Nonlinear Dimensionality Reduction

From the reviews: "This beautifully produced book covers various innovative topics in nonlinear dimensionality reduction, such as Isomap, locally linear embedding, and Laplacian eigenmaps, etc. Those topics are usually not covered by existing texts on multivariate statistical techniques. Moreover, the text offers an excellent overview of the concept of intrinsic dimension. Special attention is devoted to the topic of estimation of the intrinsic dimension, which has been previously overlooked by many researchers... A strong feature of the book is the style of presentation. The book is clearly written, ...A large number of examples and graphical displays in color help the reader in understanding the ideas. For each method discussed, the authors do a credible job by starting from motivating examples and intuitive ideas, introducing rigorous mathematical notation without being cumbersome, and ending with discussion and conclusion remarks. All in all, this is an interesting book, and I would recommend this text to those researchers who want to learn quickly about this new field of manifold learning. This book will serve as a useful and necessary resource to several advanced statistics courses in machine learning and data mining... In addition, the Matlab and R packages will surely enhance the learning resources and increase the accessibility of this book to data analysts. " (Haonan Wang, Biometrics, June 2009, 65) "The book by Lee and Verleysen presents a comprehensive summary of the state-of-the-art of the field in a very accessible manner. It is the only book I know that offers such a thorough and systematic account of this interesting and important area of research. ... Reading the book is quite enjoyable ... ." (Lasse Holmstrom, International Statistical Reviews, Vol. 76 (2), 2008) "The book provides an effective guide for selecting the right method and understanding potential pitfalls and limitations of the many alternative methods. ... All in all, Nonlinear Dimensionality Reduction may serve two groups of readers differently. To the reader already immersed in the field it is a convenient compilation of a wide variety of algorithms with references to further resources. To students or professionals in areas outside of machine learning or statistics ... it can be highly recommended as an introduction." (Kilian Q. Weinberger, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)

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