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2000


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The Kernel Trick for Distances

Schölkopf, B.

(MSR-TR-2000-51), Microsoft Research, Redmond, WA, USA, 2000 (techreport)

Abstract
A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as normbased distances in Hilbert spaces. It turns out that common kernel algorithms, such as SVMs and kernel PCA, are actually really distance based algorithms and can be run with that class of kernels, too. As well as providing a useful new insight into how these algorithms work, the present work can form the basis for conceiving new algorithms.

PDF Web [BibTex]

2000

PDF Web [BibTex]


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Kernel method for percentile feature extraction

Schölkopf, B., Platt, J., Smola, A.

(MSR-TR-2000-22), Microsoft Research, 2000 (techreport)

Abstract
A method is proposed which computes a direction in a dataset such that a speci􏰘ed fraction of a particular class of all examples is separated from the overall mean by a maximal margin􏰤 The pro jector onto that direction can be used for class􏰣speci􏰘c feature extraction􏰤 The algorithm is carried out in a feature space associated with a support vector kernel function􏰢 hence it can be used to construct a large class of nonlinear fea􏰣 ture extractors􏰤 In the particular case where there exists only one class􏰢 the method can be thought of as a robust form of principal component analysis􏰢 where instead of variance we maximize percentile thresholds􏰤 Fi􏰣 nally􏰢 we generalize it to also include the possibility of specifying negative examples􏰤

PDF [BibTex]

PDF [BibTex]

1999


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Estimating the support of a high-dimensional distribution

Schölkopf, B., Platt, J., Shawe-Taylor, J., Smola, A., Williamson, R.

(MSR-TR-99-87), Microsoft Research, 1999 (techreport)

Web [BibTex]

1999

Web [BibTex]


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Generalization Bounds via Eigenvalues of the Gram matrix

Schölkopf, B., Shawe-Taylor, J., Smola, A., Williamson, R.

(99-035), NeuroCOLT, 1999 (techreport)

[BibTex]

[BibTex]


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Sparse kernel feature analysis

Smola, A., Mangasarian, O., Schölkopf, B.

(99-04), Data Mining Institute, 1999, 24th Annual Conference of Gesellschaft f{\"u}r Klassifikation, University of Passau (techreport)

PostScript [BibTex]

PostScript [BibTex]

1996


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The DELVE user manual

Rasmussen, CE., Neal, RM., Hinton, GE., van Camp, D., Revow, M., Ghahramani, Z., Kustra, R., Tibshirani, R.

Department of Computer Science, University of Toronto, December 1996 (techreport)

Abstract
This manual describes the preliminary release of the DELVE environment. Some features described here have not yet implemented, as noted. Support for regression tasks is presently somewhat more developed than that for classification tasks. We recommend that you exercise caution when using this version of DELVE for real work, as it is possible that bugs remain in the software. We hope that you will send us reports of any problems you encounter, as well as any other comments you may have on the software or manual, at the e-mail address below. Please mention the version number of the manual and/or the software with any comments you send.

GZIP [BibTex]

1996

GZIP [BibTex]


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Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Schölkopf, B., Smola, A., Müller, K.

(44), Max Planck Institute for Biological Cybernetics Tübingen, December 1996, This technical report has also been published elsewhere (techreport)

Abstract
We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we 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 5-pixel products in 16 x 16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.

[BibTex]

[BibTex]


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Learning View Graphs for Robot Navigation

Franz, M., Schölkopf, B., Georg, P., Mallot, H., Bülthoff, H.

(33), Max Planck Institute for Biological Cybernetics, Tübingen,, July 1996 (techreport)

Abstract
We present a purely vision-based scheme for learning a parsimonious representation of an open environment. Using simple exploration behaviours, our system constructs a graph of appropriately chosen views. To navigate between views connected in the graph, we employ a homing strategy inspired by findings of insect ethology. Simulations and robot experiments demonstrate the feasibility of the proposed approach.

[BibTex]

[BibTex]

1994


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View-based cognitive mapping and path planning

Schölkopf, B., Mallot, H.

(7), Max Planck Institute for Biological Cybernetics Tübingen, November 1994, This technical report has also been published elsewhere (techreport)

Abstract
We present a scheme for learning a cognitive map of a maze from a sequence of views and movement decisions. The scheme is based on an intermediate representation called the view graph. We show that this representation carries sufficient information to reconstruct the topological and directional structure of the maze. Moreover, we present a neural network that learns the view graph during a random exploration of the maze. We use a unsupervised competitive learning rule which translates temporal sequence (rather than similarity) of views into connectedness in the network. The network uses its knowledge of the topological and directional structure of the maze to generate expectations about which views are likely to be perceived next, improving the view recognition performance. We provide an additional mechanism which uses the map to find paths between arbitrary points of the previously explored environment. The results are compared to findings of behavioural neuroscience.

[BibTex]

1994

[BibTex]