Matrix Methods In Data Mining And Pattern Recognition

This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.

Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.

Making obscure knowledge about matrix decompositions widely available, Understanding Complex Datasets: Data Mining with Matrix Decompositions discusses the most common matrix decompositions and shows how they can be used to analyze large datasets in a broad range of application areas. Without having to understand every mathematical detail, the book

Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.

Apply powerful Data Mining Methods and Models to Leverage your Data for Actionable Results Data Mining Methods and Models provides: * The latest techniques for uncovering hidden nuggets of information * The insight into how the data mining algorithms actually work * The hands-on experience of performing data mining on large data sets Data Mining Methods and Models: * Applies a "white box" methodology, emphasizing an understanding of the model structures underlying the softwareWalks the reader through the various algorithms and provides examples of the operation of the algorithms on actual large data sets, including a detailed case study, "Modeling Response to Direct-Mail Marketing" * Tests the reader's level of understanding of the concepts and methodologies, with over 110 chapter exercises * Demonstrates the Clementine data mining software suite, WEKA open source data mining software, SPSS statistical software, and Minitab statistical software * Includes a companion Web site, www.dataminingconsultant.com, where the data sets used in the book may be downloaded, along with a comprehensive set of data mining resources. Faculty adopters of the book have access to an array of helpful resources, including solutions to all exercises, a PowerPoint(r) presentation of each chapter, sample data mining course projects and accompanying data sets, and multiple-choice chapter quizzes. With its emphasis on learning by doing, this is an excellent textbook for students in business, computer science, and statistics, as well as a problem-solving reference for data analysts and professionals in the field. An Instructor's Manual presenting detailed solutions to all the problems in the book is available onlne.

This volume contains a selection of papers presented at the Seven~h Confer ence of the International Federation of Classification Societies (IFCS-2000), which was held in Namur, Belgium, July 11-14,2000. From the originally sub mitted papers, a careful review process involving two reviewers per paper, led to the selection of 65 papers that were considered suitable for publication in this book. The present book contains original research contributions, innovative ap plications and overview papers in various fields within data analysis, classifi cation, and related methods. Given the fast publication process, the research results are still up-to-date and coincide with their actual presentation at the IFCS-2000 conference. The topics captured are: • Cluster analysis • Comparison of clusterings • Fuzzy clustering • Discriminant analysis • Mixture models • Analysis of relationships data • Symbolic data analysis • Regression trees • Data mining and neural networks • Pattern recognition • Multivariate data analysis • Robust data analysis • Data science and sampling The IFCS (International Federation of Classification Societies) The IFCS promotes the dissemination of technical and scientific information data analysis, classification, related methods, and their applica concerning tions.

This updated compendium provides the linear algebra background necessary to understand and develop linear algebra applications in data mining and machine learning.Basic knowledge and advanced new topics (spectral theory, singular values, decomposition techniques for matrices, tensors and multidimensional arrays) are presented together with several applications of linear algebra (k-means clustering, biplots, least square approximations, dimensionality reduction techniques, tensors and multidimensional arrays).The useful reference text includes more than 600 exercises and supplements, many with completed solutions and MATLAB applications.The volume benefits professionals, academics, researchers and graduate students in the fields of pattern recognition/image analysis, AI, machine learning and databases.

Statistical pattern recognition is a very active area of study andresearch, which has seen many advances in recent years. New andemerging applications - such as data mining, web searching,multimedia data retrieval, face recognition, and cursivehandwriting recognition - require robust and efficient patternrecognition techniques. Statistical decision making and estimationare regarded as fundamental to the study of pattern recognition. Statistical Pattern Recognition, Second Edition has been fullyupdated with new methods, applications and references. It providesa comprehensive introduction to this vibrant area - with materialdrawn from engineering, statistics, computer science and the socialsciences - and covers many application areas, such as databasedesign, artificial neural networks, and decision supportsystems. * Provides a self-contained introduction to statistical patternrecognition. * Each technique described is illustrated by real examples. * Covers Bayesian methods, neural networks, support vectormachines, and unsupervised classification. * Each section concludes with a description of the applicationsthat have been addressed and with further developments of thetheory. * Includes background material on dissimilarity, parameterestimation, data, linear algebra and probability. * Features a variety of exercises, from 'open-book' questions tomore lengthy projects. The book is aimed primarily at senior undergraduate and graduatestudents studying statistical pattern recognition, patternprocessing, neural networks, and data mining, in both statisticsand engineering departments. It is also an excellent source ofreference for technical professionals working in advancedinformation development environments. For further information on the techniques and applicationsdiscussed in this book please visit ahref="http://www.statistical-pattern-recognition.net/"www.statistical-pattern-recognition.net/a