Matrix Methods in Data Mining and Pattern Recognition Fundamentals of Algorithms Series

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. 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. 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 include classification of handwritten digits, text mining, text summarization, pagerank computations related to the Google search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.

Preface; Part I. Linear Algebra Concepts and Matrix Decompositions: 1. Vectors and matrices in data mining and pattern recognition; 2. Vectors and matrices; 3. Linear systems and least squares; 4. Orthogonality; 5. QR decomposition; 6. Singular value decomposition; 7. Reduced rank least squares models; 8. Tensor decomposition; 9. Clustering and non-negative matrix factorization; Part II. Data Mining Applications: 10. Classification of handwritten digits; 11. Text mining; 12. Page ranking for a Web search engine; 13. Automatic key word and key sentence extraction; 14. Face recognition using rensor SVD; Part III. Computing the Matrix Decompositions: 15. Computing Eigenvalues and singular values; Bibliography; Index.

Lars Eldén is professor of numerical analysis at Linköping University in Sweden.