Generalized Principal Component Analysis Gpca

This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

This volume presents recent methodological developments in data analysis and classification. It covers a wide range of topics, including methods for classification and clustering, dissimilarity analysis, consensus methods, conceptual analysis of data, and data mining and knowledge discovery in databases. The book also presents a wide variety of applications, in fields such as biology, micro-array analysis, cyber traffic, and bank fraud detection.

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Intelligence Science and Big Data Engineering, IScIDE 2013, held in Beijing, China, in July/August 2013. The 111 papers presented were carefully peer-reviewed and selected from 390 submissions. Topics covered include information theoretic and Bayesian approaches; probabilistic graphical models; pattern recognition and computer vision; signal processing and image processing; machine learning and computational intelligence; neural networks and neuro-informatics; statistical inference and uncertainty reasoning; bioinformatics and computational biology and speech recognition and natural language processing.

Miguel Heredia Conde aims at finding novel ways to fit the valuable mathematical results of the Compressive Sensing (CS) theory to the specific case of the Photonic Mixer Device (PMD).To this end, methods are presented that take profit of the sparsity of the signals gathered by PMD sensors. In his research, the author reveals that CS enables outstanding tradeoffs between sensing effort and depth error reduction or resolution enhancement.

The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.

The Microbiome in Health and Disease, Volume 171 in the Progress in Molecular Biology and Translational Science series, provides the most topical, informative and exciting monographs available on a wide variety of research topics. The series includes in-depth knowledge on the molecular biological aspects of organismal physiology, with this release including chapters on Microbiome in health and disease, CNS development and microbiome in infants, A gut feeling in ALS, Microbiome (Virome) and virus infection, Bugs and Drugs: microbiome in medicine metabolism, Immunity, T cells, and microbiome, Salmonella (Bacterial) infection and cancer: of mice and men, and many other highly researched topics. Provides a novel theme and multiple disciplinary topics of microbiome research in basic and translational studies Presents an updated collection on bacteria, virus, fungi and their interactions in microbiome Includes a timely discussion on the tools and methods used for modeling and analysis of microbiome data

This book is intended as a manual on modern advanced statistical methods for signal processing. The objectives of signal processing are the analysis, synthesis, and modification of signals measured from different natural phenomena, including engineering applications as well. Often the measured signals are affected by noise, distortion and incompleteness, and this makes it difficult to extract significant signal information. The main topic of the book is the extraction of significant information from measured data, with the aim of reducing the data size while keeping the basic information/knowledge about the peculiarities and properties of the analyzed system; to this aim, advanced and recently developed methods in signal analysis and treatment are introduced and described in depth. More in details, the book covers the following new advanced topics (and the corresponding algorithms), including detailed descriptions and discussions: the Eigen-Coordinates (ECs) method, The statistics of the fractional moments, The quantitative "universal" label (QUL) and the universal distribution function for the relative fluctuations (UDFRF), the generalized Prony spectrum, the Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS), the discrete geometrical invariants (DGI) serving as the common platform for quantitative comparison of different random functions. Although advanced topics are discussed in signal analysis, each subject is introduced gradually, with the use of only the necessary mathematics, and avoiding unnecessary abstractions. Each chapter presents testing and verification examples on real data for each proposed method. In comparison with other books, here it is adopted a more practical approach with numerous real case studies.