Novel semisupervised high-dimensional correspondences learning method

Correspondence is one of the big challenges in machine learning and image processing. To match two high-dimensional data sets with a certain number of aligned training examples, a novel semisuper- vised method is proposed. It is mainly based on two manifold learning approaches: maximum variance unfolding MVU and locally linear em- bedding LLE. We have modified MVU to a semi-supervised version to solve the correspondence problem. Additionally, the nonuniform warps and folds caused by employing LLE alone and the computational burden of MVU disappear when they are combined. The proposed algorithm outperforms traditional methods in accuracy and efficiency. Three ex- amples are performed to demonstrate the potential of this method. © 2008

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

[2]  Kilian Q. Weinberger,et al.  Nonlinear Dimensionality Reduction by Semidefinite Programming and Kernel Matrix Factorization , 2005, AISTATS.

[3]  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..

[4]  H. Zha,et al.  Principal manifolds and nonlinear dimensionality reduction via tangent space alignment , 2004, SIAM J. Sci. Comput..

[5]  Daniel D. Lee,et al.  Learning a manifold-constrained map between image sets: applications to matching and pose estimation , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

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

[7]  Kilian Q. Weinberger,et al.  Learning a kernel matrix for nonlinear dimensionality reduction , 2004, ICML.

[8]  Chenping Hou,et al.  Learning High Dimensional Correspondences Based on Maximum Variance Unfolding , 2007, 2007 International Conference on Mechatronics and Automation.

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

[10]  Bhaskar Mehta.  Cross System Personalization by Learning Manifold Alignments , 2006, AAAI.

[11]  B. Borchers.  CSDP, A C library for semidefinite programming , 1999 .

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

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

[14]  H. Sebastian Seung,et al.  The Manifold Ways of Perception , 2000, Science.

[15]  David J. Kriegman,et al.  What Is the Set of Images of an Object Under All Possible Illumination Conditions? , 1998, International Journal of Computer Vision.

[16]  Geoffrey E. Hinton,et al.  Modeling the manifolds of images of handwritten digits , 1997, IEEE Trans. Neural Networks.

[17]  Daniel D. Lee,et al.  Learning High Dimensional Correspondences from Low Dimensional Manifolds , 2003 .