Principal manifolds for data visualization and dimension reduction / Alexander N. Gorban,Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev, editors.

"This book is a collection of reviews and original papers presented partially at the workshop 'Principal manifolds for data cartography and dimension reduction' (Leicester, August 24-26, 2006)."--P. X.

Includes bibliographical references and index.

Contents: Developments and applications of nolinear principal componet analysis - a review -- Nonlinear principal component analysis: neutral network models and applications -- Learning nonlinear principal manifolds by self-organising maps -- Elastic maps and nets for approximating principal manifolds and their application to microarray data visualization -- Topology-preserving mappong for data visualisation -- The iterative extraction approach to clustering -- Representating complex data using localized principal components with application to astronomical data -- Auto - associative models, nonlinear principal component analysis, manifolds and projection pursuit -- Beyond the concept of manifolds: principal tres, metro maps, and elastic cubic complexes -- Diffusion maps - a probabilistic interpretation fpor spectral embedding and clustering algorithms -- On bounds for diffusion, discrepancy and fill distance metrics -- Gemetric optimization methods for the analysis of gene expression data -- Dimensionality reduction and microarray data -- PCA and K.Means decipher genome.