Society for Industrial and Applied Mathematics, 2007, -234 pp.The first version of this book was a set of lecture notes for a graduate course on data mining and applications in science and technology organized by the Swedish National Graduate School in Scientific Computing (NGSSC). Since then the material has been used and further developed for an undergraduate course on numerical algorithms for data mining and IT at Link¨oping University. This is a second course in scientific computing for computer science students.
The book is intended primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. It may also be useful for early graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques.
The purpose of the book is to demonstrate that there are several very powerful numerical linear algebra techniques for solving problems in different areas of data mining and pattern recognition. To achieve this goal, it is necessary to present material that goes beyond what is normally covered in a first course in scientific computing (numerical analysis) at a Swedish university. On the other hand, since the book is application oriented, it is not possible to give a comprehensive treatment of the mathematical and numerical aspects of the linear algebra algorithms used.
The book has three parts. After a short introduction to a couple of areas of data mining and pattern recognition, linear algebra concepts and matrix decompositions are presented. I hope that this is enough for the student to use matrix decompositions in problem-solving environments such as MATLAB. Some mathematical proofs are given, but the emphasis is on the existence and properties of the matrix decompositions rather than on how they are computed. In Part II, the linear algebra techniques are applied to data mining problems. Naturally, the data mining and pattern recognition repertoire is quite limited: I have chosen problem areas that are well suited for linear algebra techniques. In order to use intelligently the powerful software for computing matrix decompositions available in MATLAB, etc., some understanding of the underlying algorithms is necessary. A very short introduction to eigenvalue and singular value algorithms is given in Part III.
I have not had the ambition to write a book of recipes: given a certain problem, here is an algorithm for its solution. That would be difficult, as the area is far too diverse to give clear-cut and simple solutions. Instead, my intention has been to give the student a set of tools that may be tried as they are but, more likely, that will need to be modified to be useful for a particular application. Some of the methods in the book are described using MATLAB scripts. They should not be considered as serious algorithms but rather as pseudocodes given for illustration purposes.
A collection of exercises and computer assignments are available at the book’s Web page: www.siam.org/books/fa04.I Linear Algebra Concepts and Matrix Decompositions
Vectors and Matrices in Data Mining and Pattern Recognition
Vectors and Matrices
Linear Systems and Least Squares
Orthogonality
QR Decomposition
Singular Value Decomposition
Reduced-Rank Least Squares Models
Tensor Decomposition
Clustering and Nonnegative Matrix Factorization
II Data Mining Applications
Classification of Handwritten Digits
Text Mining
Page Ranking for a Web Search Engine
Automatic Key Word and Key Sentence Extraction
Face Recognition Using Tensor SVD
III Computing the Matrix Decompositions
Computing Eigenvalues and Singular Values
