Kounchev,O.

Multivariate Polysplines: Applications to Numerical and Wavelet Analysis.

Mar. 2001 500 pp.
0-12-422490-3

Why this title? This is the first book on Multivariate Polysplines. Multivariate Polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate Polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, Polysplines are proving more effective than well-established methods, such as Kriging, Radial Basis Functions, Thin Plate Splines and Minimum Curvature.

Szpankowski,W.

Average Case Analysis of Algorithms on Sequences.

Mar. 2001 508 pp.
0-471-24063-X

A timely book on a timely book on a topic that has witnessed increased interest over the last decade, due to the high success rate of randomised algorithms for computational geometry, scientific visualisation, molecular biology and information theory. A wholly interdisciplinary text, covering computer science, combinatorics and probability theory, this text combines both analytical and probabilistic tools in one volume. * Focus on tools and techniques used in average case analysis of algorithms l* Tools are illustrated throughout in problems on words with applications to computational molecular biology, data compression, security, pattern matching * Extensions and exercises at the end of each chapter

Michael I. Jordan and Terrence J. Sejnowski (eds.)

Graphical Models
Foundations of Neural Computation

Graphical models use graphs to represent and manipulate joint probability distributions. They have
their roots in artificial intelligence, statistics, and neural networks. The clean mathematical formalism of the graphical models framework makes it possible to understand a wide variety of network-based approaches to computation, and in particular to understand many neural network algorithms and architectures as instances of a broader probabilistic methodology. It also makes it possible to identify novel features of neural network algorithms and architectures and to extend them to more general graphical models.

This book exemplifies the interplay between the general formal framework of graphical models and
the exploration of new algorithms and architectures. The selections range from foundational papers of historical importance to results at the cutting edge of research.

Contributors
H. Attias, C. M. Bishop, B. J. Frey, Z. Ghahramani, D. Heckerman, G. E. Hinton, R. Hofmann, R. A.
Jacobs, Michael I. Jordan, H. J. Kappen, A. Krogh, R. Neal, S. K. Riis, F. B. Rodr�еez, L. K. Saul,
Terrence J. Sejnowski, P. Smyth, M. E. Tipping, V. Tresp, Y. Weiss.

June 2001
ISBN 0-262-60042-0
435 pp. (soft cover)

Klaus Obermayer and Terrence J. Sejnowski (eds.)

Self-Organizing Map Formation
Foundations of Neural Computation

This book provides an overview of self-organizing map formation, including recent developments.
Self-organizing maps form a branch of unsupervised learning, which is the study of what can be
determined about the statistical properties of input data without explicit feedback from a teacher. The articles are drawn from the journal Neural Computation.

The book consists of five sections. The first section looks at attempts to model the organization of cortical maps and at the theory and applications of the related artificial neural network algorithms. The second section analyzes topographic maps and their formation via objective functions. The third section discusses cortical maps of stimulus features. The fourth section discusses self-organizing maps for unsupervised data analysis. The fifth section discusses
extensions of self-organizing maps, including two surprising applications of mapping algorithms to
standard computer science problems: combinatorial optimization and sorting.

Contributors
J. J. Atick, H. G. Barrow, H. U. Bauer, C. M. Bishop, H. J. Bray, J. Bruske, J. M. L. Budd, M.
Budinich, V. Cherkassky, J. Cowan, R. Durbin, E. Erwin, G. J. Goodhill, T. Graepel, D. Grier, S.
Kaski, T. Kohonen, H. Lappalainen, Z. Li, J. Lin, R. Linsker, S. P. Luttrell, D. J. C. MacKay, K. D.
Miller, G. Mitchison, F. Mulier, K. Obermayer, C. Piepenbrock, H. Ritter, K. Schulten, T. J. Sejnowski,
S. Smirnakis, G. Sommer, M. Svensen, R. Szeliski, A. Utsugi, C. K. I. Williams, L. Wiskott, L. Xu, A.
Yuille, J. Zhang.

June 2001
ISBN 0-262-65060-6
415 pp. (soft cover)