A two-step framework for highly nonlinear data unfolding

Local structures and global structures of data sets are both important information for learning from highly nonlinear data. However, existing manifold learning algorithms either neglect one of them or have limitation on describing them. In this paper, we proposed a new two-step framework that fusing the global and local information to unfold highly nonlinear data. It first learns the global structures via a new method-Distance Penalization Embedding and then refines the local structures by semi-supervised manifold learning algorithms. The effectiveness of the method has been verified by experimental results on both simulation and real world data sets.

[1]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[2]  Ann B. Lee,et al.  Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Helge J. Ritter,et al.  Principal surfaces from unsupervised kernel regression , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Li Yang,et al.  Alignment of Overlapping Locally Scaled Patches for Multidimensional Scaling and Dimensionality Reduction , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Xin Yang,et al.  Semi-supervised nonlinear dimensionality reduction , 2006, ICML.

[6]  Mikhail Belkin,et al.  Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering , 2001, NIPS.

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

[8]  Jian Yang,et al.  Unsupervised Discriminant Projection Analysis for Feature Extr , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

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

[10]  Joshua B. Tenenbaum,et al.  Global Versus Local Methods in Nonlinear Dimensionality Reduction , 2002, NIPS.

[11]  Fei Wang,et al.  Clustering with Local and Global Regularization , 2007, IEEE Transactions on Knowledge and Data Engineering.

[12]  Fei Wang,et al.  Semi-definite Manifold Alignment , 2007, ECML.

[13]  Ronald R. Coifman,et al.  Data Fusion and Multicue Data Matching by Diffusion Maps , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Jianwei Li,et al.  Combining local and global information for nonlinear dimensionality reduction , 2009, Neurocomputing.

[15]  Daoqiang Zhang,et al.  Semi-Supervised Dimensionality Reduction ∗ , 2007 .

[16]  Gang Wang,et al.  Semi-supervised Classification Using Local and Global Regularization , 2008, AAAI.

[17]  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.

[18]  Deli Zhao,et al.  Linear local tangent space alignment and application to face recognition , 2007, Neurocomputing.