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153 results (View BibTeX file of all listed publications)

2003

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Support Vector Channel Selection in BCI

Lal, T., Schröder, M., Hinterberger, T., Weston, J., Bogdan, M., Birbaumer, N., Schölkopf, B.

(120), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, December 2003 (techreport)

Abstract
Designing a Brain Computer Interface (BCI) system one can choose from a variety of features that may be useful for classifying brain activity during a mental task. For the special case of classifying EEG signals we propose the usage of the state of the art feature selection algorithms Recursive Feature Elimination [3] and Zero-Norm Optimization [13] which are based on the training of Support Vector Machines (SVM) [11]. These algorithms can provide more accurate solutions than standard filter methods for feature selection [14]. We adapt the methods for the purpose of selecting EEG channels. For a motor imagery paradigm we show that the number of used channels can be reduced significantly without increasing the classification error. The resulting best channels agree well with the expected underlying cortical activity patterns during the mental tasks. Furthermore we show how time dependent task specific information can be visualized.

ei

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2003

ei Lal, T., Schröder, M., Hinterberger, T., Weston, J., Bogdan, M., Birbaumer, N., Schölkopf, B. Support Vector Channel Selection in BCI (120), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, December 2003 (techreport)

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Texture and haptic cues in slant discrimination: Measuring the effect of texture type on cue combination

Rosas, P., Wichmann, F., Ernst, M., Wagemans, J.

Journal of Vision, 3(12):26, 2003 Fall Vision Meeting of the Optical Society of America, December 2003 (poster)

Abstract
In a number of models of depth cue combination the depth percept is constructed via a weighted average combination of independent depth estimations. The influence of each cue in such average depends on the reliability of the source of information. (Young, Landy, & Maloney, 1993; Ernst & Banks, 2002.) In particular, Ernst & Banks (2002) formulate the combination performed by the human brain as that of the minimum variance unbiased estimator that can be constructed from the available cues. Using slant discrimination and slant judgment via probe adjustment as tasks, we have observed systematic differences in performance of human observers when a number of different types of textures were used as cue to slant (Rosas, Wichmann & Wagemans, 2003). If the depth percept behaves as described above, our measurements of the slopes of the psychometric functions provide the predicted weights for the texture cue for the ranked texture types. We have combined these texture types with object motion but the obtained results are difficult to reconcile with the unbiased minimum variance estimator model (Rosas & Wagemans, 2003). This apparent failure of such model might be explained by the existence of a coupling of texture and motion, violating the assumption of independence of cues. Hillis, Ernst, Banks, & Landy (2002) have shown that while for between-modality combination the human visual system has access to the single-cue information, for within-modality combination (visual cues: disparity and texture) the single-cue information is lost, suggesting a coupling between these cues. Then, in the present study we combine the different texture types with haptic information in a slant discrimination task, to test whether in the between-modality condition the texture cue and the haptic cue to slant are combined as predicted by an unbiased, minimum variance estimator model.

ei

Web DOI [BibTex]

ei Rosas, P., Wichmann, F., Ernst, M., Wagemans, J. Texture and haptic cues in slant discrimination: Measuring the effect of texture type on cue combination Journal of Vision, 3(12):26, 2003 Fall Vision Meeting of the Optical Society of America, December 2003 (poster)

Web DOI [BibTex]

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Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

Bousquet, O.

Stochastic Inequalities and Applications, 56, pages: 213-247, Progress in Probability, (Editors: Giné, E., C. Houdré and D. Nualart), November 2003 (article)

Abstract
We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.

ei

PostScript [BibTex]

ei Bousquet, O. Concentration Inequalities for Sub-Additive Functions Using the Entropy Method Stochastic Inequalities and Applications, 56, pages: 213-247, Progress in Probability, (Editors: Giné, E., C. Houdré and D. Nualart), November 2003 (article)

PostScript [BibTex]

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Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), LNCS Vol. 2777

Schölkopf, B., Warmuth, M.

Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), COLT/Kernel 2003, pages: 746, Springer, Berlin, Germany, 16th Annual Conference on Learning Theory and 7th Kernel Workshop, November 2003, Lecture Notes in Computer Science ; 2777 (proceedings)

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DOI [BibTex]

ei Schölkopf, B., Warmuth, M. Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), LNCS Vol. 2777 Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop (COLT/Kernel 2003), COLT/Kernel 2003, pages: 746, Springer, Berlin, Germany, 16th Annual Conference on Learning Theory and 7th Kernel Workshop, November 2003, Lecture Notes in Computer Science ; 2777 (proceedings)

DOI [BibTex]

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On the Complexity of Learning the Kernel Matrix

Bousquet, O., Herrmann, D.

In Advances in Neural Information Processing Systems 15, pages: 399-406, (Editors: Becker, S. , S. Thrun, K. Obermayer), The MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

Abstract
We investigate data based procedures for selecting the kernel when learning with Support Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a logarithmic factor bigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting. We thus propose a suitable way of constraining the class. We use an efficient algorithm to solve the resulting optimization problem, present preliminary experimental results, and compare them to an alignment-based approach.

ei

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ei Bousquet, O., Herrmann, D. On the Complexity of Learning the Kernel Matrix In Advances in Neural Information Processing Systems 15, pages: 399-406, (Editors: Becker, S. , S. Thrun, K. Obermayer), The MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

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Image Reconstruction by Linear Programming

Tsuda, K., Rätsch, G.

(118), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, October 2003 (techreport)

ei

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ei Tsuda, K., Rätsch, G. Image Reconstruction by Linear Programming (118), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, October 2003 (techreport)

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Cluster Kernels for Semi-Supervised Learning

Chapelle, O., Weston, J., Schölkopf, B.

In Advances in Neural Information Processing Systems 15, pages: 585-592, (Editors: S Becker and S Thrun and K Obermayer), MIT Press, Cambridge, MA, USA, 16th Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

Abstract
We propose a framework to incorporate unlabeled data in kernel classifier, based on the idea that two points in the same cluster are more likely to have the same label. This is achieved by modifying the eigenspectrum of the kernel matrix. Experimental results assess the validity of this approach.

ei

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ei Chapelle, O., Weston, J., Schölkopf, B. Cluster Kernels for Semi-Supervised Learning In Advances in Neural Information Processing Systems 15, pages: 585-592, (Editors: S Becker and S Thrun and K Obermayer), MIT Press, Cambridge, MA, USA, 16th Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

PDF Web [BibTex]

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Mismatch String Kernels for SVM Protein Classification

Leslie, C., Eskin, E., Weston, J., Noble, W.

In Advances in Neural Information Processing Systems 15, pages: 1417-1424, (Editors: Becker, S. , S. Thrun, K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

Abstract
We introduce a class of string kernels, called mismatch kernels, for use with support vector machines (SVMs) in a discriminative approach to the protein classification problem. These kernels measure sequence similarity based on shared occurrences of k-length subsequences, counted with up to m mismatches, and do not rely on any generative model for the positive training sequences. We compute the kernels efficiently using a mismatch tree data structure and report experiments on a benchmark SCOP dataset, where we show that the mismatch kernel used with an SVM classifier performs as well as the Fisher kernel, the most successful method for remote homology detection, while achieving considerable computational savings.

ei

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ei Leslie, C., Eskin, E., Weston, J., Noble, W. Mismatch String Kernels for SVM Protein Classification In Advances in Neural Information Processing Systems 15, pages: 1417-1424, (Editors: Becker, S. , S. Thrun, K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

PDF Web [BibTex]

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Real-Time Face Detection

Kienzle, W.

Biologische Kybernetik, Eberhard-Karls-Universitaet Tuebingen, Tuebingen, Germany, October 2003 (diplomathesis)

ei

[BibTex]

ei Kienzle, W. Real-Time Face Detection Biologische Kybernetik, Eberhard-Karls-Universitaet Tuebingen, Tuebingen, Germany, October 2003 (diplomathesis)

[BibTex]

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Kernel Dependency Estimation

Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V.

In Advances in Neural Information Processing Systems 15, pages: 873-880, (Editors: S Becker and S Thrun and K Obermayer), MIT Press, Cambridge, MA, USA, 16th Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

ei

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ei Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V. Kernel Dependency Estimation In Advances in Neural Information Processing Systems 15, pages: 873-880, (Editors: S Becker and S Thrun and K Obermayer), MIT Press, Cambridge, MA, USA, 16th Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

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Linear Combinations of Optic Flow Vectors for Estimating Self-Motion: a Real-World Test of a Neural Model

Franz, MO., Chahl, JS.

In Advances in Neural Information Processing Systems 15, pages: 1319-1326, (Editors: Becker, S., S. Thrun and K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

Abstract
The tangential neurons in the fly brain are sensitive to the typical optic flow patterns generated during self-motion. In this study, we examine whether a simplified linear model of these neurons can be used to estimate self-motion from the optic flow. We present a theory for the construction of an estimator consisting of a linear combination of optic flow vectors that incorporates prior knowledge both about the distance distribution of the environment, and about the noise and self-motion statistics of the sensor. The estimator is tested on a gantry carrying an omnidirectional vision sensor. The experiments show that the proposed approach leads to accurate and robust estimates of rotation rates, whereas translation estimates turn out to be less reliable.

ei

PDF Web [BibTex]

ei Franz, MO., Chahl, JS. Linear Combinations of Optic Flow Vectors for Estimating Self-Motion: a Real-World Test of a Neural Model In Advances in Neural Information Processing Systems 15, pages: 1319-1326, (Editors: Becker, S., S. Thrun and K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

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Clustering with the Fisher score

Tsuda, K., Kawanabe, M., Müller, K.

In Advances in Neural Information Processing Systems 15, pages: 729-736, (Editors: Becker, S. , S. Thrun, K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

Abstract
Recently the Fisher score (or the Fisher kernel) is increasingly used as a feature extractor for classification problems. The Fisher score is a vector of parameter derivatives of loglikelihood of a probabilistic model. This paper gives a theoretical analysis about how class information is preserved in the space of the Fisher score, which turns out that the Fisher score consists of a few important dimensions with class information and many nuisance dimensions. When we perform clustering with the Fisher score, K-Means type methods are obviously inappropriate because they make use of all dimensions. So we will develop a novel but simple clustering algorithm specialized for the Fisher score, which can exploit important dimensions. This algorithm is successfully tested in experiments with artificial data and real data (amino acid sequences).

ei

PDF Web [BibTex]

ei Tsuda, K., Kawanabe, M., Müller, K. Clustering with the Fisher score In Advances in Neural Information Processing Systems 15, pages: 729-736, (Editors: Becker, S. , S. Thrun, K. Obermayer), MIT Press, Cambridge, MA, USA, Sixteenth Annual Conference on Neural Information Processing Systems (NIPS), October 2003 (inproceedings)

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Marginalized Kernels between Labeled Graphs

Kashima, H., Tsuda, K., Inokuchi, A.

In 20th International Conference on Machine Learning, pages: 321-328, (Editors: Faucett, T. and N. Mishra), 20th International Conference on Machine Learning, August 2003 (inproceedings)

ei

PDF [BibTex]

ei Kashima, H., Tsuda, K., Inokuchi, A. Marginalized Kernels between Labeled Graphs In 20th International Conference on Machine Learning, pages: 321-328, (Editors: Faucett, T. and N. Mishra), 20th International Conference on Machine Learning, August 2003 (inproceedings)

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Sparse Gaussian Processes: inference, subspace identification and model selection

Csato, L., Opper, M.

In Proceedings, pages: 1-6, (Editors: Van der Hof, , Wahlberg), The Netherlands, 13th IFAC Symposium on System Identifiaction, August 2003, electronical version; Index ThA02-2 (inproceedings)

Abstract
Gaussian Process (GP) inference is a probabilistic kernel method where the GP is treated as a latent function. The inference is carried out using the Bayesian online learning and its extension to the more general iterative approach which we call TAP/EP learning. Sparsity is introduced in this context to make the TAP/EP method applicable to large datasets. We address the prohibitive scaling of the number of parameters by defining a subset of the training data that is used as the support the GP, thus the number of required parameters is independent of the training set, similar to the case of ``Support--‘‘ or ``Relevance--Vectors‘‘. An advantage of the full probabilistic treatment is that allows the computation of the marginal data likelihood or evidence, leading to hyper-parameter estimation within the GP inference. An EM algorithm to choose the hyper-parameters is proposed. The TAP/EP learning is the E-step and the M-step then updates the hyper-parameters. Due to the sparse E-step the resulting algorithm does not involve manipulation of large matrices. The presented algorithm is applicable to a wide variety of likelihood functions. We present results of applying the algorithm on classification and nonstandard regression problems for artificial and real datasets.

ei

PDF GZIP [BibTex]

ei Csato, L., Opper, M. Sparse Gaussian Processes: inference, subspace identification and model selection In Proceedings, pages: 1-6, (Editors: Van der Hof, , Wahlberg), The Netherlands, 13th IFAC Symposium on System Identifiaction, August 2003, electronical version; Index ThA02-2 (inproceedings)

PDF GZIP [BibTex]

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Adaptive, Cautious, Predictive control with Gaussian Process Priors

Murray-Smith, R., Sbarbaro, D., Rasmussen, CE., Girard, A.

In Proceedings of the 13th IFAC Symposium on System Identification, pages: 1195-1200, (Editors: Van den Hof, P., B. Wahlberg and S. Weiland), Proceedings of the 13th IFAC Symposium on System Identification, August 2003 (inproceedings)

Abstract
Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example.

ei

PDF [BibTex]

ei Murray-Smith, R., Sbarbaro, D., Rasmussen, CE., Girard, A. Adaptive, Cautious, Predictive control with Gaussian Process Priors In Proceedings of the 13th IFAC Symposium on System Identification, pages: 1195-1200, (Editors: Van den Hof, P., B. Wahlberg and S. Weiland), Proceedings of the 13th IFAC Symposium on System Identification, August 2003 (inproceedings)

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Statistical Learning Theory

Bousquet, O.

Machine Learning Summer School, August 2003 (talk)

ei

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ei Bousquet, O. Statistical Learning Theory Machine Learning Summer School, August 2003 (talk)

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Remarks on Statistical Learning Theory

Bousquet, O.

Machine Learning Summer School, August 2003 (talk)

ei

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ei Bousquet, O. Remarks on Statistical Learning Theory Machine Learning Summer School, August 2003 (talk)

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On the Representation, Learning and Transfer of Spatio-Temporal Movement Characteristics

Ilg, W., Bakir, GH., Mezger, J., Giese, MA.

In Humanoids Proceedings, pages: 0-0, Humanoids Proceedings, July 2003, electronical version (inproceedings)

Abstract
In this paper we present a learning-based approach for the modelling of complex movement sequences. Based on the method of Spatio-Temporal Morphable Models (STMMS. We derive a hierarchical algorithm that, in a first step, identifies automatically movement elements in movement sequences based on a coarse spatio-temporal description, and in a second step models these movement primitives by approximation through linear combinations of learned example movement trajectories. We describe the different steps of the algorithm and show how it can be applied for modelling and synthesis of complex sequences of human movements that contain movement elements with variable style. The proposed method is demonstrated on different applications of movement representation relevant for imitation learning of movement styles in humanoid robotics.

ei

PDF [BibTex]

ei Ilg, W., Bakir, GH., Mezger, J., Giese, MA. On the Representation, Learning and Transfer of Spatio-Temporal Movement Characteristics In Humanoids Proceedings, pages: 0-0, Humanoids Proceedings, July 2003, electronical version (inproceedings)

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Statistical Learning Theory, Capacity and Complexity

Schölkopf, B.

Complexity, 8(4):87-94, July 2003 (article)

Abstract
We give an exposition of the ideas of statistical learning theory, followed by a discussion of how a reinterpretation of the insights of learning theory could potentially also benefit our understanding of a certain notion of complexity.

ei

Web DOI [BibTex]

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Ranking on Data Manifolds

Zhou, D., Weston, J., Gretton, A., Bousquet, O., Schölkopf, B.

(113), Max Planck Institute for Biological Cybernetics, 72076 Tuebingen, Germany, June 2003 (techreport)

Abstract
The Google search engine has had a huge success with its PageRank web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the World Wide Web using random walk. This algorithm can only be used for graph data, however. Here we propose a simple universal ranking algorithm for vectorial data, based on the exploration of the intrinsic global geometric structure revealed by a huge amount of data. Experimental results from image and text to bioinformatics illustrates the validity of our algorithm.

ei

PDF [BibTex]

ei Zhou, D., Weston, J., Gretton, A., Bousquet, O., Schölkopf, B. Ranking on Data Manifolds (113), Max Planck Institute for Biological Cybernetics, 72076 Tuebingen, Germany, June 2003 (techreport)

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Kernel Hebbian Algorithm for Iterative Kernel Principal Component Analysis

Kim, K., Franz, M., Schölkopf, B.

(109), MPI f. biologische Kybernetik, Tuebingen, June 2003 (techreport)

Abstract
A new method for performing a kernel principal component analysis is proposed. By kernelizing the generalized Hebbian algorithm, one can iteratively estimate the principal components in a reproducing kernel Hilbert space with only linear order memory complexity. The derivation of the method, a convergence proof, and preliminary applications in image hyperresolution are presented. In addition, we discuss the extension of the method to the online learning of kernel principal components.

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ei Kim, K., Franz, M., Schölkopf, B. Kernel Hebbian Algorithm for Iterative Kernel Principal Component Analysis (109), MPI f. biologische Kybernetik, Tuebingen, June 2003 (techreport)

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Learning with Local and Global Consistency

Zhou, D., Bousquet, O., Lal, T., Weston, J., Schölkopf, B.

(112), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, June 2003 (techreport)

Abstract
We consider the learning problem in the transductive setting. Given a set of points of which only some are labeled, the goal is to predict the label of the unlabeled points. A principled clue to solve such a learning problem is the consistency assumption that a classifying function should be sufficiently smooth with respect to the structure revealed by these known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.

ei

[BibTex]

ei Zhou, D., Bousquet, O., Lal, T., Weston, J., Schölkopf, B. Learning with Local and Global Consistency (112), Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, June 2003 (techreport)

[BibTex]

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Dealing with large Diagonals in Kernel Matrices

Weston, J., Schölkopf, B., Eskin, E., Leslie, C., Noble, W.

Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

Abstract
In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well: We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine, which is a common kernel approach for pattern recognition.

ei

PDF DOI [BibTex]

ei Weston, J., Schölkopf, B., Eskin, E., Leslie, C., Noble, W. Dealing with large Diagonals in Kernel Matrices Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

PDF DOI [BibTex]

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Implicit Wiener Series

Franz, M., Schölkopf, B.

(114), Max Planck Institute for Biological Cybernetics, June 2003 (techreport)

Abstract
The Wiener series is one of the standard methods to systematically characterize the nonlinearity of a neural system. The classical estimation method of the expansion coefficients via cross-correlation suffers from severe problems that prevent its application to high-dimensional and strongly nonlinear systems. We propose a new estimation method based on regression in a reproducing kernel Hilbert space that overcomes these problems. Numerical experiments show performance advantages in terms of convergence, interpretability and system size that can be handled.

ei

PDF [BibTex]

ei Franz, M., Schölkopf, B. Implicit Wiener Series (114), Max Planck Institute for Biological Cybernetics, June 2003 (techreport)

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Machine Learning approaches to protein ranking: discriminative, semi-supervised, scalable algorithms

Weston, J., Leslie, C., Elisseeff, A., Noble, W.

(111), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2003 (techreport)

Abstract
A key tool in protein function discovery is the ability to rank databases of proteins given a query amino acid sequence. The most successful method so far is a web-based tool called PSI-BLAST which uses heuristic alignment of a profile built using the large unlabeled database. It has been shown that such use of global information via an unlabeled data improves over a local measure derived from a basic pairwise alignment such as performed by PSI-BLAST's predecessor, BLAST. In this article we look at ways of leveraging techniques from the field of machine learning for the problem of ranking. We show how clustering and semi-supervised learning techniques, which aim to capture global structure in data, can significantly improve over PSI-BLAST.

ei

PDF [BibTex]

ei Weston, J., Leslie, C., Elisseeff, A., Noble, W. Machine Learning approaches to protein ranking: discriminative, semi-supervised, scalable algorithms (111), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2003 (techreport)

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The em Algorithm for Kernel Matrix Completion with Auxiliary Data

Tsuda, K., Akaho, S., Asai, K.

Journal of Machine Learning Research, 4, pages: 67-81, May 2003 (article)

ei

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ei Tsuda, K., Akaho, S., Asai, K. The em Algorithm for Kernel Matrix Completion with Auxiliary Data Journal of Machine Learning Research, 4, pages: 67-81, May 2003 (article)

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Constructing Descriptive and Discriminative Non-linear Features: Rayleigh Coefficients in Kernel Feature Spaces

Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):623-628, May 2003 (article)

Abstract
We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher‘s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

ei

DOI [BibTex]

ei Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K. Constructing Descriptive and Discriminative Non-linear Features: Rayleigh Coefficients in Kernel Feature Spaces IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):623-628, May 2003 (article)

DOI [BibTex]

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The Geometry Of Kernel Canonical Correlation Analysis

Kuss, M., Graepel, T.

(108), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2003 (techreport)

Abstract
Canonical correlation analysis (CCA) is a classical multivariate method concerned with describing linear dependencies between sets of variables. After a short exposition of the linear sample CCA problem and its analytical solution, the article proceeds with a detailed characterization of its geometry. Projection operators are used to illustrate the relations between canonical vectors and variates. The article then addresses the problem of CCA between spaces spanned by objects mapped into kernel feature spaces. An exact solution for this kernel canonical correlation (KCCA) problem is derived from a geometric point of view. It shows that the expansion coefficients of the canonical vectors in their respective feature space can be found by linear CCA in the basis induced by kernel principal component analysis. The effect of mappings into higher dimensional feature spaces is considered critically since it simplifies the CCA problem in general. Then two regularized variants of KCCA are discussed. Relations to other methods are illustrated, e.g., multicategory kernel Fisher discriminant analysis, kernel principal component regression and possible applications thereof in blind source separation.

ei

PDF [BibTex]

ei Kuss, M., Graepel, T. The Geometry Of Kernel Canonical Correlation Analysis (108), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2003 (techreport)

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A case based comparison of identification with neural network and Gaussian process models.

Kocijan, J., Banko, B., Likar, B., Girard, A., Murray-Smith, R., Rasmussen, CE.

In Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS 2003, 1, pages: 137-142, (Editors: Ruano, E.A.), Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS, April 2003 (inproceedings)

Abstract
In this paper an alternative approach to black-box identification of non-linear dynamic systems is compared with the more established approach of using artificial neural networks. The Gaussian process prior approach is a representative of non-parametric modelling approaches. It was compared on a pH process modelling case study. The purpose of modelling was to use the model for control design. The comparison revealed that even though Gaussian process models can be effectively used for modelling dynamic systems caution has to be axercised when signals are selected.

ei

PDF [BibTex]

ei Kocijan, J., Banko, B., Likar, B., Girard, A., Murray-Smith, R., Rasmussen, CE. A case based comparison of identification with neural network and Gaussian process models. In Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS 2003, 1, pages: 137-142, (Editors: Ruano, E.A.), Proceedings of the International Conference on Intelligent Control Systems and Signal Processing ICONS, April 2003 (inproceedings)

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On-Line One-Class Support Vector Machines. An Application to Signal Segmentation

Gretton, A., Desobry, ..

In IEEE ICASSP Vol. 2, pages: 709-712, IEEE ICASSP, April 2003 (inproceedings)

Abstract
In this paper, we describe an efficient algorithm to sequentially update a density support estimate obtained using one-class support vector machines. The solution provided is an exact solution, which proves to be far more computationally attractive than a batch approach. This deterministic technique is applied to the problem of audio signal segmentation, with simulations demonstrating the computational performance gain on toy data sets, and the accuracy of the segmentation on audio signals.

ei

PostScript [BibTex]

ei Gretton, A., Desobry, .. On-Line One-Class Support Vector Machines. An Application to Signal Segmentation In IEEE ICASSP Vol. 2, pages: 709-712, IEEE ICASSP, April 2003 (inproceedings)

PostScript [BibTex]

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The Kernel Mutual Information

Gretton, A., Herbrich, R., Smola, A.

Max Planck Institute for Biological Cybernetics, April 2003 (techreport)

Abstract
We introduce two new functions, the kernel covariance (KC) and the kernel mutual information (KMI), to measure the degree of independence of several continuous random variables. The former is guaranteed to be zero if and only if the random variables are pairwise independent; the latter shares this property, and is in addition an approximate upper bound on the mutual information, as measured near independence, and is based on a kernel density estimate. We show that Bach and Jordan‘s kernel generalised variance (KGV) is also an upper bound on the same kernel density estimate, but is looser. Finally, we suggest that the addition of a regularising term in the KGV causes it to approach the KMI, which motivates the introduction of this regularisation. The performance of the KC and KMI is verified in the context of instantaneous independent component analysis (ICA), by recovering both artificial and real (musical) signals following linear mixing.

ei

PostScript [BibTex]

ei Gretton, A., Herbrich, R., Smola, A. The Kernel Mutual Information Max Planck Institute for Biological Cybernetics, April 2003 (techreport)

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The Kernel Mutual Information

Gretton, A., Herbrich, R., Smola, A.

In IEEE ICASSP Vol. 4, pages: 880-883, IEEE ICASSP, April 2003 (inproceedings)

Abstract
We introduce a new contrast function, the kernel mutual information (KMI), to measure the degree of independence of continuous random variables. This contrast function provides an approximate upper bound on the mutual information, as measured near independence, and is based on a kernel density estimate of the mutual information between a discretised approximation of the continuous random variables. We show that Bach and Jordan‘s kernel generalised variance (KGV) is also an upper bound on the same kernel density estimate, but is looser. Finally, we suggest that the addition of a regularising term in the KGV causes it to approach the KMI, which motivates the introduction of this regularisation.

ei

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ei Gretton, A., Herbrich, R., Smola, A. The Kernel Mutual Information In IEEE ICASSP Vol. 4, pages: 880-883, IEEE ICASSP, April 2003 (inproceedings)

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Tractable Inference for Probabilistic Data Models

Csato, L., Opper, M., Winther, O.

Complexity, 8(4):64-68, April 2003 (article)

Abstract
We present an approximation technique for probabilistic data models with a large number of hidden variables, based on ideas from statistical physics. We give examples for two nontrivial applications. © 2003 Wiley Periodicals, Inc.

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ei Csato, L., Opper, M., Winther, O. Tractable Inference for Probabilistic Data Models Complexity, 8(4):64-68, April 2003 (article)

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Feature selection and transduction for prediction of molecular bioactivity for drug design

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B.

Bioinformatics, 19(6):764-771, April 2003 (article)

Abstract
Motivation: In drug discovery a key task is to identify characteristics that separate active (binding) compounds from inactive (non-binding) ones. An automated prediction system can help reduce resources necessary to carry out this task. Results: Two methods for prediction of molecular bioactivity for drug design are introduced and shown to perform well in a data set previously studied as part of the KDD (Knowledge Discovery and Data Mining) Cup 2001. The data is characterized by very few positive examples, a very large number of features (describing three-dimensional properties of the molecules) and rather different distributions between training and test data. Two techniques are introduced specifically to tackle these problems: a feature selection method for unbalanced data and a classifier which adapts to the distribution of the the unlabeled test data (a so-called transductive method). We show both techniques improve identification performance and in conjunction provide an improvement over using only one of the techniques. Our results suggest the importance of taking into account the characteristics in this data which may also be relevant in other problems of a similar type.

ei

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Dynamic movement primitives - A framework for motor control in humans and humanoid robots

Schaal, S.

In The International Symposium on Adaptive Motion of Animals and Machines, Kyoto, Japan, March 4-8, 2003, March 2003, clmc (inproceedings)

Abstract
Sensory-motor integration is one of the key issues in robotics. In this paper, we propose an approach to rhythmic arm movement control that is synchronized with an external signal based on exploiting a simple neural oscillator network. Trajectory generation by the neural oscillator is a biologically inspired method that can allow us to generate a smooth and continuous trajectory. The parameter tuning of the oscillators is used to generate a synchronized movement with wide intervals. We adopted the method for the drumming task as an example task. By using this method, the robot can realize synchronized drumming with wide drumming intervals in real time. The paper also shows the experimental results of drumming by a humanoid robot.

am

link (url) [BibTex]

am Schaal, S. Dynamic movement primitives - A framework for motor control in humans and humanoid robots In The International Symposium on Adaptive Motion of Animals and Machines, Kyoto, Japan, March 4-8, 2003, March 2003, clmc (inproceedings)

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Rademacher and Gaussian averages in Learning Theory

Bousquet, O.

Universite de Marne-la-Vallee, March 2003 (talk)

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ei Bousquet, O. Rademacher and Gaussian averages in Learning Theory Universite de Marne-la-Vallee, March 2003 (talk)

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Use of the Zero-Norm with Linear Models and Kernel Methods

Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M.

Journal of Machine Learning Research, 3, pages: 1439-1461, March 2003 (article)

Abstract
We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

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ei Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M. Use of the Zero-Norm with Linear Models and Kernel Methods Journal of Machine Learning Research, 3, pages: 1439-1461, March 2003 (article)

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Phase Information and the Recognition of Natural Images

Braun, D., Wichmann, F., Gegenfurtner, K.

6, pages: 138, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Fourier phase plays an important role in determining image structure. For example, when the phase spectrum of an image showing a ower is swapped with the phase spectrum of an image showing a tank, then we will usually perceive a tank in the resulting image, even though the amplitude spectrum is still that of the ower. Also, when the phases of an image are randomly swapped across frequencies, the resulting image becomes impossible to recognize. Our goal was to evaluate the e ect of phase manipulations in a more quantitative manner. On each trial subjects viewed two images of natural scenes. The subject had to indicate which one of the two images contained an animal. The spectra of the images were manipulated by adding random phase noise at each frequency. The phase noise was uniformly distributed in the interval [;+], where  was varied between 0 degree and 180 degrees. Image pairs were displayed for 100 msec. Subjects were remarkably resistant to the addition of phase noise. Even with [120; 120] degree noise, subjects still were at a level of 75% correct. The introduction of phase noise leads to a reduction of image contrast. Subjects were slightly better than a simple prediction based on this contrast reduction. However, when contrast response functions were measured in the same experimental paradigm, we found that performance in the phase noise experiment was signi cantly lower than that predicted by the corresponding contrast reduction.

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Web [BibTex]

ei Braun, D., Wichmann, F., Gegenfurtner, K. Phase Information and the Recognition of Natural Images 6, pages: 138, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

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Introduction: Robots with Cognition?

Franz, MO.

6, pages: 38, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (talk)

Abstract
Using robots as models of cognitive behaviour has a long tradition in robotics. Parallel to the historical development in cognitive science, one observes two major, subsequent waves in cognitive robotics. The first is based on ideas of classical, cognitivist Artificial Intelligence (AI). According to the AI view of cognition as rule-based symbol manipulation, these robots typically try to extract symbolic descriptions of the environment from their sensors that are used to update a common, global world representation from which, in turn, the next action of the robot is derived. The AI approach has been successful in strongly restricted and controlled environments requiring well-defined tasks, e.g. in industrial assembly lines. AI-based robots mostly failed, however, in the unpredictable and unstructured environments that have to be faced by mobile robots. This has provoked the second wave in cognitive robotics which tries to achieve cognitive behaviour as an emergent property from the interaction of simple, low-level modules. Robots of the second wave are called animats as their architecture is designed to closely model aspects of real animals. Using only simple reactive mechanisms and Hebbian-type or evolutionary learning, the resulting animats often outperformed the highly complex AI-based robots in tasks such as obstacle avoidance, corridor following etc. While successful in generating robust, insect-like behaviour, typical animats are limited to stereotyped, fixed stimulus-response associations. If one adopts the view that cognition requires a flexible, goal-dependent choice of behaviours and planning capabilities (H.A. Mallot, Kognitionswissenschaft, 1999, 40-48) then it appears that cognitive behaviour cannot emerge from a collection of purely reactive modules. It rather requires environmentally decoupled structures that work without directly engaging the actions that it is concerned with. This poses the current challenge to cognitive robotics: How can we build cognitive robots that show the robustness and the learning capabilities of animats without falling back into the representational paradigm of AI? The speakers of the symposium present their approaches to this question in the context of robot navigation and sensorimotor learning. In the first talk, Prof. Helge Ritter introduces a robot system for imitation learning capable of exploring various alternatives in simulation before actually performing a task. The second speaker, Angelo Arleo, develops a model of spatial memory in rat navigation based on his electrophysiological experiments. He validates the model on a mobile robot which, in some navigation tasks, shows a performance comparable to that of the real rat. A similar model of spatial memory is used to investigate the mechanisms of territory formation in a series of robot experiments presented by Prof. Hanspeter Mallot. In the last talk, we return to the domain of sensorimotor learning where Ralf M{\"o}ller introduces his approach to generate anticipatory behaviour by learning forward models of sensorimotor relationships.

ei

Web [BibTex]

ei Franz, MO. Introduction: Robots with Cognition? 6, pages: 38, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (talk)

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Constraints measures and reproduction of style in robot imitation learning

Bakir, GH., Ilg, W., Franz, MO., Giese, M.

6, pages: 70, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Imitation learning is frequently discussed as a method for generating complex behaviors in robots by imitating human actors. The kinematic and the dynamic properties of humans and robots are typically quite di erent, however. For this reason observed human trajectories cannot be directly transferred to robots, even if their geometry is humanoid. Instead the human trajectory must be approximated by trajectories that can be realized by the robot. During this approximation deviations from the human trajectory may arise that change the style of the executed movement. Alternatively, the style of the movement might be well reproduced, but the imitated trajectory might be suboptimal with respect to di erent constraint measures from robotics control, leading to non-robust behavior. Goal of the presented work is to quantify this trade-o between \imitation quality" and constraint compatibility for the imitation of complex writing movements. In our experiment, we used trajectory data from human writing movements (see the abstract of Ilg et al. in this volume). The human trajectories were mapped onto robot trajectories by minimizing an error measure that integrates constraints that are important for the imitation of movement style and a regularizing constraint that ensures smooth joint trajectories with low velocities. In a rst experiment, both the end-e ector position and the shoulder angle of the robot were optimized in order to achieve good imitation together with accurate control of the end-e ector position. In a second experiment only the end-e ector trajectory was imitated whereas the motion of the elbow joint was determined using the optimal inverse kinematic solution for the robot. For both conditions di erent constraint measures (dexterity and relative jointlimit distances) and a measure for imitation quality were assessed. By controling the weight of the regularization term we can vary continuously between robot behavior optimizing imitation quality, and behavior minimizing joint velocities.

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ei Bakir, GH., Ilg, W., Franz, MO., Giese, M. Constraints measures and reproduction of style in robot imitation learning 6, pages: 70, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

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Study of Human Classification using Psychophysics and Machine Learning

Graf, A., Wichmann, F., Bülthoff, H., Schölkopf, B.

6, pages: 149, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), Febuary 2003 (poster)

Abstract
We attempt to reach a better understanding of classi cation in humans using both psychophysical and machine learning techniques. In our psychophysical paradigm the stimuli presented to the human subjects are modi ed using machine learning algorithms according to their responses. Frontal views of human faces taken from a processed version of the MPI face database are employed for a gender classi cation task. The processing assures that all heads have same mean intensity, same pixel-surface area and are centered. This processing stage is followed by a smoothing of the database in order to eliminate, as much as possible, scanning artifacts. Principal Component Analysis is used to obtain a low-dimensional representation of the faces in the database. A subject is asked to classify the faces and experimental parameters such as class (i.e. female/male), con dence ratings and reaction times are recorded. A mean classi cation error of 14.5% is measured and, on average, 0.5 males are classi ed as females and 21.3females as males. The mean reaction time for the correctly classi ed faces is 1229 +- 252 [ms] whereas the incorrectly classi ed faces have a mean reaction time of 1769 +- 304 [ms] showing that the reaction times increase with the subject's classi- cation error. Reaction times are also shown to decrease with increasing con dence, both for the correct and incorrect classi cations. Classi cation errors, reaction times and con dence ratings are then correlated to concepts of machine learning such as separating hyperplane obtained when considering Support Vector Machines, Relevance Vector Machines, boosted Prototype and K-means Learners. Elements near the separating hyperplane are found to be classi ed with more errors than those away from it. In addition, the subject's con dence increases when moving away from the hyperplane. A preliminary analysis on the available small number of subjects indicates that K-means classi cation seems to re ect the subject's classi cation behavior best. The above learnersare then used to generate \special" elements, or representations, of the low-dimensional database according to the labels given by the subject. A memory experiment follows where the representations are shown together with faces seen or unseen during the classi cation experiment. This experiment aims to assess the representations by investigating whether some representations, or special elements, are classi ed as \seen before" despite that they never appeared in the classi cation experiment, possibly hinting at their use during human classi cation.

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ei Graf, A., Wichmann, F., Bülthoff, H., Schölkopf, B. Study of Human Classification using Psychophysics and Machine Learning 6, pages: 149, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), Febuary 2003 (poster)

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A Representation of Complex Movement Sequences Based on Hierarchical Spatio-Temporal Correspondence for Imitation Learning in Robotics

Ilg, W., Bakir, GH., Franz, MO., Giese, M.

6, pages: 74, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

Abstract
Imitation learning of complex movements has become a popular topic in neuroscience, as well as in robotics. A number of conceptual as well as practical problems are still unsolved. One example is the determination of the aspects of movements which are relevant for imitation. Problems concerning the movement representation are twofold: (1) The movement characteristics of observed movements have to be transferred from the perceptual level to the level of generated actions. (2) Continuous spaces of movements with variable styles have to be approximated based on a limited number of learned example sequences. Therefore, one has to use representation with a high generalisation capability. We present methods for the representation of complex movement sequences that addresses these questions in the context of the imitation learning of writing movements using a robot arm with human-like geometry. For the transfer of complex movements from perception to action we exploit a learning-based method that represents complex action sequences by linear combination of prototypical examples (Ilg and Giese, BMCV 2002). The method of hierarchical spatio-temporal morphable models (HSTMM) decomposes action sequences automatically into movement primitives. These primitives are modeled by linear combinations of a small number of learned example trajectories. The learned spatio-temporal models are suitable for the analysis and synthesis of long action sequences, which consist of movement primitives with varying style parameters. The proposed method is illustrated by imitation learning of complex writing movements. Human trajectories were recorded using a commercial motion capture system (VICON). In the rst step the recorded writing sequences are decomposed into movement primitives. These movement primitives can be analyzed and changed in style by de ning linear combinations of prototypes with di erent linear weight combinations. Our system can imitate writing movements of di erent actors, synthesize new writing styles and can even exaggerate the writing movements of individual actors. Words and writing movements of the robot look very natural, and closely match the natural styles. These preliminary results makes the proposed method promising for further applications in learning-based robotics. In this poster we focus on the acquisition of the movement representation (identi cation and segmentation of movement primitives, generation of new writing styles by spatio-temporal morphing). The transfer of the generated writing movements to the robot considering the given kinematic and dynamic constraints is discussed in Bakir et al (this volume).

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ei Ilg, W., Bakir, GH., Franz, MO., Giese, M. A Representation of Complex Movement Sequences Based on Hierarchical Spatio-Temporal Correspondence for Imitation Learning in Robotics 6, pages: 74, (Editors: H.H. Bülthoff, K.R. Gegenfurtner, H.A. Mallot, R. Ulrich, F.A. Wichmann), 6. T{\"u}binger Wahrnehmungskonferenz (TWK), February 2003 (poster)

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Hierarchical Spatio-Temporal Morphable Models for Representation of complex movements for Imitation Learning

Ilg, W., Bakir, GH., Franz, MO., Giese, M.

In 11th International Conference on Advanced Robotics, (2):453-458, (Editors: Nunes, U., A. de Almeida, A. Bejczy, K. Kosuge and J.A.T. Machado), 11th International Conference on Advanced Robotics, January 2003 (inproceedings)

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ei Ilg, W., Bakir, GH., Franz, MO., Giese, M. Hierarchical Spatio-Temporal Morphable Models for Representation of complex movements for Imitation Learning In 11th International Conference on Advanced Robotics, (2):453-458, (Editors: Nunes, U., A. de Almeida, A. Bejczy, K. Kosuge and J.A.T. Machado), 11th International Conference on Advanced Robotics, January 2003 (inproceedings)

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An Introduction to Variable and Feature Selection.

Guyon, I., Elisseeff, A.

Journal of Machine Learning, 3, pages: 1157-1182, 2003 (article)

ei

[BibTex]

ei Guyon, I., Elisseeff, A. An Introduction to Variable and Feature Selection. Journal of Machine Learning, 3, pages: 1157-1182, 2003 (article)

[BibTex]

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Feature Selection for Support Vector Machines by Means of Genetic Algorithms

Fröhlich, H., Chapelle, O., Schölkopf, B.

In 15th IEEE International Conference on Tools with AI, pages: 142-148, 15th IEEE International Conference on Tools with AI, 2003 (inproceedings)

ei

[BibTex]

ei Fröhlich, H., Chapelle, O., Schölkopf, B. Feature Selection for Support Vector Machines by Means of Genetic Algorithms In 15th IEEE International Conference on Tools with AI, pages: 142-148, 15th IEEE International Conference on Tools with AI, 2003 (inproceedings)

[BibTex]

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Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting

Quiñonero-Candela, J., Girard, A., Larsen, J., Rasmussen, CE.

In IEEE International Conference on Acoustics, Speech and Signal Processing, 2, pages: 701-704, IEEE International Conference on Acoustics, Speech and Signal Processing, 2003 (inproceedings)

Abstract
The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.

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ei Quiñonero-Candela, J., Girard, A., Larsen, J., Rasmussen, CE. Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting In IEEE International Conference on Acoustics, Speech and Signal Processing, 2, pages: 701-704, IEEE International Conference on Acoustics, Speech and Signal Processing, 2003 (inproceedings)

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Unsupervised Clustering of Images using their Joint Segmentation

Seldin, Y., Starik, S., Werman, M.

In The 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV 2003), pages: 1-24, 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV), 2003 (inproceedings)

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ei Seldin, Y., Starik, S., Werman, M. Unsupervised Clustering of Images using their Joint Segmentation In The 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV 2003), pages: 1-24, 3rd International Workshop on Statistical and Computational Theories of Vision (SCTV), 2003 (inproceedings)

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