Relevant bibliographies by topics / Statistical graph analysis

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Statistical graph analysis'

Author: Grafiati
Published: 13 February 2024

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Journal articles on the topic "Statistical graph analysis"

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Jain, Brijnesh J. "Statistical graph space analysis." Pattern Recognition 60 (December 2016): 802–12. http://dx.doi.org/10.1016/j.patcog.2016.06.023.

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Martins, Maria Maria Pereira, Carolina Fernandes de Carvalho, and Carlos Eduardo Ferreira Monteiro. "The analysis of statistical graphs constructed by primary school teachers." Acta Scientiae 23, no. 6 (November 18, 2021): 28–57. http://dx.doi.org/10.17648/acta.scientiae.6762.

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Background: Statistical graphs are widely used in society and are important in presenting data related to different topics. Statistics education aims improve the teaching and learning of statistics, which include the approaches to statistics graphs. Objectives: This article analyses the construction of statistical graphs by in-service teachers and their reasons for choosing these graphs. Design: It was conducted an empirical study from a qualitative perspective which investigated teachers’ choices and constructions of statistical graphs. Setting and Participants: The participants were 22 primary school teachers from public schools located in Recife Metropolitan Area, Brazil. They expressed their intention to be interviewed when they responded to a questionnaire applied among a larger number of teachers. Data collection and analysis: The interviews were composed of two tasks comprised of statistical data in which participants had to choose a type of graph, justify the choice, and construct a graph of a chosen type. It was carried out a content analysis of speech protocols. Results: The reasons for participants’ choices seemed to be related to their familiarity with the type of graph, and they constructed graphs with high levels of complexity. Conclusions: The results of this study emphasised the importance of primary school teachers developing specific knowledge about graphs through pre-service and in-service elementary school teacher education. The results from this research study offer new questions concerning the construction and the choice for statistical graphs, which include the influence of new technologies and the use of textbooks.
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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 02 (June 1988): 315–30. http://dx.doi.org/10.1017/s0001867800016992.

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Various types of graph statistics for graphs and digraphs are presented as numerators of incompleteU-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.
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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 2 (June 1988): 315–30. http://dx.doi.org/10.2307/1427392.

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Various types of graph statistics for graphs and digraphs are presented as numerators of incomplete U-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.
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Lin, Zhenxian, Jiagang Wang, and Chengmao Wu. "Robust Spectral Clustering Incorporating Statistical Sub-Graph Affinity Model." Axioms 11, no. 6 (June 5, 2022): 269. http://dx.doi.org/10.3390/axioms11060269.

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Hyperspectral image (HSI) clustering is a challenging work due to its high complexity. Subspace clustering has been proven to successfully excavate the intrinsic relationships between data points, while traditional subspace clustering methods ignore the inherent structural information between data points. This study uses graph convolutional subspace clustering (GCSC) for robust HSI clustering. The model remaps the self-expression of the data to non-Euclidean domains, which can generate a robust graph embedding dictionary. The EKGCSC model can achieve a globally optimal closed-form solution by using a subspace clustering model with the Frobenius norm and a Gaussian kernel function, making it easier to implement, train, and apply. However, the presence of noise can have a noteworthy negative impact on the segmentation performance. To diminish the impact of image noise, the concept of sub-graph affinity is introduced, where each node in the primary graph is modeled as a sub-graph describing the neighborhood around the node. A statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty image noise by using more information. The model used in this work was named statistical sub-graph affinity kernel graph convolutional subspace clustering (SSAKGCSC). Experiment results on Salinas, Indian Pines, Pavia Center, and Pavia University data sets showed that the SSAKGCSC model can achieve improved segmentation performance and better noise resistance ability.
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Hora, Akihito. "Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (April 1998): 221–46. http://dx.doi.org/10.1142/s0219025798000144.

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Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.
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Kalikova, A. "Statistical analysis of random walks on network." Scientific Journal of Astana IT University, no. 5 (July 27, 2021): 77–83. http://dx.doi.org/10.37943/aitu.2021.99.34.007.

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This paper describes an investigation of analytical formulas for parameters in random walks. Random walks are used to model situations in which an object moves in a sequence of steps in randomly chosen directions. Given a graph and a starting point, we select a neighbor of it at random, and move to this neighbor; then we select a neighbor of this point at random, and move to it etc. It is a fundamental dynamic process that arise in many models in mathematics, physics, informatics and can be used to model random processes inherent to many important applications. Different aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of hitting time, commute time, cover time are discussed in various works. In some papers, authors have derived an analytical expression for the distribution of the cover time for a random walk over an arbitrary graph that was tested for small values of n. However, this work will show the simplified analytical expressions for distribution of hitting time, commute time, cover time for bigger values of n. Moreover, this work will present the probability mass function and the cumulative distribution function for hitting time, commute time.
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Turab, Ali, Wutiphol Sintunavarat, and Jong-Suk Ro. "On Novel Mathematical Modeling for Studying a Class of Nonlinear Caputo-Type Fractional-Order Boundary Value Problems Emerging in CGT." Fractal and Fractional 7, no. 2 (January 17, 2023): 99. http://dx.doi.org/10.3390/fractalfract7020099.

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Chemical graph theory (CGT) is a field of mathematical science that applies classical graph theory to chemical structures and processes. Chemical graphs are the principal data format used in cheminformatics to illustrate chemical interactions. Several researchers have addressed boundary-value problems using star graphs. Star graphs were used since their method requires a central point linked to other vertices but not to itself. Our objective is to expand the mechanism by introducing the idea of an isobutane graph that has the chemical formula C4H10 and CAS number 75-28-5. By using the appropriate fixed point theory findings, this paper investigates the existence of solutions to fractional boundary value problems of Caputo type on such graphs. Additionally, two examples are provided to strengthen our important conclusions.
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Zhao, Jin-Hua. "A local algorithm and its percolation analysis of bipartite z-matching problem." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (May 1, 2023): 053401. http://dx.doi.org/10.1088/1742-5468/acd105.

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Abstract A z-matching on a bipartite graph is a set of edges, among which each vertex of two types of the graph is adjacent to at most 1 and at most z ( ⩾ 1 ) edges, respectively. The z-matching problem concerns finding z-matchings with the maximum size. Our approach to this combinatorial optimization problem is twofold. From an algorithmic perspective, we adopt a local algorithm as a linear approximate solver to find z-matchings on any graph instance, whose basic component is a generalized greedy leaf removal procedure in graph theory. From a theoretical perspective, on uncorrelated random bipartite graphs, we develop a mean-field theory for the percolation phenomenon underlying the local algorithm, leading to an analytical estimation of z-matching sizes on random graphs. Our analytical theory corrects the prediction by belief propagation algorithm at zero-temperature limit in (Kreačić and Bianconi 2019 Europhys. Lett. 126 028001). Besides, our theoretical framework extends a core percolation analysis of k-XORSAT problems to a general context of uncorrelated random hypergraphs with arbitrary degree distributions of factor and variable nodes.
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Ghazwani, Haleemah, Muhammad Faisal Nadeem, Faiza Ishfaq, and Ali N. A. Koam. "On Entropy of Some Fractal Structures." Fractal and Fractional 7, no. 5 (April 30, 2023): 378. http://dx.doi.org/10.3390/fractalfract7050378.

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Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distribution. Shannon’s entropy theory initiates graph entropies and develops information-theoretic magnitudes for structural computational evidence of organic graphs and complex networks. Graph entropy measurements are valuable in several scientific fields, such as computing, chemistry, biology, and discrete mathematics. In this study, we investigate the entropy of fractal-type networks by considering cycle, complete, and star networks as base graphs using degree-based topological indices.
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Dissertations / Theses on the topic "Statistical graph analysis"

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Fairbanks, James Paul. "Graph analysis combining numerical, statistical, and streaming techniques." Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54972.

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Graph analysis uses graph data collected on a physical, biological, or social phenomena to shed light on the underlying dynamics and behavior of the agents in that system. Many fields contribute to this topic including graph theory, algorithms, statistics, machine learning, and linear algebra. This dissertation advances a novel framework for dynamic graph analysis that combines numerical, statistical, and streaming algorithms to provide deep understanding into evolving networks. For example, one can be interested in the changing influence structure over time. These disparate techniques each contribute a fragment to understanding the graph; however, their combination allows us to understand dynamic behavior and graph structure. Spectral partitioning methods rely on eigenvectors for solving data analysis problems such as clustering. Eigenvectors of large sparse systems must be approximated with iterative methods. This dissertation analyzes how data analysis accuracy depends on the numerical accuracy of the eigensolver. This leads to new bounds on the residual tolerance necessary to guarantee correct partitioning. We present a novel stopping criterion for spectral partitioning guaranteed to satisfy the Cheeger inequality along with an empirical study of the performance on real world networks such as web, social, and e-commerce networks. This work bridges the gap between numerical analysis and computational data analysis.
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Soriani, Nicola. "Topics in Statistical Models for Network Analysis." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422100.

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Network Analysis is a set of statistical and mathematical techniques for the study of relational data arising from a system of connected entities. Most of the results for network data have been obtained in the field of Social Network Analysis (SNA), which mainly focuses on the relationships among a set of individual actors and organizations. The thesis considers some topics in statistical models for network data, with focus in particular on models used in SNA. The core of the thesis is represented by Chapters 3, 4 and 5. In Chapter 3, an alternative approach to estimate the Exponential Random Graph Models (ERGMs) is discussed. In Chapter 4, a comparison between ERGMs and Latent Space models in terms of goodness of fit is considered. In Chapter 5, alternative methods to estimate the p2 class of models are proposed.
La Network Analysis è un insieme di tecniche statistiche e matematiche per lo studio di dati relazionali per un sistema di entità interconnesse. Molti dei risultati per i dati di rete provengono dalla Social Network Analysis (SNA), incentrata principalmente sullo studio delle relazioni tra un insieme di individui e organizzazioni. La tesi tratta alcuni argomenti riguardanti la modellazione statistica per dati di rete, con particolare attenzione ai modelli utilizzati in SNA. Il nucleo centrale della tesi è rappresentato dai Capitoli 3, 4 e 5. Nel Capitolo 3, viene proposto un approccio alternativo per la stima dei modelli esponenziali per grafi casuali (Exponential Random Graph Models - ERGMs). Nel capitolo 4, l'approccio di modellazione ERGM e quello a Spazio Latente vengono confrontati in termini di bontà di adattamento. Nel capitolo 5, vengono proposti metodi alternativi per la stima della classe di modelli p2.
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GRASSI, FRANCESCO. "Statistical and Graph-Based Signal Processing: Fundamental Results and Application to Cardiac Electrophysiology." Doctoral thesis, Politecnico di Torino, 2018. http://hdl.handle.net/11583/2710580.

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The goal of cardiac electrophysiology is to obtain information about the mechanism, function, and performance of the electrical activities of the heart, the identification of deviation from normal pattern and the design of treatments. Offering a better insight into cardiac arrhythmias comprehension and management, signal processing can help the physician to enhance the treatment strategies, in particular in case of atrial fibrillation (AF), a very common atrial arrhythmia which is associated to significant morbidities, such as increased risk of mortality, heart failure, and thromboembolic events. Catheter ablation of AF is a therapeutic technique which uses radiofrequency energy to destroy atrial tissue involved in the arrhythmia sustenance, typically aiming at the electrical disconnection of the of the pulmonary veins triggers. However, recurrence rate is still very high, showing that the very complex and heterogeneous nature of AF still represents a challenging problem. Leveraging the tools of non-stationary and statistical signal processing, the first part of our work has a twofold focus: firstly, we compare the performance of two different ablation technologies, based on contact force sensing or remote magnetic controlled, using signal-based criteria as surrogates for lesion assessment. Furthermore, we investigate the role of ablation parameters in lesion formation using the late-gadolinium enhanced magnetic resonance imaging. Secondly, we hypothesized that in human atria the frequency content of the bipolar signal is directly related to the local conduction velocity (CV), a key parameter characterizing the substrate abnormality and influencing atrial arrhythmias. Comparing the degree of spectral compression among signals recorded at different points of the endocardial surface in response to decreasing pacing rate, our experimental data demonstrate a significant correlation between CV and the corresponding spectral centroids. However, complex spatio-temporal propagation pattern characterizing AF spurred the need for new signals acquisition and processing methods. Multi-electrode catheters allow whole-chamber panoramic mapping of electrical activity but produce an amount of data which need to be preprocessed and analyzed to provide clinically relevant support to the physician. Graph signal processing has shown its potential on a variety of applications involving high-dimensional data on irregular domains and complex network. Nevertheless, though state-of-the-art graph-based methods have been successful for many tasks, so far they predominantly ignore the time-dimension of data. To address this shortcoming, in the second part of this dissertation, we put forth a Time-Vertex Signal Processing Framework, as a particular case of the multi-dimensional graph signal processing. Linking together the time-domain signal processing techniques with the tools of GSP, the Time-Vertex Signal Processing facilitates the analysis of graph structured data which also evolve in time. We motivate our framework leveraging the notion of partial differential equations on graphs. We introduce joint operators, such as time-vertex localization and we present a novel approach to significantly improve the accuracy of fast joint filtering. We also illustrate how to build time-vertex dictionaries, providing conditions for efficient invertibility and examples of constructions. The experimental results on a variety of datasets suggest that the proposed tools can bring significant benefits in various signal processing and learning tasks involving time-series on graphs. We close the gap between the two parts illustrating the application of graph and time-vertex signal processing to the challenging case of multi-channels intracardiac signals.
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Meinhardt, Llopis Enric. "Morphological and statistical techniques for the analysis of 3D images." Doctoral thesis, Universitat Pompeu Fabra, 2011. http://hdl.handle.net/10803/22719.

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Aquesta tesi proposa una estructura de dades per emmagatzemar imatges tridimensionals. L'estructura da dades té forma d'arbre i codifica les components connexes dels conjunts de nivell de la imatge. Aquesta estructura és la eina bàsica per moltes aplicacions proposades: operadors morfològics tridimensionals, visualització d'imatges mèdiques, anàlisi d'histogrames de color, seguiment d'objectes en vídeo i detecció de vores. Motivada pel problema de la completació de vores, la tesi conté un estudi de com l'eliminació de soroll mitjançant variació total anisòtropa es pot fer servir per calcular conjunts de Cheeger en mètriques anisòtropes. Aquests conjunts de Cheeger anisòtrops es poden utilitzar per trobar òptims globals d'alguns funcionals per completar vores. També estan relacionats amb certs invariants afins que s'utilitzen en reconeixement d'objectes, i en la tesi s'explicita aquesta relació.
This thesis proposes a tree data structure to encode the connected components of level sets of 3D images. This data structure is applied as a main tool in several proposed applications: 3D morphological operators, medical image visualization, analysis of color histograms, object tracking in videos and edge detection. Motivated by the problem of edge linking, the thesis contains also an study of anisotropic total variation denoising as a tool for computing anisotropic Cheeger sets. These anisotropic Cheeger sets can be used to find global optima of a class of edge linking functionals. They are also related to some affine invariant descriptors which are used in object recognition, and this relationship is laid out explicitly.
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Tavernari, Daniele. "Statistical and network-based methods for the analysis of chromatin accessibility maps in single cells." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12297/.

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In questo lavoro, metodi provenienti dalla Fisica, dalla Statistica e dalla Teoria dei Grafi sono stati impiegati per caratterizzare ed analizzare profili di apertura e accessibilità della cromatina ottenuti con la tecnica ATAC-seq in singole cellule, nella fattispecie linfociti B provenienti da tre pazienti affetti da Leucemia Linfocitica Cronica. Una pipeline bioinformatica è stata sviluppata per processare i dati di sequencing ed ottenere le posizioni accessibili del genoma per ciascuna cellula. La quantità di regioni aperte e la loro distribuzione spaziale lungo il DNA sono state caratterizzate. Infine, l’apertura simultanea nelle stesse singole cellule di regioni regolatrici è stata impiegata come metrica per valutare relazioni funzionali, e in questo modo grafi tra enhancer e promoter sono stati costruiti e le loro proprietà sono state analizzate. La distribuzione spaziale lungo il genoma di regioni aperte consecutive ricapitola proprietà strutturali come gli array di nucleosomi e le strutture a loop della cromatina. Inoltre, i profili di accessibilità delle regioni regolatrici sono significativamente conservati nelle singole cellule. I network tra enhancer e promoter forniscono un modo per caratterizzare la rilevanza di ciascuna regione regolatrice in termini di centralità. Le statistiche sulla connettività tra enhancer e promoter confermano il modello di relazione uno-a-uno come il più frequente, in cui un promoter è regolato dall'enhancer ad esso più vicino. Infine, anche il funzionamento dei superenhancer è stato indagato. In conclusione, ATAC-seq si rivela un'efficace tecnica per indagare l'apertura della cromatina in singole cellule, i cui profili di accessibilità ricapitolano caratteristiche strutturali e funzionali della cromatina. Al fine di indagare i meccanismi della malattia, il panorama di accessibilità dei lifociti tumorali può essere confrontato con quello di cellule sane e cellule trattate con farmaci epigenetici.
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Valba, Olga. "Statistical analysis of networks and biophysical systems of complex architecture." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00919606.

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Complex organization is found in many biological systems. For example, biopolymers could possess very hierarchic structure, which provides their functional peculiarity. Understating such, complex organization allows describing biological phenomena and predicting molecule functions. Besides, we can try to characterize the specific phenomenon by some probabilistic quantities (variances, means, etc), assuming the primary biopolymer structure to be randomly formed according to some statistical distribution. Such a formulation is oriented toward evolutionary problems.Artificially constructed biological network is another common object of statistical physics with rich functional properties. A behavior of cells is a consequence of complex interactions between its numerous components, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond and to adapt to changing environment. Recent theoretical advances allow us to describe cellular network structure using graph concepts to reveal the principal organizational features shared with numerous non-biological networks.The aim of this thesis is to develop bunch of methods for studying statistical and dynamic objects of complex architecture and, in particular, scale-free structures, which have no characteristic spatial and/or time scale. For such systems, the use of standard mathematical methods, relying on the average behavior of the whole system, is often incorrect or useless, while a detailed many-body description is almost hopeless because of the combinatorial complexity of the problem. Here we focus on two problems.The first part addresses to statistical analysis of random biopolymers. Apart from the evolutionary context, our studies cover more general problems of planar topology appeared in description of various systems, ranging from gauge theory to biophysics. We investigate analytically and numerically a phase transition of a generic planar matching problem, from the regime, where almost all the vertices are paired, to the situation, where a finite fraction of them remains unmatched.The second part of this work focus on statistical properties of networks. We demonstrate the possibility to define co-expression gene clusters within a network context from their specific motif distribution signatures. We also show how a method based on the shortest path function (SPF) can be applied to gene interactions sub-networks of co-expression gene clusters, to efficiently predict novel regulatory transcription factors (TFs). The biological significance of this method by applying it on groups of genes with a shared regulatory locus, found by genetic genomics, is presented. Finally, we discuss formation of stable patters of motifs in networks under selective evolution in context of creation of islands of "superfamilies".
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Kamal, Tariq. "Computational Cost Analysis of Large-Scale Agent-Based Epidemic Simulations." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82507.

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Agent-based epidemic simulation (ABES) is a powerful and realistic approach for studying the impacts of disease dynamics and complex interventions on the spread of an infection in the population. Among many ABES systems, EpiSimdemics comes closest to the popular agent-based epidemic simulation systems developed by Eubank, Longini, Ferguson, and Parker. EpiSimdemics is a general framework that can model many reaction-diffusion processes besides the Susceptible-Exposed-Infectious-Recovered (SEIR) models. This model allows the study of complex systems as they interact, thus enabling researchers to model and observe the socio-technical trends and forces. Pandemic planning at the world level requires simulation of over 6 billion agents, where each agent has a unique set of demographics, daily activities, and behaviors. Moreover, the stochastic nature of epidemic models, the uncertainty in the initial conditions, and the variability of reactions require the computation of several replicates of a simulation for a meaningful study. Given the hard timelines to respond, running many replicates (15-25) of several configurations (10-100) (of these compute-heavy simulations) can only be possible on high-performance clusters (HPC). These agent-based epidemic simulations are irregular and show poor execution performance on high-performance clusters due to the evolutionary nature of their workload, large irregular communication and load imbalance. For increased utilization of HPC clusters, the simulation needs to be scalable. Many challenges arise when improving the performance of agent-based epidemic simulations on high-performance clusters. Firstly, large-scale graph-structured computation is central to the processing of these simulations, where the star-motif quality nodes (natural graphs) create large computational imbalances and communication hotspots. Secondly, the computation is performed by classes of tasks that are separated by global synchronization. The non-overlapping computations cause idle times, which introduce the load balancing and cost estimation challenges. Thirdly, the computation is overlapped with communication, which is difficult to measure using simple methods, thus making the cost estimation very challenging. Finally, the simulations are iterative and the workload (computation and communication) may change through iterations, as a result introducing load imbalances. This dissertation focuses on developing a cost estimation model and load balancing schemes to increase the runtime efficiency of agent-based epidemic simulations on high-performance clusters. While developing the cost model and load balancing schemes, we perform the static and dynamic load analysis of such simulations. We also statically quantified the computational and communication workloads in EpiSimdemics. We designed, developed and evaluated a cost model for estimating the execution cost of large-scale parallel agent-based epidemic simulations (and more generally for all constrained producer-consumer parallel algorithms). This cost model uses computational imbalances and communication latencies, and enables the cost estimation of those applications where the computation is performed by classes of tasks, separated by synchronization. It enables the performance analysis of parallel applications by computing its execution times on a number of partitions. Our evaluations show that the model is helpful in performance prediction, resource allocation and evaluation of load balancing schemes. As part of load balancing algorithms, we adopted the Metis library for partitioning bipartite graphs. We have also developed lower-overhead custom schemes called Colocation and MetColoc. We performed an evaluation of Metis, Colocation, and MetColoc. Our analysis showed that the MetColoc schemes gives a performance similar to Metis, but with half the partitioning overhead (runtime and memory). On the other hand, the Colocation scheme achieves a similar performance to Metis on a larger number of partitions, but at extremely lower partitioning overhead. Moreover, the memory requirements of Colocation scheme does not increase as we create more partitions. We have also performed the dynamic load analysis of agent-based epidemic simulations. For this, we studied the individual and joint effects of three disease parameter (transmissiblity, infection period and incubation period). We quantified the effects using an analytical equation with separate constants for SIS, SIR and SI disease models. The metric that we have developed in this work is useful for cost estimation of constrained producer-consumer algorithms, however, it has some limitations. The applicability of the metric is application, machine and data-specific. In the future, we plan to extend the metric to increase its applicability to a larger set of machine architectures, applications, and datasets.
Ph. D.
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Jiang, Shan. "Statistical Modeling of Multi-Dimensional Knowledge Diffusion Networks: An ERGM-Based Framework." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/555946.

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Knowledge diffusion networks consist of individuals who exchange knowledge and knowledge flows connecting the individuals. By studying knowledge diffusion in a network perspective, it helps us understand how the connections between individuals affect the knowledge diffusion processes. Existing research on knowledge diffusion networks mostly adopts a uni-dimensional perspective, where all the individuals in the networks are assumed to be of the same type. It also assumes that there is only one type of knowledge flow in the network. This dissertation proposes a multi-dimensional perspective of knowledge diffusion networks and examines the patterns of knowledge diffusion with Exponential Random Graph Model (ERGM) based approaches. The objective of this dissertation is to propose a framework that effectively addresses the multi-dimensionality of knowledge diffusion networks, to enable researchers and practitioners to conceptualize the multi-dimensional knowledge diffusion networks in various domains, and to provide implications on how to stimulate and control the knowledge diffusion process. The dissertation consists of three essays, all of which examine the multi-dimensional knowledge diffusion networks in a specific context, but each focuses on a different aspect of knowledge diffusion. Chapter 2 focuses on how structural properties of networks affect various types of knowledge diffusion processes in the domain of commercial technology. The study uses ERGM to simultaneously model multiple types of knowledge flows and examine their interactions. The objective is to understand the impacts of network structures on knowledge diffusion processes. Chapter 3 focuses on examining the impact of individual attributes and the attributes of knowledge on knowledge diffusion in the context of scientific innovation. Based on social capital theory, the study also utilizes ERGM to examine how knowledge transfer and knowledge co-creation can be affected by the attributes of individual researchers and the attributes of scientific knowledge. Chapter 4 considers the dynamic aspect of knowledge diffusion and proposes a novel network model extending ERGM to identify dynamic patterns of knowledge diffusion in social media. In the proposed model, dynamic patterns in social media networks are modeled based on the nodal attributes of individuals and the temporal information of network ties.
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Lamont, Morné Michael Connell. "Binary classification trees : a comparison with popular classification methods in statistics using different software." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52718.

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Thesis (MComm) -- Stellenbosch University, 2002.
ENGLISH ABSTRACT: Consider a data set with a categorical response variable and a set of explanatory variables. The response variable can have two or more categories and the explanatory variables can be numerical or categorical. This is a typical setup for a classification analysis, where we want to model the response based on the explanatory variables. Traditional statistical methods have been developed under certain assumptions such as: the explanatory variables are numeric only and! or the data follow a multivariate normal distribution. hl practice such assumptions are not always met. Different research fields generate data that have a mixed structure (categorical and numeric) and researchers are often interested using all these data in the analysis. hl recent years robust methods such as classification trees have become the substitute for traditional statistical methods when the above assumptions are violated. Classification trees are not only an effective classification method, but offer many other advantages. The aim of this thesis is to highlight the advantages of classification trees. hl the chapters that follow, the theory of and further developments on classification trees are discussed. This forms the foundation for the CART software which is discussed in Chapter 5, as well as other software in which classification tree modeling is possible. We will compare classification trees to parametric-, kernel- and k-nearest-neighbour discriminant analyses. A neural network is also compared to classification trees and finally we draw some conclusions on classification trees and its comparisons with other methods.
AFRIKAANSE OPSOMMING: Beskou 'n datastel met 'n kategoriese respons veranderlike en 'n stel verklarende veranderlikes. Die respons veranderlike kan twee of meer kategorieë hê en die verklarende veranderlikes kan numeries of kategories wees. Hierdie is 'n tipiese opset vir 'n klassifikasie analise, waar ons die respons wil modelleer deur gebruik te maak van die verklarende veranderlikes. Tradisionele statistiese metodes is ontwikkelonder sekere aannames soos: die verklarende veranderlikes is slegs numeries en! of dat die data 'n meerveranderlike normaal verdeling het. In die praktyk word daar nie altyd voldoen aan hierdie aannames nie. Verskillende navorsingsvelde genereer data wat 'n gemengde struktuur het (kategories en numeries) en navorsers wil soms al hierdie data gebruik in die analise. In die afgelope jare het robuuste metodes soos klassifikasie bome die alternatief geword vir tradisionele statistiese metodes as daar nie aan bogenoemde aannames voldoen word nie. Klassifikasie bome is nie net 'n effektiewe klassifikasie metode nie, maar bied baie meer voordele. Die doel van hierdie werkstuk is om die voordele van klassifikasie bome uit te wys. In die hoofstukke wat volg word die teorie en verdere ontwikkelinge van klassifikasie bome bespreek. Hierdie vorm die fondament vir die CART sagteware wat bespreek word in Hoofstuk 5, asook ander sagteware waarin klassifikasie boom modelering moontlik is. Ons sal klassifikasie bome vergelyk met parametriese-, "kernel"- en "k-nearest-neighbour" diskriminant analise. 'n Neurale netwerk word ook vergelyk met klassifikasie bome en ten slote word daar gevolgtrekkings gemaak oor klassifikasie bome en hoe dit vergelyk met ander metodes.
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Noel, Jonathan A. "Extremal combinatorics, graph limits and computational complexity." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:8743ff27-b5e9-403a-a52a-3d6299792c7b.

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This thesis is primarily focused on problems in extremal combinatorics, although we will also consider some questions of analytic and algorithmic nature. The d-dimensional hypercube is the graph with vertex set {0,1}d where two vertices are adjacent if they differ in exactly one coordinate. In Chapter 2 we obtain an upper bound on the 'saturation number' of Qm in Qd. Specifically, we show that for m ≥ 2 fixed and d large there exists a subgraph G of Qd of bounded average degree such that G does not contain a copy of Qm but, for every G' such that G ⊊ G' ⊆ Qd, the graph G' contains a copy of Qm. This result answers a question of Johnson and Pinto and is best possible up to a factor of O(m). In Chapter 3, we show that there exists ε > 0 such that for all k and for n sufficiently large there is a collection of at most 2(1-ε)k subsets of [n] which does not contain a chain of length k+1 under inclusion and is maximal subject to this property. This disproves a conjecture of Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi and Patkós. We also prove that there exists a constant c ∈ (0,1) such that the smallest such collection is of cardinality 2(1+o(1))ck for all k. In Chapter 4, we obtain an exact expression for the 'weak saturation number' of Qm in Qd. That is, we determine the minimum number of edges in a spanning subgraph G of Qd such that the edges of E(Qd)\E(G) can be added to G, one edge at a time, such that each new edge completes a copy of Qm. This answers another question of Johnson and Pinto. We also obtain a more general result for the weak saturation of 'axis aligned' copies of a multidimensional grid in a larger grid. In the r-neighbour bootstrap process, one begins with a set A0 of 'infected' vertices in a graph G and, at each step, a 'healthy' vertex becomes infected if it has at least r infected neighbours. If every vertex of G is eventually infected, then we say that A0 percolates. In Chapter 5, we apply ideas from weak saturation to prove that, for fixed r ≥ 2, every percolating set in Qd has cardinality at least (1+o(1))(d choose r-1)/r. This confirms a conjecture of Balogh and Bollobás and is asymptotically best possible. In addition, we determine the minimum cardinality exactly in the case r=3 (the minimum cardinality in the case r=2 was already known). In Chapter 6, we provide a framework for proving lower bounds on the number of comparable pairs in a subset S of a partially ordered set (poset) of prescribed size. We apply this framework to obtain an explicit bound of this type for the poset 𝒱(q,n) consisting of all subspaces of 𝔽qnordered by inclusion which is best possible when S is not too large. In Chapter 7, we apply the result from Chapter 6 along with the recently developed 'container method,' to obtain an upper bound on the number of antichains in 𝒱(q,n) and a bound on the size of the largest antichain in a p-random subset of 𝒱(q,n) which holds with high probability for p in a certain range. In Chapter 8, we construct a 'finitely forcible graphon' W for which there exists a sequence (εi)∞i=1 tending to zero such that, for all i ≥ 1, every weak εi-regular partition of W has at least exp(εi-2/25log∗εi-2) parts. This result shows that the structure of a finitely forcible graphon can be much more complex than was anticipated in a paper of Lovász and Szegedy. For positive integers p,q with p/q ❘≥ 2, a circular (p,q)-colouring of a graph G is a mapping V(G) → ℤp such that any two adjacent vertices are mapped to elements of ℤp at distance at least q from one another. The reconfiguration problem for circular colourings asks, given two (p,q)-colourings f and g of G, is it possible to transform f into g by recolouring one vertex at a time so that every intermediate mapping is a p,q-colouring? In Chapter 9, we show that this question can be answered in polynomial time for 2 ≤ p/q < 4 and is PSPACE-complete for p/q ≥ 4.
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Books on the topic "Statistical graph analysis"

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Kalyagin, V. A., A. P. Koldanov, P. A. Koldanov, and P. M. Pardalos. Statistical Analysis of Graph Structures in Random Variable Networks. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60293-2.

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Langtangen, Hans Petter. Solving PDEs in Python: The FEniCS Tutorial I. Cham: Springer Nature, 2017.

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Structure in complex networks. Berlin: Springer, 2009.

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Basford, Kaye E. Graphical analysis of multiresponse data: Illustrated with a plant breeding trial : interdisciplinary statistics. Boca Raton, Fla: Chapman & Hall/CRC, 1999.

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Basford, Kaye E. Graphical analysis of multiresponse data: Illustrated with a plant breeding trial. Boca Raton, Fla: Chapman & Hall/CRC, 1999.

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Whittaker, J. Graphical models in applied multivariate statistics. Chichester [England]: Wiley, 1990.

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Philippe, Mathis, ed. Graphs and networks. London: ISTE, 2007.

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Barthélemy, Jean-Pierre. Trees and proximity representations. Chichester: Wiley, 1991.

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Philippe, Mathis, ed. Graphs and networks: Multilevel modeling. 2nd ed. London: J. Wiley & Sons, 2010.

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Philippe, Mathis, ed. Graphs and networks: Multilevel modeling. 2nd ed. London: J. Wiley & Sons, 2010.

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Book chapters on the topic "Statistical graph analysis"

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Marasinghe, Mervyn G., and William J. Kennedy. "Statistical Graphics Using SAS/GRAPH." In SAS for Data Analysis, 1–58. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-77372-8_3.

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Rupp, Matthias. "Graph Kernels." In Statistical and Machine Learning Approaches for Network Analysis, 217–43. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118346990.ch8.

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Lange, Kenneth. "Descent Graph Methods." In Mathematical and Statistical Methods for Genetic Analysis, 169–201. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21750-5_9.

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Ah-Pine, Julien. "Graph Clustering by Maximizing Statistical Association Measures." In Advances in Intelligent Data Analysis XII, 56–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41398-8_6.

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Gras, Régis, Antoine Bodin, Raphaël Couturier, and Pablo Gregori. "Fractal Dimension of an Implicative Graph." In The Theory of Statistical Implicative Analysis, 179–89. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003458777-16.

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Miasnikof, Pierre, Alexander Y. Shestopaloff, Anthony J. Bonner, and Yuri Lawryshyn. "A Statistical Performance Analysis of Graph Clustering Algorithms." In Lecture Notes in Computer Science, 170–84. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92871-5_11.

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vor der Brück, Tim. "Hyponym Extraction Employing a Weighted Graph Kernel." In Statistical and Machine Learning Approaches for Network Analysis, 303–25. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118346990.ch11.

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Gras, Régis, Antoine Bodin, Raphaël Couturier, and Pablo Gregori. "A Mechanical Metaphor of the Implicative Graph of Statistical Implicative Analysis." In The Theory of Statistical Implicative Analysis, 201–6. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003458777-18.

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Kutzelnigg, Reinhard. "The Structure of an Evolving Random Bipartite Graph." In Statistical and Machine Learning Approaches for Network Analysis, 191–215. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118346990.ch7.

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Li, Shoumei, and Yukio Ogura. "Convergence in graph for fuzzy valued martingales and smartingales." In Statistical Modeling, Analysis and Management of Fuzzy Data, 72–89. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-7908-1800-0_5.

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Conference papers on the topic "Statistical graph analysis"

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Fairbanks, James, David Ediger, Rob McColl, David A. Bader, and Eric Gilbert. "A statistical framework for streaming graph analysis." In ASONAM '13: Advances in Social Networks Analysis and Mining 2013. New York, NY, USA: ACM, 2013. http://dx.doi.org/10.1145/2492517.2492620.

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Chen, Jia, Gang Wang, Yanning Shen, and Georgios B. Giannakis. "Canonical Correlation Analysis with Common Graph Priors." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450749.

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Villafane-Delgado, Marisel, and Selin Aviyente. "Temporal network tracking based on tensor factor analysis of graph signal spectrum." In 2016 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2016. http://dx.doi.org/10.1109/ssp.2016.7551718.

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Kim, Won Hwa, Vikas Singh, Moo K. Chung, Nagesh Adluru, Barbara B. Bendlin, and Sterling C. Johnson. "Multi-resolution statistical analysis on graph structured data in neuroimaging." In 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI 2015). IEEE, 2015. http://dx.doi.org/10.1109/isbi.2015.7164173.

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Madhuri, Mrs A., and T. Uma Devi. "Statistical Analysis of Design Aspects on Various Graph Embedding Learning Classifiers." In 2023 7th International Conference on Computing Methodologies and Communication (ICCMC). IEEE, 2023. http://dx.doi.org/10.1109/iccmc56507.2023.10083741.

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Xue-Xin Liu, S. X.-D. Tan, and Hai Wang. "Parallel statistical analysis of analog circuits by GPU-accelerated graph-based approach." In 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE 2012). IEEE, 2012. http://dx.doi.org/10.1109/date.2012.6176615.

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Kaurov, B. "A NEW APPROACH TO THE CONSTRUCTION OF A HUMAN AGING SCHEME." In XIV International Scientific Conference "System Analysis in Medicine". Far Eastern Scientific Center of Physiology and Pathology of Respiration, 2020. http://dx.doi.org/10.12737/conferencearticle_5fe01d9bae6739.66243641.

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A new approach to the construction of a diagram of human aging is presented, based on the shift of emphasis from the visual display of a graph to its computer analysis. The disadvantages of the old approach and the advantages of the new one are shown. On the basis of the new approach, the graphical system “AgeMap” was created and the statistical analysis of the graph of human aging, consisting of 2200 nodes, was carried out. The prospect of further application of this system is shown.
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Pavan Perin, Andréa, and Celso Ribeiro Campos. "Reading and Interpretation of Statistical Graphics by 2nd Year Students of High School." In Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. International Association for Statistical Education, 2022. http://dx.doi.org/10.52041/iase.icots11.t2f1.

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This paper aims to analyze students' understanding about graphs and tables concerning the level of reading that is necessary for them to interpret and communicate information presented through these graphs and tables. A formative assessment attached to a didactic activity was carried out in a class of 29 high school students. The students' production was analyzed according to assumptions of the discursive textual analysis methodology. The results indicated that students recognize that the reading of graphs and tables passes through different levels, which range from literal reading to that which requires the search for implicit information. The students pointed out that certain information was clear in the graph, and they just needed to point them out, whereas other information required students to combine and integrate information so that it could be understood.
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Freeley, Jennifer, Dmvtro Mishagli, Tom Brazil, and Elena Blokhina. "Statistical Simulations of Delay Propagation in Large Scale Circuits Using Graph Traversal and Kernel Function Decomposition." In 2018 15th International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD). IEEE, 2018. http://dx.doi.org/10.1109/smacd.2018.8434901.

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Ma, Xin, Guorong Wu, and Won Hwa Kim. "Enriching Statistical Inferences on Brain Connectivity for Alzheimer's Disease Analysis via Latent Space Graph Embedding." In 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI). IEEE, 2020. http://dx.doi.org/10.1109/isbi45749.2020.9098641.

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Reports on the topic "Statistical graph analysis"

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Juden, Matthew, Tichaona Mapuwei, Till Tietz, Rachel Sarguta, Lily Medina, Audrey Prost, Macartan Humphreys, et al. Process Outcome Integration with Theory (POInT): academic report. Centre for Excellence and Development Impact and Learning (CEDIL), March 2023. http://dx.doi.org/10.51744/crpp5.

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This paper describes the development and testing of a novel approach to evaluating development interventions – the POInT approach. The authors used Bayesian causal modelling to integrate process and outcome data to generate insights about all aspects of the theory of change, including outcomes, mechanisms, mediators and moderators. They partnered with two teams who had evaluated or were evaluating complex development interventions: The UPAVAN team had evaluated a nutrition-sensitive agriculture intervention in Odisha, India, and the DIG team was in the process of evaluating a disability-inclusive poverty graduation intervention in Uganda. The partner teams’ theory of change were adapted into a formal causal model, depicted as a directed acyclic graph (DAG). The DAG was specified in the statistical software R, using the CausalQueries package, having extended the package to handle large models. Using a novel prior elicitation strategy to elicit beliefs over many more parameters than has previously been possible, the partner teams’ beliefs about the nature and strength of causal links in the causal model (priors) were elicited and combined into a single set of shared prior beliefs. The model was updated on data alone as well as on data plus priors to generate posterior models under different assumptions. Finally, the prior and posterior models were queried to learn about estimates of interest, and the relative role of prior beliefs and data in the combined analysis.
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Striuk, Andrii, Olena Rybalchenko, and Svitlana Bilashenko. Development and Using of a Virtual Laboratory to Study the Graph Algorithms for Bachelors of Software Engineering. [б. в.], November 2020. http://dx.doi.org/10.31812/123456789/4462.

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The paper presents an analysis of the importance of studying graph algorithms, the reasons for the need to implement this project and its subsequent use. The existing analogues analysis is carried out, due to which a list of advantages and disadvantages is formed and taken into account in developing the virtual laboratory. A web application is created that clearly illustrates the work of graph algorithms, such as Depth-First Search, Dijkstra’s Shortest Path, Floyd- Warshall, Kruskal Minimum Cost Spanning Tree Algorithm. A simple and user- friendly interface is developed and it is supported by all popular browsers. The software product is provided with user registration and authorization functions, chat communication, personal cabinet editing and viewing the statistics on web- application use. An additional condition is taken into account at the design stage, namely the flexibility of the architecture, which envisaged the possibility of easy expansion of an existing functionality. Virtual laboratory is used at Kryvyi Rih National University to training students of specialty 121 Software Engineering in the disciplines “Algorithms and Data Structures” and “Discrete Structures”.
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