论文信息 - Manifold Learning and Dimensionality Reduction with Diffusion Maps

Manifold Learning and Dimensionality Reduction with Diffusion Maps

This report gives an introduction to diffusion maps, some of their underlying theory, as well as their applications in spectral clustering. First, the shortcomings of linear methods such as PCA are shown to motivate the use of graph-based methods. We then explain Locally Linear Embedding [9], Isomap [11] and Laplacian eigenmaps [1], before we give details on diffusion maps and anisotropic diffusion processes.

Richard Socher | R. Socher

[1] Lawrence K. Saul,et al. Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold , 2003, J. Mach. Learn. Res..

[2] Stéphane Lafon,et al. Diffusion maps , 2006 .

[3] J. Tenenbaum,et al. A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[4] Ulrike von Luxburg,et al. Graph Laplacians and their Convergence on Random Neighborhood Graphs , 2006, J. Mach. Learn. Res..

[5] S T Roweis,et al. Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[6] Eric R. Ziegel,et al. The Elements of Statistical Learning , 2003, Technometrics.

[7] Mikhail Belkin,et al. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.