Relevant bibliographies by topics / Non-Euclidean Data

Academic literature on the topic 'Non-Euclidean Data'

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Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Non-Euclidean Data"

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Kanzawa, Yuchi. "Entropy-Regularized Fuzzy Clustering for Non-Euclidean Relational Data and Indefinite Kernel Data." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 7 (November 20, 2012): 784–92. http://dx.doi.org/10.20965/jaciii.2012.p0784.

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In this paper, an entropy-regularized fuzzy clustering approach for non-Euclidean relational data and indefinite kernel data is developed that has not previously been discussed. It is important because relational data and kernel data are not always Euclidean and positive semi-definite, respectively. It is theoretically determined that an entropy-regularized approach for both non-Euclidean relational data and indefinite kernel data can be applied without using a β-spread transformation, and that two other options make the clustering results crisp for both data types. These results are in contrast to those from the standard approach. Numerical experiments are employed to verify the theoretical results, and the clustering accuracy of three entropy-regularized approaches for non-Euclidean relational data, and three for indefinite kernel data, is compared.
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Faraway, Julian J. "Regression for non-Euclidean data using distance matrices." Journal of Applied Statistics 41, no. 11 (April 23, 2014): 2342–57. http://dx.doi.org/10.1080/02664763.2014.909794.

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Xu, Weiping, Edwin R. Hancock, and Richard C. Wilson. "Ricci flow embedding for rectifying non-Euclidean dissimilarity data." Pattern Recognition 47, no. 11 (November 2014): 3709–25. http://dx.doi.org/10.1016/j.patcog.2014.04.021.

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Doherty, K. A. J., R. G. Adams, and N. Davey. "Unsupervised learning with normalised data and non-Euclidean norms." Applied Soft Computing 7, no. 1 (January 2007): 203–10. http://dx.doi.org/10.1016/j.asoc.2005.05.005.

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Shi, Xiaoping, Yuehua Wu, and Calyampudi Radhakrishna Rao. "Consistent and powerful non-Euclidean graph-based change-point test with applications to segmenting random interfered video data." Proceedings of the National Academy of Sciences 115, no. 23 (May 21, 2018): 5914–19. http://dx.doi.org/10.1073/pnas.1804649115.

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The change-point detection has been carried out in terms of the Euclidean minimum spanning tree (MST) and shortest Hamiltonian path (SHP), with successful applications in the determination of authorship of a classic novel, the detection of change in a network over time, the detection of cell divisions, etc. However, these Euclidean graph-based tests may fail if a dataset contains random interferences. To solve this problem, we present a powerful non-Euclidean SHP-based test, which is consistent and distribution-free. The simulation shows that the test is more powerful than both Euclidean MST- and SHP-based tests and the non-Euclidean MST-based test. Its applicability in detecting both landing and departure times in video data of bees’ flower visits is illustrated.
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Laub, Julian, Volker Roth, Joachim M. Buhmann, and Klaus-Robert Müller. "On the information and representation of non-Euclidean pairwise data." Pattern Recognition 39, no. 10 (October 2006): 1815–26. http://dx.doi.org/10.1016/j.patcog.2006.04.016.

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Bhattacharya, Rabi, and Rachel Oliver. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images." Sankhya A 81, no. 1 (February 27, 2018): 1–36. http://dx.doi.org/10.1007/s13171-018-0127-9.

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Yamamoto, Takeshi, Katsuhiro Honda, Akira Notsu, and Hidetomo Ichihashi. "Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 8 (October 20, 2011): 1050–56. http://dx.doi.org/10.20965/jaciii.2011.p1050.

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Relational data is common in many real-world applications. Linear fuzzy clustering models have been extended for handling relational data based on Fuzzyc-Medoids (FCMdd) framework. In this paper, with the goal being to handle non-Euclidean data, β-spread transformation of relational data matrices used in Non-Euclidean-type Relational Fuzzy (NERF)c-means is applied before FCMdd-type linear cluster extraction. β-spread transformation modifies data elements to avoid negative values for clustering criteria of distances between objects and linear prototypes. In numerical experiments, typical features of the proposed approach are demonstrated not only using artificially generated data but also in a document classification task with a document-keyword co-occurrence relation.
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Hu, Kai, Jiasheng Wu, Yaogen Li, Meixia Lu, Liguo Weng, and Min Xia. "FedGCN: Federated Learning-Based Graph Convolutional Networks for Non-Euclidean Spatial Data." Mathematics 10, no. 6 (March 21, 2022): 1000. http://dx.doi.org/10.3390/math10061000.

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Federated Learning (FL) can combine multiple clients for training and keep client data local, which is a good way to protect data privacy. There are many excellent FL algorithms. However, most of these can only process data with regular structures, such as images and videos. They cannot process non-Euclidean spatial data, that is, irregular data. To address this problem, we propose a Federated Learning-Based Graph Convolutional Network (FedGCN). First, we propose a Graph Convolutional Network (GCN) as a local model of FL. Based on the classical graph convolutional neural network, TopK pooling layers and full connection layers are added to this model to improve the feature extraction ability. Furthermore, to prevent pooling layers from losing information, cross-layer fusion is used in the GCN, giving FL an excellent ability to process non-Euclidean spatial data. Second, in this paper, a federated aggregation algorithm based on an online adjustable attention mechanism is proposed. The trainable parameter ρ is introduced into the attention mechanism. The aggregation method assigns the corresponding attention coefficient to each local model, which reduces the damage caused by the inefficient local model parameters to the global model and improves the fault tolerance and accuracy of the FL algorithm. Finally, we conduct experiments on six non-Euclidean spatial datasets to verify that the proposed algorithm not only has good accuracy but also has a certain degree of generality. The proposed algorithm can also perform well in different graph neural networks.
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Honda, Katsuhiro, Takeshi Yamamoto, Akira Notsu, and Hidetomo Ichihashi. "Visualization of Non-Euclidean Relational Data by Robust Linear Fuzzy Clustering Based on FCMdd Framework." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 2 (March 20, 2013): 312–17. http://dx.doi.org/10.20965/jaciii.2013.p0312.

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Visualization is a fundamental approach for revealing intrinsic structures in multidimensional observation. This paper considers visualization of non-Euclidean relational data by extracting local linear substructures. In order to extract robust linear clusters, an FCMdd-based linear fuzzy clustering model is applied in conjunction with a robust measure of alternativec-means. Non-Euclidean data matrices are handled with β-spread transformation in a manner similar to that of NERFc-Means. In several experiments, robust feature maps derived by the robust clustering model are compared with feature maps given by the conventional clustering model and Multi-Dimensional Scaling (MDS).
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Dissertations / Theses on the topic "Non-Euclidean Data"

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Xu, Weiping. "Non-Euclidean dissimilarity data in pattern recognition." Thesis, University of York, 2012. http://etheses.whiterose.ac.uk/3848/.

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This thesis addresses problems in dissimilarity (proximity) learning, particularly focusing on identifying the sources and rectifying the non-Euclidean dissimilarity in pattern recog- nition. We aim to develop a framework for analyzing the non-Euclidean dissimilarity by combining the methods from differential geometry and manifold learning theory. The algorithms are applied to objects represented by the dissimilarity measures. In Chapter 3 we describe how to reveal the origins of the non-Euclidean behaviors of the dissimilarity matrix for the purpose of rectifying the dissimilarities. We com- mence by developing a new measure which gauges the extent to which individual data give rises to departures from metricity in a set of dissimilarity data. This allows us to as- sess whether the non-Euclidean artifacts in a dataset can be attributed to individual objects or are distributed uniformly. The second novel contribution of Chapter 3 is to provide sim- ple empirical tests that can be used to determine the sources of the negative dissimilarity eigenvalues. We consider three sources of the negative dissimilarity eigenvalues, namely a) that the data resides on a manifold, b) that the objects may be extended and c) that there is Gaussian noise. We experiment with the algorithms on a set of public dissimilarities used in various applications available from the EU SIMBAD project. In Chapter 4, we propose a framework for rectifying the dissimilarities using Ricci flow on the manifolds so that the non-Euclidean artifacts are eliminated, as the second main contribution of this thesis. We consider the objects of interest to be represented by points on a manifold consisting of local patches with constant curvatures, and the given dissimilarities to be the geodesic distances on the manifold between these points. In dif- ferential geometry, Ricci flow changes the metric of a Riemannian manifold according to the curvature of the manifold. We seek to flatten the curved manifold so that a corrected set of Euclidean distances are obtained. We achieve this by deforming the manifold usingRicci flow. In the first technique, we consider each edge as a local patch and apply Ricci flow independently to flatten each patch. In this way, the local structure of the manifold is ignored, as Ricci flow is applied independently on each edge. To overcome this prob- lem, we propose a second technique, where add a curvature regularization process before evolving the manifold. Specifically we use the heat kernel to smooth out the curvatures on the edges. The results show both improved numerical stability and lower classification error in the embedded space. To reduce the reliance on the piecewise embedding and its effects on individual edges, we extend the previous two techniques and develop a third means of correcting non- Euclidean dissimilarity data as the first contribution of Chapter 5. This is done by using a tangent space reprojection to inflate the local hyperspherical patches and align the local patches with the shortest edge-connected path. These three Ricci-flow-based techniques proposed through this thesis are investigated as a means of correcting the dissimilarities so that the the non-Euclidean artefacts are eliminated. We experiment on two datasets represented by dissimilarities, namely the CoilYork and the Chickenpieces datasets. In the framework for correcting the non-Euclidean dissimilarities using the Ricci flow process, estimating the curvatures of the embedded manifold is an important component prior deforming the manifold. The second contribution of Chapter 5 is the investigation of the effects of the piecewise embedding methods (the kernel embedding and the Isomap embedding) on the curvatures computation and the introduction of a new way of com- puting the curvatures from a set of dissimilarities. We consider each local patch on a hypersphere, and deduce the enclosed volume of the points in terms of the curvature. We estimate the curvature by fitting the volume. We illustrate the utility of this method for estimating curvatures on the artificial dataset (2-sphere dataset).
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Richardson, Richardson. "Edgard Varèse and the Visual Avant-Garde: A Comparative Study of Intégrales and Works of Art by Marcel Duchamp." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1123684300.

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Zajíc, Jiří. "Modern Methods for Tree Graph Structures Rendering." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-412891.

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Tento projekt se věnuje problematice zobrazení velkých hierarchických struktur, zejména možnostem vizualizace stromových grafů. Cílem je implementace hyperbolického prohlížeče ve webovém prostředí, který využívá potenciálu neeukleidovské geometrie k promítnutí stromu na hyperbolickou rovinu. Velký důraz je kladen na uživatelsky přívětivou manipulaci se zobrazovaným modelem a snadnou orientaci.
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Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.

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Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.
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Lind, Crystal. "The gravitational Vlasov-Poisson system on the unit 2-sphere with initial data along a great circle." Thesis, 2014. http://hdl.handle.net/1828/5613.

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The Vlasov-Poisson system is most commonly used to model the movement of charged particles in a plasma or of stars in a galaxy. It consists of a kinetic equation known as the Vlasov equation coupled with a force determined by the Poisson equation. The system in Euclidean space is well-known and has been extensively studied under various assumptions. In this paper, we derive the Vlasov-Poisson equations assuming the particles exist only on the 2-sphere, then take an in-depth look at particles which initially lie along a great circle of the sphere. We show that any great circle is an invariant set of the equations of motion and prove that the total energy, number of particles, and entropy of the system are conserved for circular initial distributions.
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Book chapters on the topic "Non-Euclidean Data"

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Camiz, Sergio. "Comparison of Euclidean Approximations of non-Euclidean Distances." In Studies in Classification, Data Analysis, and Knowledge Organization, 139–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-60126-2_18.

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Eltzner, Benjamin, and Stephan Huckemann. "Bootstrapping Descriptors for Non-Euclidean Data." In Lecture Notes in Computer Science, 12–19. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68445-1_2.

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Cao, Hong, Ping Wang, Runing Ma, and Jundi Ding. "On Non-Euclidean Metrics Based Clustering." In Intelligent Science and Intelligent Data Engineering, 655–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36669-7_80.

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Xu, Weiping, Edwin R. Hancock, and Richard C. Wilson. "Rectifying Non-euclidean Similarity Data through Tangent Space Reprojection." In Pattern Recognition and Image Analysis, 379–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21257-4_47.

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Huckemann, Stephan, and Benjamin Eltzner. "Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces." In Handbook of Variational Methods for Nonlinear Geometric Data, 317–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31351-7_10.

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Rokka Chhetri, Sujit, and Mohammad Abdullah Al Faruque. "Non-euclidean Data-Driven Modeling Using Graph Convolutional Neural Networks." In Data-Driven Modeling of Cyber-Physical Systems using Side-Channel Analysis, 185–207. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37962-9_9.

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Casey, Stephen D. "Harmonic Analysis in Non-Euclidean Spaces: Theory and Application." In Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, 565–601. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55556-0_6.

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Miche, Yoan, Ian Oliver, Silke Holtmanns, Anton Akusok, Amaury Lendasse, and Kaj-Mikael Björk. "On Mutual Information over Non-Euclidean Spaces, Data Mining and Data Privacy Levels." In Proceedings in Adaptation, Learning and Optimization, 371–83. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28373-9_32.

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Ontrup, Jorg, and Helge Ritter. "Text Categorization and Semantic Browsing with Self-Organizing Maps on Non-euclidean Spaces." In Principles of Data Mining and Knowledge Discovery, 338–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44794-6_28.

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Bhattacharya, Rabi, and Lizhen Lin. "Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments." In Sojourns in Probability Theory and Statistical Physics - II, 1–43. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0298-9_1.

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Conference papers on the topic "Non-Euclidean Data"

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Allan, Alexander, Ross Humphrey, and Giuseppe Di Fatta. "Non-Euclidean Internet Coordinates Embedding." In 2013 IEEE 13th International Conference on Data Mining Workshops (ICDMW). IEEE, 2013. http://dx.doi.org/10.1109/icdmw.2013.113.

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Yang, Jing, Kai Xie, and Ning An. "Causal Discovery on Non-Euclidean Data." In KDD '22: The 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3534678.3539485.

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Münch, Maximilian, Christoph Raab, Michael Biehl, and Frank-Michael Schleif. "Structure Preserving Encoding of Non-euclidean Similarity Data." In 9th International Conference on Pattern Recognition Applications and Methods. SCITEPRESS - Science and Technology Publications, 2020. http://dx.doi.org/10.5220/0008955100430051.

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Celińska-Kopczyńska, Dorota, and Eryk Kopczyński. "Non-Euclidean Self-Organizing Maps." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/269.

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Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical).
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Xu, Weiping, Edwin R. Hancock, and Richard C. Wilson. "Rectifying Non-Euclidean Similarity Data Using Ricci Flow Embedding." In 2010 20th International Conference on Pattern Recognition (ICPR). IEEE, 2010. http://dx.doi.org/10.1109/icpr.2010.812.

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Miller, Benjamin A., Nadya T. Bliss, and Patrick J. Wolfe. "Toward signal processing theory for graphs and non-Euclidean data." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5494930.

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Yamamoto, Takeshi, Katsuhiro Honda, Akira Notsu, and Hidetomo Ichihashi. "FCMdd-type linear fuzzy clustering for incomplete non-Euclidean relational data." In 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2011. http://dx.doi.org/10.1109/fuzzy.2011.6007379.

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Zhang, Yanfu, Lei Luo, Wenhan Xian, and Heng Huang. "Learning Better Visual Data Similarities via New Grouplet Non-Euclidean Embedding." In 2021 IEEE/CVF International Conference on Computer Vision (ICCV). IEEE, 2021. http://dx.doi.org/10.1109/iccv48922.2021.00977.

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Lu, Binbin, Martin Charlton, and Paul Harris. "Geographically Weighted Regression using a non-euclidean distance metric with simulation data." In 2012 First International Conference on Agro-Geoinformatics. IEEE, 2012. http://dx.doi.org/10.1109/agro-geoinformatics.2012.6311652.

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Shoji Hirano and Shusaku Tsumoto. "Dealing with granularity on non-euclidean relational data based on indiscernibility level." In 2007 IEEE International Conference on Systems, Man and Cybernetics. IEEE, 2007. http://dx.doi.org/10.1109/icsmc.2007.4413884.

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