an:05161643
Zbl 1120.68092
Eld??n, Lars
Matrix methods in data mining and pattern recognition
EN
Fundamentals of Algorithms 4. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-26-9). x, 224~p. (2007).
00421492
2007
b
68T10 68T05 68-01 65F10 65F15 65F25 68U10 68U15 65Y15
textbook; linear systems; least squares problems; matrix decompositions; eigenvalues; singular values; QR algorithms; data mining; pattern recognition
The book is concerned with the presentation of several very powerful numerical linear algebra techniques for solving problems in different areas of data mining and pattern recognition. It has three parts. The first one presents in 9 chapters the necessary concepts of linear algebra and matrix decompositions such as: linear systems and least squares, orthogonality, QR, singular values and tensor decompositions, clustering and nonnegative matrix factorization. They give the students the possibility of using matrix decompositions in problem-solving environments such as MATLAB. Part two of the book is dedicated to applications in data mining and pattern recognition. In Chapters 10 to 14 the author presents some problem areas that are well suited for linear algebra techniques such as: text mining, page ranking for web search engines, key word and sentence extraction, face recognition. The presentation contains relevant examples and MATLAB applications. In Part III, the author comes back to numerical linear algebra and gives some basic information about eigenvalue and singular value algorithms such as: power method, inverse iteration, QR algorithm for symmetric matrices, the nonsymmetric eigenvalue problem, Arnoldi and Lanczos algorithms.
The book is primarily intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course, but also for early graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques. In this sense, it gives the students a set of basic tools which can easily be modified and adapted to become useful for a particular application. A collection of exercises and computer assignments are available at the book's Web page: \url{http://www.siam.org/books/fa04}.
Constantin Popa (Constan??a)