High-Dimensional Data Analysis

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional str

Gives a comprehensive and systematic account of high-dimensional data analysis, including variable selection via regularization methods and sure independent feature screening methods. It is a valuable

This book features research contributions from The Abel Symposium on Statistical Analysis for High-Dimensional Data, held in Nyvagar, Lofoten, Norway, in May 2014.The focus of the symposium was on sta

This book offers a coherent and comprehensive approach to feature subset selection in the scope of classification problems, explaining the foundations, real application problems and the challenges of

This new edition answers the need for a comprehensive, cutting-edge overview of this important and emerging field—effectively outlining all phases of this revolutionary analytical technique, from prep

'Big data' poses challenges that require both classical multivariate methods and contemporary techniques from machine learning and engineering. This modern text equips you for the new world - integrating the old and the new, fusing theory and practice and bridging the gap to statistical learning. The theoretical framework includes formal statements that set out clearly the guaranteed 'safe operating zone' for the methods and allow you to assess whether data is in the zone, or near enough. Extensive examples showcase the strengths and limitations of different methods with small classical data, data from medicine, biology, marketing and finance, high-dimensional data from bioinformatics, functional data from proteomics, and simulated data. High-dimension low-sample-size data gets special attention. Several data sets are revisited repeatedly to allow comparison of methods. Generous use of colour, algorithms, Matlab code, and problem sets complete the package. Suitable for master's/graduat

This ready reference discusses different methods for statistically analyzing and validating data created with high-throughput methods. As opposed to other titles, this book focusses on systems approac

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches,

Over the last few years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal

Multivariate analysis is a mainstay of statistical tools in the analysis of biomedical data. It concerns with associating data matrices of n rows by p columns, with rows representing samples (or pati

There is a growing need for a more automated system of partitioning data sets into groups, or clusters. For example, digital libraries and the World Wide Web continue to grow exponentially, the ability to find useful information increasingly depends on the indexing infrastructure or search engine. Clustering techniques can be used to discover natural groups in data sets and to identify abstract structures that might reside there, without having any background knowledge of the characteristics of the data. Clustering has been used in a variety of areas, including computer vision, VLSI design, data mining, bio-informatics (gene expression analysis), and information retrieval, to name just a few. This book focuses on a few of the most important clustering algorithms, providing a detailed account of these major models in an information retrieval context. The beginning chapters introduce the classic algorithms in detail, while the later chapters describe clustering through divergences and sh

Mathematical models are used to simulate complex real-world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty.

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clust

Biclustering is a data-mining technique that allows simultaneous clustering of rows and columns within a matrix. This book focuses on biclustering as an unsupervised learning method for high-dimension

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches,

This book consists of surveys of high-frequency financial data analysis and econometric forecasting. Some of the chapters were presented as tutorials to an audience in the Econometric Forecasting and

Now thoroughly revised and up-dated, this book describes techniques for handling and analysing data obtained from high-energy and nuclear physics experiments. The observation of particle interactions involves the analysis of large and complex data samples. Beginning with a chapter on real-time data triggering and filtering, the book describes methods of selecting the relevant events from a sometimes huge background. The use of pattern recognition techniques to group the huge number of measurements into physically meaningful objects like particle tracks or showers is then examined and the track and vertex fitting methods necessary to extract the maximum amount of information from the available measurements are explained. The final chapter describes tools and methods which are useful to the experimenter in the physical interpretation and in the presentation of the results. This indispensable guide will appeal to graduate students, researchers and computer and electronic engineers involve

This book is published open access under a CC BY 4.0 license.It covers aspects of unsupervised machine learning used for knowledge discovery in data science and introduces a data-driven approach to cl

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It featu