Matrix Methods in Data Mining and Pattern Recognition

Elden (numerical analysis, Linkoping U.) uses as examples handwritten digits, text summarization, pagerank computations made famous by a certain very popular search engine (the name of which is now used as a verb) and face recognition to explain how to use very powerful linear algebra techniques to mine data and recognize patterns. He introduces vectors and matrices in data mining and pattern recognition, then gives more details on vectors and matrices, including their inner products, vector norms and linear independence bases. He explains linear systems and least squares, orthogonality, QR decomposition, singular value decomposition, reduced-rank least squares models, tensor decomposition, clustering and nonnegative matrix factorization. In the next section he applies the abstract to real life, throwing in an exercise on extracting an automatic key word and key sentence, and closes with instructions on computing matrix decomposition, including computing eigenvalues and singular values. Annotation c2007 Book News, Inc., Portland, OR (booknews.com)

Lars Elden is professor of numerical analysis at Linkoping University in Sweden. He was head of the Mathematics Department at Linkoping University from 1997 to 2001 and Director of the National Supercomputer Centre, Linkoping, from 1990 to 1991. 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).