# B. Schölkopf

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- Publications
- Influence

Nonlinear Component Analysis as a Kernel Eigenvalue Problem

- B. Schölkopf, Alex Smola, K. Müller
- Mathematics, Computer Science
- Neural Computation
- 1 July 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… Expand

A tutorial on support vector regression

- Alex Smola, B. Schölkopf
- Computer Science
- Stat. Comput.
- 1 August 2004

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV… Expand

Estimating the Support of a High-Dimensional Distribution

- B. Schölkopf, John C. Platt, J. Shawe-Taylor, Alex Smola, R. Williamson
- Medicine, Computer Science
- Neural Computation
- 1 July 2001

Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a simple subset S of input space such that the probability that a test point drawn… Expand

Learning with Local and Global Consistency

- Dengyong Zhou, O. Bousquet, T. N. Lal, J. Weston, B. Schölkopf
- Computer Science
- NIPS
- 9 December 2003

We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised… Expand

A Kernel Two-Sample Test

- A. Gretton, K. Borgwardt, Malte J. Rasch, B. Schölkopf, Alex Smola
- Computer Science, Mathematics
- J. Mach. Learn. Res.
- 1 March 2012

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is… Expand

A Kernel Method for the Two-Sample-Problem

- A. Gretton, K. Borgwardt, Malte J. Rasch, B. Schölkopf, Alex Smola
- Computer Science, Mathematics
- NIPS
- 4 December 2006

We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a… Expand

A gene expression map of Arabidopsis thaliana development

- M. Schmid, T. S. Davison, +6 authors J. Lohmann
- Medicine, Biology
- Nature Genetics
- 3 April 2005

Regulatory regions of plant genes tend to be more compact than those of animal genes, but the complement of transcription factors encoded in plant genomes is as large or larger than that found in… Expand

Kernel Principal Component Analysis

- B. Schölkopf, Alex Smola, K. Müller
- Computer Science
- ICANN
- 8 October 1997

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… Expand

New Support Vector Algorithms

- B. Schölkopf, Alex Smola, R. Williamson, Peter L. Bartlett
- Computer Science, Medicine
- Neural Computation
- 1 May 2000

We propose a new class of support vector algorithms for regression and classification. In these algorithms, a parameter lets one effectively control the number of support vectors. While this can be… Expand

Measuring Statistical Dependence with Hilbert-Schmidt Norms

- A. Gretton, O. Bousquet, Alex Smola, B. Schölkopf
- Computer Science, Mathematics
- ALT
- 8 October 2005

We propose an independence criterion based on the eigen-spectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm… Expand