Nonlinear Component Analysis as a Kernel Eigenvalue Problem Export

@misc{scholkopf-smola-1998, abstract = {We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in high--dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5--pixel products in 16\Theta16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition. AS and KRM are with GMD First (Forschungszentrum Informationstechnik), Rudower Chaussee 5, 12489 Berlin. AS and BS were supported by grants from the Studienstiftung des deutschen Volkes. BS thanks the GMD First for hospitality during two visits. AS and BS thank V. Vapnik for introducing them to kernel representations of dot products during joint work on Support Vector machines. This work profited from discussions w...}, author = {Kybernetik, F��r B. and Smola, Alexander and Sch\"{o}lkopf, Bernhard and Smola, Er and M\"{u}ller, Klaus-Robert and Bottou, L. and Burges, C. and Bulthoff, H. and Gegenfurtner, K. and Haffner, P.}, citeulike-article-id = {3840257}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.8911}, keywords = {eigen, kernel, pca}, posted-at = {2009-09-27 20:00:56}, priority = {5}, title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.8911}, year = {1998} }

TY - ELEC ID - scholkopf-smola-1998 L3 - citeulike-article-id:3840257 N2 - We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in high--dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5--pixel products in 16\Theta16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition. AS and KRM are with GMD First (Forschungszentrum Informationstechnik), Rudower Chaussee 5, 12489 Berlin. AS and BS were supported by grants from the Studienstiftung des deutschen Volkes. BS thanks the GMD First for hospitality during two visits. AS and BS thank V. Vapnik for introducing them to kernel representations of dot products during joint work on Support Vector machines. This work profited from discussions w... TI - Nonlinear Component Analysis as a Kernel Eigenvalue Problem KW - eigen KW - kernel KW - pca AU - Kybernetik, F��r AU - Smola, Alexander AU - Schölkopf, Bernhard AU - Smola, Er AU - Müller, Klaus-Robert AU - Bottou, L AU - Burges, C AU - Bulthoff, H AU - Gegenfurtner, K AU - Haffner, P PY - 1998/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.8911 ER -