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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)

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 learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled… (More)

- Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alexander J. Smola, Robert C. Williamson
- Neural Computation
- 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 from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f… (More)

- Alexander J. Smola, Bernhard Schölkopf
- Statistics and Computing
- 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 machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications… (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)

- Markus Schmid, Timothy Davison, +6 authors Jan U Lohmann
- Nature genetics
- 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 those of animals. Plants therefore provide an opportunity to study how transcriptional programs control multicellular development. We analyzed global gene… (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)

- Bernhard Schölkopf, Alexander J. Smola, Robert C. Williamson, Peter L. Bartlett
- Neural Computation
- 2000

We describe a new class of Support Vector algorithms for regression and classi cation In these algorithms a parameter lets one e ectively con trol the number of Support Vectors While this can be useful in its own right the parametrization has the additional bene t of enabling us to eliminate one of the other free parameters of the algorithm the accuracy… (More)

- Sören Sonnenburg, Gunnar Rätsch, Christin Schäfer, Bernhard Schölkopf
- Journal of Machine Learning Research
- 2006

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear… (More)

We consider the scenario where training and test data are drawn from different distributions, commonly referred to as sample selection bias. Most algorithms for this setting try to first recover sampling distributions and then make appropriate corrections based on the distribution estimate. We present a nonparametric method which directly produces… (More)