Monthly
288 pp. per issue, 6 x 9,
illustrated
Founded: 1989
ISSN 0899-7667
E-ISSN 1530-888X
2008 ISI Impact Factor: 2.378
|
July 1, 1998, Vol. 10, No. 5, Pages 1299-1319
Posted Online March 13, 2006.
(doi:10.1162/089976698300017467)
© 1998 Massachusetts Institute of Technology
Nonlinear Component Analysis as a Kernel Eigenvalue Problem Bernhard SchölkopfMax-Planck-Institut für biologische Kybernetik, 72076 Tübingen, Germany Alexander SmolaGMD First (Forschungszentrum Informationstechnik), 12489 Berlin, Germany Klaus-Robert MüllerGMD First (Forschungszentrum Informationstechnik), 12489 Berlin, Germany A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one 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 five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition. Cited byAntónio R. C. Paiva, Il Park, José C. Príncipe. (2009) A Reproducing Kernel Hilbert Space Framework for Spike Train Signal Processing. Neural Computation 21:2, 424-449 Online publication date: 1-Feb-2009. Abstract
| Full Text
| PDF (254 KB)
| PDF Plus (214 KB) Kai Zhang, James T. Kwok. (2009) Density-Weighted Nyström Method for Computing Large Kernel Eigensystems. Neural Computation 21:1, 121-146 Online publication date: 1-Jan-2009. Abstract
| Full Text
| PDF (1152 KB)
| PDF Plus (782 KB) Dit-Yan Yeung, Hong Chang, Guang Dai. (2008) A Scalable Kernel-Based Semisupervised Metric Learning Algorithm with Out-of-Sample Generalization Ability. Neural Computation 20:11, 2839-2861 Online publication date: 1-Nov-2008. Abstract
| PDF (825 KB)
| PDF Plus (251 KB) Knut Bernhardt. (2008) Finding Alternatives and Reduced Formulations for Process-Based Models. Evolutionary Computation 16:1, 63-88 Online publication date: 1-Mar-2008. Abstract
| PDF (690 KB)
| PDF Plus (366 KB) Geert Gins, Ilse Y. Smets, Jan F. Van Impe. (2008) Efficient Tracking of the Dominant Eigenspace of a Normalized Kernel Matrix. Neural Computation 20:2, 523-554 Online publication date: 1-Feb-2008. Abstract
| PDF (547 KB)
| PDF Plus (389 KB) Ping Zhong, Masao Fukushima. (2007) Second-Order Cone Programming Formulations for Robust Multiclass Classification. Neural Computation 19:1, 258-282 Online publication date: 1-Jan-2007. Abstract
| PDF (155 KB)
| PDF Plus (161 KB) Yoshua Bengio, Martin Monperrus, Hugo Larochelle. (2006) Nonlocal Estimation of Manifold Structure. Neural Computation 18:10, 2509-2528 Online publication date: 1-Oct-2006. Abstract
| PDF (212 KB)
| PDF Plus (278 KB) Yoshikazu Washizawa, Yukihiko Yamashita. (2006) Kernel Projection Classifiers with Suppressing Features of Other Classes. Neural Computation 18:8, 1932-1950 Online publication date: 1-Aug-2006. Abstract
| PDF (153 KB)
| PDF Plus (151 KB) Pietro Berkes, Laurenz Wiskott. (2006) On the Analysis and Interpretation of Inhomogeneous Quadratic Forms as Receptive Fields. Neural Computation 18:8, 1868-1895 Online publication date: 1-Aug-2006. Abstract
| PDF (356 KB)
| PDF Plus (356 KB) Wenming Zheng. (2006) Class-Incremental Generalized Discriminant Analysis. Neural Computation 18:4, 979-1006 Online publication date: 1-Apr-2006. Abstract
| PDF (1607 KB)
| PDF Plus (1616 KB) Qing Song. (2005) A Robust Information Clustering Algorithm. Neural Computation 17:12, 2672-2698 Online publication date: 1-Dec-2005. Abstract
| PDF (306 KB)
| PDF Plus (509 KB) Yoshua Bengio, Olivier Delalleau, Nicolas Le Roux, Jean-François Paiement, Pascal Vincent, Marie Ouimet. (2004) Learning Eigenfunctions Links Spectral Embedding and Kernel PCA. Neural Computation 16:10, 2197-2219 Online publication date: 1-Oct-2004. Abstract
| PDF (149 KB)
| PDF Plus (175 KB) Wenming Zheng, Li Zhao, Cairong Zou. (2004) A Modified Algorithm for Generalized Discriminant Analysis. Neural Computation 16:6, 1283-1297 Online publication date: 1-Jun-2004. Abstract
| PDF (249 KB)
| PDF Plus (275 KB) Mikhail Belkin, Partha Niyogi. (2003) Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation 15:6, 1373-1396 Online publication date: 1-Jun-2003. Abstract
| PDF (782 KB)
| PDF Plus (810 KB) Guilherme de A. Barreto, Aluizio F. R. Araújo, Stefan C. Kremer. (2003) A Taxonomy for Spatiotemporal Connectionist Networks Revisited: The Unsupervised Case. Neural Computation 15:6, 1255-1320 Online publication date: 1-Jun-2003. Abstract
| PDF (412 KB)
| PDF Plus (470 KB) Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, Klaus-Robert Müller. (2003) Kernel-Based Nonlinear Blind Source Separation. Neural Computation 15:5, 1089-1124 Online publication date: 1-May-2003. Abstract
| PDF (8645 KB)
| PDF Plus (8670 KB) T. Van Gestel, J. A. K. Suykens, G. Lanckriet, A. Lambrechts, B. De Moor, J. Vandewalle. (2002) Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis. Neural Computation 14:5, 1115-1147 Online publication date: 1-May-2002. Abstract
| PDF (406 KB)
| PDF Plus (435 KB) Mark Girolami. (2002) Orthogonal Series Density Estimation and the Kernel Eigenvalue Problem. Neural Computation 14:3, 669-688 Online publication date: 1-Mar-2002. Abstract
| PDF (4083 KB)
| PDF Plus (4110 KB) Roman Rosipal, Mark Girolami. (2001) An Expectation-Maximization Approach to Nonlinear Component Analysis. Neural Computation 13:3, 505-510 Online publication date: 1-Mar-2001. Abstract
| PDF (179 KB)
| PDF Plus (192 KB) G. Baudat, F. Anouar. (2000) Generalized Discriminant Analysis Using a Kernel Approach. Neural Computation 12:10, 2385-2404 Online publication date: 1-Oct-2000. Abstract
| PDF (1032 KB)
| PDF Plus (324 KB) Bernhard Schölkopf, Alex J. Smola, Robert C. Williamson, Peter L. Bartlett. (2000) New Support Vector Algorithms. Neural Computation 12:5, 1207-1245 Online publication date: 1-May-2000. Abstract
| PDF (1169 KB)
| PDF Plus (392 KB) |
RSS (TOC Alert)
PDF