Spectral clustering and biclustering. Learning large graphs and contingency tables (Q2844997)

The main aim of this monograph is to bridge the gap between graph theory and statistics. This is achieved using ideas on how graphs and contingency tables can be considered as statistical data and how they can be analyzed. For this analysis the author uses either well-known methods of statistical multivariate analysis or methods that are reminiscent of them. In fact, the author wants to provide answers to questions that arise when statisticians are dealing with large weighted graphs or rectangular arrays. With this perspective in mind, the present monograph consists of an introduction, five chapters and three appendices. In the appendices supplementary material related to linear algebra and functional analysis, probability (random vectors and matrices) and multivariate analysis methods are given.NEWLINENEWLINEChapter 1 (``Multivariate analysis techniques for representing graphs and contingency tables'') is devoted to multivariate techniques (principal component analysis and correspondence analysis) for representing edge-weighted graphs and contingency tables. In Chapter 2 (``Multiway cuts and spectra''), minimum ratio and normalized multiway cut problems are presented together with modularity cuts. Chapter 3 (``Large networks, perturbation of block structures'') applies the results of the previous two chapters to the spectral clustering of large networks. In Chapter 4 (``Testable graph and contingency table parameters''), the theory of convergent graph sequences and graphons is used for vertex- and edge-weighted graphs and contingency tables. In Chapter 5 (``Statistical learning of networks''), classical and modern statistical methods, which are parametric and nonparametric, are applied to find the underlying clusters of a given network or to classify graphs or contingency tables given some distinct prototypes.NEWLINENEWLINESummarizing, this monograph endeavors to bridge the gap between graph theory and statistics and offers a novel treatment of spectral clustering and biclustering of networks. The author has written an interesting book, which is intended to serve the need of researchers and professionals mining large datasets related to networks. Moreover, the book could also be very useful for graduate level courses among others in data mining or applied graph theory. At the end of each chapter, references are provided what will help readers wishing to further pursue this area. Finally, a supporting website is provided.