Nonlinear Component Analysis as a Kernel Eigenvalue Problem
1996
Technical Report
ei
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 x 16 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.
Author(s): | Schölkopf, B. and Smola, AJ. and Müller, K-R. |
Number (issue): | 44 |
Year: | 1996 |
Month: | December |
Day: | 0 |
Department(s): | Empirical Inference |
Bibtex Type: | Technical Report (techreport) |
Institution: | Max Planck Institute for Biological Cybernetics Tübingen |
Digital: | 0 |
Note: | This technical report has also been <a href="/main/publication.php?machwas=view_e&edit_lfnr=730">published elsewhere</a> |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
BibTex @techreport{1509, title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem}, author = {Sch{\"o}lkopf, B. and Smola, AJ. and M{\"u}ller, K-R.}, number = {44}, organization = {Max-Planck-Gesellschaft}, institution = {Max Planck Institute for Biological Cybernetics Tübingen}, school = {Biologische Kybernetik}, month = dec, year = {1996}, note = {This technical report has also been <a href="/main/publication.php?machwas=view_e&edit_lfnr=730">published elsewhere</a>}, doi = {}, month_numeric = {12} } |