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- Bernhard Schölkopf, Alexander J. Smola, Klaus-Robert Müller
- Neural Computation
- 1998

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… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you… (More)

A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can e ciently compute principal components in high{ dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible d{pixel products in images. We give the derivation… (More)

- Klaus-Robert Müller, Sebastian Mika, Gunnar Rätsch, Koji Tsuda, Bernhard Schölkopf
- IEEE Trans. Neural Networks
- 2001

This paper provides an introduction to support vector machines, kernel Fisher discriminant analysis, and kernel principal component analysis, as examples for successful kernel-based learning methods. We first give a short background about Vapnik-Chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and… (More)

- Bernhard Schölkopf, Sebastian Mika, +4 authors Alexander J. Smola
- IEEE Trans. Neural Networks
- 1999

This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods.… (More)

Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in… (More)

- Benjamin Blankertz, Klaus-Robert Müller, +7 authors Niels Birbaumer
- IEEE transactions on neural systems and…
- 2006

A brain-computer interface (BCI) is a system that allows its users to control external devices with brain activity. Although the proof-of-concept was given decades ago, the reliable translation of user intent into device control commands is still a major challenge. Success requires the effective interaction of two adaptive controllers: the user's brain,… (More)

- Yann LeCun, Léon Bottou, Genevieve B. Orr, Klaus-Robert Müller
- Neural Networks: Tricks of the Trade
- 2012

- Guido Dornhege, Benjamin Blankertz, Gabriel Curio, Klaus-Robert Müller
- IEEE Trans. Biomed. Engineering
- 2004

Noninvasive electroencephalogram (EEG) recordings provide for easy and safe access to human neocortical processes which can be exploited for a brain-computer interface (BCI). At present, however, the use of BCIs is severely limited by low bit-transfer rates. We systematically analyze and develop two recent concepts, both capable of enhancing the information… (More)

- Benjamin Blankertz, Steven Lemm, Matthias Sebastian Treder, Stefan Haufe, Klaus-Robert Müller
- NeuroImage
- 2011

Analyzing brain states that correspond to event related potentials (ERPs) on a single trial basis is a hard problem due to the high trial-to-trial variability and the unfavorable ratio between signal (ERP) and noise (artifacts and neural background activity). In this tutorial, we provide a comprehensive framework for decoding ERPs, elaborating on linear… (More)