The long-term objective of this work is to define a methodology to efficiently integrate the concept of Affective Engineering in the Industrial Designing
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Golkov, Vladimir [Verfasser], Daniel [Akademischer Betreuer] Cremers, Daniel [Gutachter] Cremers, and Bastian [Gutachter] Goldlücke. "Deep learning and variational analysis for high-dimensional and geometric biomedical data / Vladimir Golkov ; Gutachter: Daniel Cremers, Bastian Goldlücke ; Betreuer: Daniel Cremers." München : Universitätsbibliothek der TU München, 2021. http://nbn-resolving.de/urn:nbn:de:bvb:91-diss-20210826-1615936-1-7.
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Johansson, Tom. "Att urskilja det kritiska : En variationsteoretisk studie om undervisning med växande geometriska mönster." Thesis, Högskolan för lärande och kommunikation, Högskolan i Jönköping, Matematikdidaktisk forskning, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-44563.
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Undervisning med växande geometriska mönster ses som en bro mellan aritmetiskt och algebraiskt tänkande genom att elever möter uppgifter som möjliggör generalisering av aritmetiska uttryck. Eftersom svenska elever i internationella tester visar upp bättre resultat inom aritmetik än algebra är syftet med studien att ta reda på vilka aspekter som är kritiska för elevers utveckling från ett aritmetiskt till ett algebraiskt tänkande. Studien är en learning study där en lektion planerades och genomfördes i tre klasser i årskurs 5 och 6. Lektionerna kompletterades med ett för- och eftertest som tillsammans med lektionerna bidrog till studiens resultat. Vid planering och analys av lektionerna tillämpades variationsteorin som fokuserar på vilket lärande som möjliggörs, vilket lärande som sker och vad som kan förbättra lärande. Resultatet är att det kan vara kritiskt för elever att urskilja regelbundenheten i växande geometriska mönster och att särskilja regelbundenheten från proportionalitet. En ytterligare kritisk aspekt kan vara att urskilja bokstävers betydelse inom matematik. I resultatet framkommer även att två av de variationsmönster som använts kan möjliggöra urskiljning av aspekter som kan vara kritiska för elever. Vid undervisning med växande geometriska mönster finns det flera aspekter som lärare behöver möjliggöra för elever att urskilja. Genom att använda genomtänkta variationsmönster kan aspekterna synliggöras och därmed utveckla elevers förståelse för algebra.Teaching of growing geometrical patterns should be seen as a bridge between arithmetic and algebraic thinking, that through giving the students tasks that enables generalization of arithmetic expressions. Swedish students’ results show that they perform better arithmetically than algebraically therefore, the aim of this study is to ascertain which aspects that are critical to students’ development from an arithmetic thinking to an algebraic thinking. This study is a learning study where a lesson was planned and performed in three different classes in grade 5 and 6. The lessons included a pre-test and a posttest to further validate the study and the tests, combined with the lessons, contributed to the result of the study. When planning and analyzing the lessons the theory that was applied was variation theory which focuses on what is learned, what learning that takes place and what can be improved to further the learning. The result of this study shows that it can be critical for students to discern regularities in growing geometrical patterns and also to separate regularity from proportionality. Furthermore, the study found another critical aspect which is to discern the meaning of letters within mathematics. The result also reveals two variation patterns which enables discerning of aspects that appear critical for students. When teaching about growing geometrical patterns there are several aspects teachers need to make possible for students to discern. Through utilization of variation patterns that are well prepared and thought through these aspects can be visualized and consequently auxiliary advance students understanding for algebra.
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Tai, Yiyang. "Machine Learning Uplink Power Control in Single Input Multiple Output Cell-free Networks." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-279462.
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This thesis considers the uplink of cell-free single input multiple output systems, in which the access points employ matched-filter reception. In this setting, our objectiveis to develop a scalable uplink power control scheme that relies only on large-scale channel gain estimates and is robust to changes in the environment. Specifically, we formulate the problem as max-min and max-product signal-to-interference ratio optimization tasks, which can be solved by geometric programming. Next, we study the performance of supervised and unsupervised learning approaches employing a feed-forward neural network. We find that both approaches perform close to the optimum achieved by geometric programming, while the unsupervised scheme avoids the pre-computation of training data that supervised learning would necessitate for every system or environment modification.Den här avhandlingen tar hänsyn till upplänken till cellfria multipla utgångssystem med en enda ingång, där åtkomstpunkterna använder matchad filtermottagning. I den här inställningen är vårt mål att utveckla ett skalbart styrsystem för upplänkskraft som endast förlitar sig på storskaliga uppskattningar av kanalökningar och är robusta för förändringar i miljön. Specifikt formulerar vi problemet som maxmin och max-produkt signal-till-störningsförhållande optimeringsuppgifter, som kan lösas genom geometrisk programmering. Därefter studerar vi resultatet av övervakade och okontrollerade inlärningsmetoder som använder ett framåtriktat neuralt nätverk. Vi finner att båda metoderna fungerar nära det optimala som uppnås genom geometrisk programmering, medan det övervakade schemat undviker förberäkningen av träningsdata som övervakat inlärning skulle kräva för varje system- eller miljöändring.
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Ling, Suiyi. "Perceptual representations of structural and geometric information in images : bio-inspired and machine learning approaches : application to visual quality assessment of immersive media." Thesis, Nantes, 2018. http://www.theses.fr/2018NANT4061/document.
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Ce travail vise à mieux évaluer la qualité perceptuelle des images contenant des distorsions structurelles et géométriques notamment dans le contexte de médias immersifs. Nous proposons et explorons un cadre algorithmique hiérarchique de la perception visuelle. Inspiré par le système visuel humain, nous investiguons plusieurs niveaux de représentations des images : bas niveau (caractéristiques élémentaires comme les segments), niveau intermédiaire (motif complexe, encodage de contours), haut niveau (abstraction et reconnaissance des données visuelles). La première partie du manuscrit traite des représentations bas niveau pour la structure et texture. U n modèle basé filtre bilatéral est d’abord introduit pour qualifier les rôles respectifs de l’information texturale et structurelle dans diverses tâches d’évaluation (utilité, qualité. . . ). Une mesure de qualité d’image/vidéo est proposée pour quantifier les déformations de structure spatiales et temporelles perçues en utilisant une métrique dite élastique. La seconde partie du mémoire explore les représentations de niveaux intermédiaires. Un modèle basé « schetch token » et un autre basé sur codage d’un arbre de contexte sont présentés pour évaluer la qualité perçue. La troisième partie traite des représentations haut niveau. Deux approches d’apprentissage machine sont proposées pour apprendre ces représentations : une basée sur un technique de convolutional sparse coding, l’autre sur des réseaux profonds de type generative adversarial network. Au long du manuscrit, plusieurs expériences sont menées sur différentes bases de données pour plusieurs applications (FTV, visualisation multi-vues, images panoramiques 360. . . ) ainsi que des études utilisateursThis work aims to better evaluate the perceptual quality of image/video that contains structural and geometric related distortions in the context of immersive multimedia. We propose and explore a hierarchical framework of visual perception for image/video. Inspired by representation mechanism of the visual system, low-level (elementary visual features, e.g. edges), mid-level (intermediate visual patterns, e.g. codebook of edges), and higher-level (abstraction of visual input, e.g. category of distorted edges) image/video representations are investigated for quality assessment. The first part of this thesis addresses the low-level structure and texture related representations. A bilateral filter-based model is first introduced to qualify the respective role of structure and texture information in various assessment tasks (utility, quality . . . ). An image quality/video quality measure is proposed to quantify structure deformation spatially and temporally using new elastic metric. The second part explores mid-level structure related representations. A sketch-token based model and a context tree based model are presented in this part for the image and video quality evaluation. The third part explores higher-level structure related representations. Two machine learning approaches are proposed to learn higher-level representation: a convolutional sparse coding based and a generative adversarial network. Along the thesis, experiments an user studies have been conducted on different databases for different applications where special structure related distortions are observed (FTV, multi-view rendering, omni directional imaging . . . )