Title Matrix Methods in Data Mining and Pattern Recognition, 2/e
Subtitle Fundamentals of Algorithms
Author Lars Eldén
ISBN 9781611975857
List price USD 69.00
Price outside India Available on Request
Original price
Binding Paperback
No of pages 244
Book size 178 x 254 mm
Publishing year 2019
Original publisher SIAM - Society for Industrial and Applied Mathematics (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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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.



Part I: Linear Algebra Concepts and Matrix Decompositions

Chapter 1. Vectors and Matrices in Data Mining and Pattern Recognition • Data Mining and Pattern Recognition • Vectors and Matrices • Purpose of the Book • Programming Environments • Floating Point Computations • Notation and Conventions

Chapter 2. Vectors and Matrices • Matrix-Vector Multiplication • Matrix-Matrix Multiplication • Inner Product and Vector Norms • Matrix Norms • Linear Independence: Bases • The Rank of a Matrix

Chapter 3. Linear Systems and Least Squares • LU Decomposition • Symmetric, Positive Definite Matrices • Perturbation Theory and Condition Number • Rounding Errors in Gaussian Elimination • Banded Matrices • The Least Squares Problem

Chapter 4. Orthogonality • Orthogonal Vectors and Matrices • Elementary Orthogonal Matrices • Number of Floating Point Operations • Orthogonal Transformations in Floating Point Arithmetic

Chapter 5. QR Decomposition • Orthogonal Transformation to Triangular Form • Solving the Least Squares Problem • Computing or Not Computing Q • Flop Count for QR Factorization • Error in the Solution of the Least Squares Problem • Updating the Solution of a Least Squares Problem

Chapter 6. Singular Value Decomposition • The Decomposition • Fundamental Subspaces • Matrix Approximation • Principal Component Analysis • Solving Least Squares Problems • Condition Number and Perturbation Theory for the Least Squares Problem • Rank-Deficient and Underdetermined Systems • Computing the SVD • The Eigenvalue Decomposition of a Symmetric Matrix • Complete Orthogonal Decomposition

Chapter 7. Reduced-Rank Least Squares Models • Truncated SVD: Principal Component Regression • A Krylov Subspace Method

Chapter 8. Tensor Decomposition • Introduction • Basic Tensor Concepts • A Tensor SVD • Approximating a Tensor by HOSVD

Chapter 9. Clustering and Nonnegative Matrix Factorization • The k-Means Algorithm • Nonnegative Matrix Factorization

Chapter 10. Graphs and Matrices • Graphs and Adjacency Matrices • Connectedness and Reducibility • Graph Laplacians and Spectral Partitioning • Bipartite Graphs


Part II: Data Mining Applications

Chapter 11. Classification of Handwritten Digits • Handwritten Digits and a Simple Algorithm • Classification Using SVD Bases • Tangent Distance

Chapter 12. Text Mining • Preprocessing the Documents and Queries • The Vector Space Model • Latent Semantic Indexing • Clustering • Nonnegative Matrix Factorization • LGK Bidiagonalization • Average Performance

Chapter 13. Page Ranking for a Web Search Engine • PageRank • Random Walk and Markov Chains • The Power Method for PageRank Computation • HITS

Chapter 14. Automatic Key Word and Key Sentence Extraction • Saliency Score • Key Sentence Extraction from a Rank-k Approximation

Chapter 15. Face Recognition Using Tensor SVD • Tensor Representation • Face Recognition • Face Recognition with HOSVD Compression

Chapter 16. Spectral Graph Partitioning • Large and Sparse Laplacians • A Network of Political Blogs • Text Classification • Multiway Partitioning


Part III: Computing the Matrix Decompositions

Chapter 17. Computing Eigenvalues and Singular Values • Perturbation Theory • The Power Method and Inverse Iteration • Similarity Reduction to Tridiagonal Form • The QR Algorithm for a Symmetric Tridiagonal Matrix • Computing the SVD • The Nonsymmetric Eigenvalue Problem • Sparse Matrices • The Arnoldi and Lanczos Methods • Software



About the Author:

Lars Eldén is a retired professor of scientific computing at Linköping University in Sweden, where he was head of the mathematics department and director of the National Supercomputer Centre. He is the author, along with L. Wittmeyer-Koch and H. Bruun Nielsen, of Introduction to Numerical Computation: Analysis and MATLAB Illustrations (Studentlitteratur AB, 2004).

Target Audience:

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. 


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