Dimension Reduction

A Guided Tour
1. Auflage 2010
ISBN: 978-1-60198-378-7
Verlag: Now Publishers

Buch, Englisch, Band 7, 104 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Foundations and Trends® in Machine Learning

We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although the review focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nyström method, which links several of the manifold algorithms, is also reviewed. We use a publicly available dataset to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.

Autoren/Hrsg.

Burges, Christopher J.C.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1: Introduction 2: Estimating the Dimension 3: Projective Methods 4: Manifold Modeling 5: Pointers and Conclusions. Acknowledgements. References. A Appendix: The Nearest Positive Semidefinite Matrix