论文信息 - Spline Embedding for Nonlinear Dimensionality Reduction

Spline Embedding for Nonlinear Dimensionality Reduction

This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.

[1] Nicolas Le Roux,et al. Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

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

[3] F. Bookstein. Thin-plate splines and decomposition of deformation , 1989 .

[4] Kilian Q. Weinberger,et al. Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, CVPR.

[5] D. Donoho,et al. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[8] Jean Duchon,et al. Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[9] 张振跃,et al. Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment , 2004 .