A kernel view of the dimensionality reduction of manifolds Export

@misc{citeulike:2487225, 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.}, author = {Ham, J. and Lee, D. and Mika, S. and Scholkopf, B.}, citeulike-article-id = {2487225}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.5533}, keywords = {kernels, learning, manifolds}, posted-at = {2008-03-07 22:05:38}, priority = {2}, title = {A kernel view of the dimensionality reduction of manifolds}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.5533}, year = {2004} }

TY - GEN ID - citeulike:2487225 L3 - citeulike-article-id:2487225 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. TI - A kernel view of the dimensionality reduction of manifolds KW - kernels KW - learning KW - manifolds AU - Ham, J AU - Lee, D AU - Mika, S AU - Scholkopf, B PY - 2004/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.5533 ER -