Twin Kernel Embedding with Relaxed Constraints on Dimensionality Reduction for Structured Data

This paper proposes a new nonlinear dimensionality reduction algorithm called RCTKE for highly structured data. It is built on the original TKE by incorporating a mapping function into the objective functional of TKE as regularization terms where the mapping function can be learned from training data and be used for novel samples. The experimental results on highly structured data is used to verify the effectiveness of the algorithm.

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

[2]  Johan A. K. Suykens,et al.  Data Visualization and Dimensionality Reduction Using Kernel Maps With a Reference Point , 2008, IEEE Transactions on Neural Networks.

[3]  Shuicheng Yan,et al.  Neighborhood preserving embedding , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

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

[5]  Dimitris K. Agrafiotis,et al.  Stochastic proximity embedding , 2003, J. Comput. Chem..

[6]  Xiaofei He,et al.  Locality Preserving Projections , 2003, NIPS.

[7]  Hongyuan Zha,et al.  Isometric Embedding and Continuum ISOMAP , 2003, ICML.

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

[9]  Junbin Gao,et al.  Learning Optimal Kernel from Distance Metric in Twin Kernel Embedding for Dimensionality Reduction and Visualization of Fingerprints , 2007, ADMA.

[10]  Huafeng Xu,et al.  Exploring the nonlinear geometry of protein homology , 2003, Protein science : a publication of the Protein Society.

[11]  Junbin Gao,et al.  Visualization of Protein Structure Relationships Using Twin Kernel Embedding , 2007, 2007 1st International Conference on Bioinformatics and Biomedical Engineering.

[12]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[13]  Anil K. Jain,et al.  Nonlinear Manifold Learning for Data Stream , 2004, SDM.

[14]  Junbin Gao,et al.  Kernel Laplacian Eigenmaps for Visualization of Non-vectorial Data , 2006, Australian Conference on Artificial Intelligence.

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

[16]  G. Baudat,et al.  Generalized Discriminant Analysis Using a Kernel Approach , 2000, Neural Computation.

[17]  Dimitris K Agrafiotis,et al.  A modified update rule for stochastic proximity embedding. , 2003, Journal of molecular graphics & modelling.

[18]  Thomas Gärtner,et al.  A survey of kernels for structured data , 2003, SKDD.

[19]  I. Jolliffe.  Principal Component Analysis , 2002 .

[20]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[21]  William Stafford Noble,et al.  A structural alignment kernel for protein structures , 2007, Bioinform..

[22]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[23]  Junbin Gao,et al.  Visualization of Non-vectorial Data Using Twin Kernel Embedding , 2006, 2006 International Workshop on Integrating AI and Data Mining.

[24]  Anil K. Jain,et al.  Incremental nonlinear dimensionality reduction by manifold learning , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Nello Cristianini,et al.  Classification using String Kernels , 2000 .