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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… (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 eeciently compute principal components in highh dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible dpixel products in images. We give the derivation… (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)

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

- Gunnar Rätsch, Takashi Onoda, Klaus-Robert Müller
- Machine Learning
- 2001

Recently ensemble methods like ADABOOST have been applied successfully in many problems, while seemingly defying the problems of overfitting. ADABOOST rarely overfits in the low noise regime, however, we show that it clearly does so for higher noise levels. Central to the understanding of this fact is the margin distribution. ADABOOST can be viewed as a… (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)

- 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)

- Andreas Ziehe, Pavel Laskov, Guido Nolte, Klaus-Robert Müller
- Journal of Machine Learning Research
- 2004

A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses di-agonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the… (More)

- Benjamin Blankertz, Klaus-Robert Müller, +9 authors Niels Birbaumer
- IEEE Trans. Biomed. Engineering
- 2004

Interest in developing a new method of man-to-machine communication--a brain-computer interface (BCI)--has grown steadily over the past few decades. BCIs create a new communication channel between the brain and an output device by bypassing conventional motor output pathways of nerves and muscles. These systems use signals recorded from the scalp, the… (More)