Nonlinear Dimensionality Reduction

This book reviews well-known methods for reducing the dimensionality of numerical databases as well as recent developments in nonlinear dimensionality reduction. All are described from a unifying point of view, which highlights their respective strengths and shortcomings.

This book describes existing and advanced methods to reduce the dimensionality of numerical databases. For each method, the description starts from intuitive ideas, develops the necessary mathematical details and ends by outlining the algorithmic implementation. Methods are compared with each other with the help of different illustrative examples.

Covers a wide range of methods to reduce the dimensionality of data and presents a unifying point of view Includes supplementary material: sn.pub/extras

Zusammenfassung
However, since the late nineties, many new methods have been developed and nonlinear dimensionality reduction, also called manifold learning, has become a hot topic. The purpose of the book is to summarize clear facts and ideas about well-known methods as well as recent developments in the topic of nonlinear dimensionality reduction.

Inhalt
High-Dimensional Data.- Characteristics of an Analysis Method.- Estimation of the Intrinsic Dimension.- Distance Preservation.- Topology Preservation.- Method comparisons.- Conclusions.