A kernel view of the dimensionality reduction of manifolds Export

@inproceedings{citeulike:909788, abstract = {We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.}, address = {New York, NY, USA}, author = {Ham, Jihun and Lee, Daniel D. and Mika, Sebastian and Sch\"{o}lkopf, Bernhard}, booktitle = {ICML '04: Proceedings of the twenty-first international conference on Machine learning}, citeulike-article-id = {909788}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1015417}, citeulike-linkout-1 = {http://dx.doi.org/10.1145/1015330.1015417}, doi = {10.1145/1015330.1015417}, isbn = {1-58113-828-5}, keywords = {kernels, manifold}, location = {Banff, Alberta, Canada}, pages = {47+}, posted-at = {2009-10-09 13:35:42}, priority = {2}, publisher = {ACM}, title = {A kernel view of the dimensionality reduction of manifolds}, url = {http://dx.doi.org/10.1145/1015330.1015417}, year = {2004} }

TY - CONF ID - citeulike:909788 L3 - citeulike-article-id:909788 N2 - We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples. CY - Banff, Alberta, Canada SN - 1-58113-828-5 AD - New York, NY, USA TI - A kernel view of the dimensionality reduction of manifolds PB - ACM T2 - ICML '04: Proceedings of the twenty-first international conference on Machine learning SP - 47 KW - kernels KW - manifold AU - Ham, Jihun AU - Lee, Daniel AU - Mika, Sebastian AU - Schölkopf, Bernhard PY - 2004/// UR - http://dx.doi.org/10.1145/1015330.1015417 ER -