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2007


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MR-Based PET Attenuation Correction: Method and Validation

Hofmann, M., Steinke, F., Scheel, V., Charpiat, G., Brady, M., Schölkopf, B., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M16-6):1-2, November 2007 (poster)

Abstract
PET/MR combines the high soft tissue contrast of Magnetic Resonance Imaging (MRI) and the functional information of Positron Emission Tomography (PET). For quantitative PET information, correction of tissue photon attenuation is mandatory. Usually in conventional PET, the attenuation map is obtained from a transmission scan, which uses a rotating source, or from the CT scan in case of combined PET/CT. In the case of a PET/MR scanner, there is insufficient space for the rotating source and ideally one would want to calculate the attenuation map from the MR image instead. Since MR images provide information about proton density of the different tissue types, it is not trivial to use this data for PET attenuation correction. We present a method for predicting the PET attenuation map from a given the MR image, using a combination of atlas-registration and recognition of local patterns. Using "leave one out cross validation" we show on a database of 16 MR-CT image pairs that our method reliably allows estimating the CT image from the MR image. Subsequently, as in PET/CT, the PET attenuation map can be predicted from the CT image. On an additional dataset of MR/CT/PET triplets we quantitatively validate that our approach allows PET quantification with an error that is smaller than what would be clinically significant. We demonstrate our approach on T1-weighted human brain scans. However, the presented methods are more general and current research focuses on applying the established methods to human whole body PET/MRI applications.

PDF PDF [BibTex]

2007

PDF PDF [BibTex]


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Estimating receptive fields without spike-triggering

Macke, J., Zeck, G., Bethge, M.

37th annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37(768.1):1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


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Evaluation of Deformable Registration Methods for MR-CT Atlas Alignment

Scheel, V., Hofmann, M., Rehfeld, N., Judenhofer, M., Claussen, C., Pichler, B.

2007 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC 2007), 2007(M13-121):1, November 2007 (poster)

Abstract
Deformable registration methods are essential for multimodality imaging. Many different methods exist but due to the complexity of the deformed images a direct comparison of the methods is difficult. One particular application that requires high accuracy registration of MR-CT images is atlas-based attenuation correction for PET/MR. We compare four deformable registration algorithms for 3D image data included in the Open Source "National Library of Medicine Insight Segmentation and Registration Toolkit" (ITK). An interactive landmark based registration using MiraView (Siemens) has been used as gold standard. The automatic algorithms provided by ITK are based on the metrics Mattes mutual information as well as on normalized mutual information. The transformations are calculated by interpolating over a uniform B-Spline grid laying over the image to be warped. The algorithms were tested on head images from 10 subjects. We implemented a measure which segments head interior bone and air based on the CT images and l ow intensity classes of corresponding MRI images. The segmentation of bone is performed by individually calculating the lowest Hounsfield unit threshold for each CT image. The compromise is made by quantifying the number of overlapping voxels of the remaining structures. We show that the algorithms provided by ITK achieve similar or better accuracy than the time-consuming interactive landmark based registration. Thus, ITK provides an ideal platform to generate accurately fused datasets from different modalities, required for example for building training datasets for Atlas-based attenuation correction.

PDF [BibTex]

PDF [BibTex]


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A time/frequency decomposition of information transmission by LFPs and spikes in the primary visual cortex

Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M., Logothetis, N., Panzeri, S.

37th Annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37, pages: 1, November 2007 (poster)

Web [BibTex]

Web [BibTex]


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Mining expression-dependent modules in the human interaction network

Georgii, E., Dietmann, S., Uno, T., Pagel, P., Tsuda, K.

BMC Bioinformatics, 8(Suppl. 8):S4, November 2007 (poster)

PDF DOI [BibTex]

PDF DOI [BibTex]


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A Hilbert Space Embedding for Distributions

Smola, A., Gretton, A., Song, L., Schölkopf, B.

Proceedings of the 10th International Conference on Discovery Science (DS 2007), 10, pages: 40-41, October 2007 (poster)

Abstract
While kernel methods are the basis of many popular techniques in supervised learning, they are less commonly used in testing, estimation, and analysis of probability distributions, where information theoretic approaches rule the roost. However it becomes difficult to estimate mutual information or entropy if the data are high dimensional.

PDF PDF DOI [BibTex]

PDF PDF DOI [BibTex]


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Bayesian Estimators for Robins-Ritov’s Problem

Harmeling, S., Toussaint, M.

(EDI-INF-RR-1189), School of Informatics, University of Edinburgh, October 2007 (techreport)

Abstract
Bayesian or likelihood-based approaches to data analysis became very popular in the field of Machine Learning. However, there exist theoretical results which question the general applicability of such approaches; among those a result by Robins and Ritov which introduce a specific example for which they prove that a likelihood-based estimator will fail (i.e. it does for certain cases not converge to a true parameter estimate, even given infinite data). In this paper we consider various approaches to formulate likelihood-based estimators in this example, basically by considering various extensions of the presumed generative model of the data. We can derive estimators which are very similar to the classical Horvitz-Thompson and which also account for a priori knowledge of an observation probability function.

PDF [BibTex]

PDF [BibTex]


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Learning with Transformation Invariant Kernels

Walder, C., Chapelle, O.

(165), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2007 (techreport)

Abstract
Abstract. This paper considers kernels invariant to translation, rotation and dilation. We show that no non-trivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d. case and provide some novel analysis, including an elementary derivation of a c.p.d. representer theorem. On the practical side, we give a support vector machine (s.v.m.) algorithm for arbitrary c.p.d. kernels. For the thin-plate kernel this leads to a classifier with only one parameter (the amount of regularisation), which we demonstrate to be as effective as an s.v.m. with the Gaussian kernel, even though the Gaussian involves a second parameter (the length scale).

PDF [BibTex]

PDF [BibTex]


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Studying the effects of noise correlations on population coding using a sampling method

Ecker, A., Berens, P., Bethge, M., Logothetis, N., Tolias, A.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 21, September 2007 (poster)

PDF [BibTex]

PDF [BibTex]


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Scalable Semidefinite Programming using Convex Perturbations

Kulis, B., Sra, S., Jegelka, S.

(TR-07-47), University of Texas, Austin, TX, USA, September 2007 (techreport)

Abstract
Several important machine learning problems can be modeled and solved via semidefinite programs. Often, researchers invoke off-the-shelf software for the associated optimization, which can be inappropriate for many applications due to computational and storage requirements. In this paper, we introduce the use of convex perturbations for semidefinite programs (SDPs). Using a particular perturbation function, we arrive at an algorithm for SDPs that has several advantages over existing techniques: a) it is simple, requiring only a few lines of MATLAB, b) it is a first-order method which makes it scalable, c) it can easily exploit the structure of a particular SDP to gain efficiency (e.g., when the constraint matrices are low-rank). We demonstrate on several machine learning applications that the proposed algorithm is effective in finding fast approximations to large-scale SDPs.

PDF [BibTex]

PDF [BibTex]


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Near-Maximum Entropy Models for Binary Neural Representations of Natural Images

Berens, P., Bethge, M.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 19, September 2007 (poster)

Abstract
Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data---the model parameters can be derived in closed form and sampling is easy. We demonstrate its usefulness by studying a simple neural representation model of natural images. For the first time, we are able to directly compare predictions from a pairwise maximum entropy model not only in small groups of neurons, but also in larger populations of more than thousand units. Our results indicate that in such larger networks interactions exist that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics extrem ely well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

PDF [BibTex]

PDF [BibTex]


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Sparse Multiscale Gaussian Process Regression

Walder, C., Kim, K., Schölkopf, B.

(162), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Abstract
Most existing sparse Gaussian process (g.p.) models seek computational advantages by basing their computations on a set of m basis functions that are the covariance function of the g.p. with one of its two inputs fixed. We generalise this for the case of Gaussian covariance function, by basing our computations on m Gaussian basis functions with arbitrary diagonal covariance matrices (or length scales). For a fixed number of basis functions and any given criteria, this additional flexibility permits approximations no worse and typically better than was previously possible. Although we focus on g.p. regression, the central idea is applicable to all kernel based algorithms, such as the support vector machine. We perform gradient based optimisation of the marginal likelihood, which costs O(m2n) time where n is the number of data points, and compare the method to various other sparse g.p. methods. Our approach outperforms the other methods, particularly for the case of very few basis functions, i.e. a very high sparsity ratio.

PDF [BibTex]

PDF [BibTex]


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Efficient Subwindow Search for Object Localization

Blaschko, M., Hofmann, T., Lampert, C.

(164), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2007 (techreport)

Abstract
Recent years have seen huge advances in object recognition from images. Recognition rates beyond 95% are the rule rather than the exception on many datasets. However, most state-of-the-art methods can only decide if an object is present or not. They are not able to provide information on the object location or extent within in the image. We report on a simple yet powerful scheme that extends many existing recognition methods to also perform localization of object bounding boxes. This is achieved by maximizing the classification score over all possible subrectangles in the image. Despite the impression that this would be computationally intractable, we show that in many situations efficient algorithms exist which solve a generalized maximum subrectangle problem. We show how our method is applicable to a variety object detection frameworks and demonstrate its performance by applying it to the popular bag of visual words model, achieving competitive results on the PASCAL VOC 2006 dataset.

PDF [BibTex]

PDF [BibTex]


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Learning the Influence of Spatio-Temporal Variations in Local Image Structure on Visual Saliency

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M.

10th T{\"u}binger Wahrnehmungskonferenz (TWK 2007), 10, pages: 1, July 2007 (poster)

Abstract
Computational models for bottom-up visual attention traditionally consist of a bank of Gabor-like or Difference-of-Gaussians filters and a nonlinear combination scheme which combines the filter responses into a real-valued saliency measure [1]. Recently it was shown that a standard machine learning algorithm can be used to derive a saliency model from human eye movement data with a very small number of additional assumptions. The learned model is much simpler than previous models, but nevertheless has state-of-the-art prediction performance [2]. A central result from this study is that DoG-like center-surround filters emerge as the unique solution to optimizing the predictivity of the model. Here we extend the learning method to the temporal domain. While the previous model [2] predicts visual saliency based on local pixel intensities in a static image, our model also takes into account temporal intensity variations. We find that the learned model responds strongly to temporal intensity changes ocurring 200-250ms before a saccade is initiated. This delay coincides with the typical saccadic latencies, indicating that the learning algorithm has extracted a meaningful statistic from the training data. In addition, we show that the model correctly predicts a significant proportion of human eye movements on previously unseen test data.

Web [BibTex]

Web [BibTex]


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Cluster Identification in Nearest-Neighbor Graphs

Maier, M., Hein, M., von Luxburg, U.

(163), Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany, May 2007 (techreport)

Abstract
Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are ``identified‘‘: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds on the probability that cluster identification is successful, and use them to predict ``optimal‘‘ values of k for the mutual and symmetric k-nearest-neighbor graphs. We point out different properties of the mutual and symmetric nearest-neighbor graphs related to the cluster identification problem.

PDF [BibTex]

PDF [BibTex]


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Better Codes for the P300 Visual Speller

Biessmann, F., Hill, N., Farquhar, J., Schölkopf, B.

G{\"o}ttingen Meeting of the German Neuroscience Society, 7, pages: 123, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


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Exploring model selection techniques for nonlinear dimensionality reduction

Harmeling, S.

(EDI-INF-RR-0960), School of Informatics, University of Edinburgh, March 2007 (techreport)

Abstract
Nonlinear dimensionality reduction (NLDR) methods have become useful tools for practitioners who are faced with the analysis of high-dimensional data. Of course, not all NLDR methods are equally applicable to a particular dataset at hand. Thus it would be useful to come up with model selection criteria that help to choose among different NLDR algorithms. This paper explores various approaches to this problem and evaluates them on controlled data sets. Comprehensive experiments will show that model selection scores based on stability are not useful, while scores based on Gaussian processes are helpful for the NLDR problem.

PDF Web [BibTex]

PDF Web [BibTex]


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Do We Know What the Early Visual System Computes?

Bethge, M., Kayser, C.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 352, March 2007 (poster)

Abstract
Decades of research provided much data and insights into the mechanisms of the early visual system. Currently, however, there is great controversy on whether these findings can provide us with a thorough functional understanding of what the early visual system does, or formulated differently, of what it computes. At the Society for Neuroscience meeting 2005 in Washington, a symposium was held on the question "Do we know that the early visual system does", which was accompanied by a widely regarded publication in the Journal of Neuroscience. Yet, that discussion was rather specialized as it predominantly addressed the question of how well neural responses in retina, LGN, and cortex can be predicted from noise stimuli, but did not emphasize the question of whether we understand what the function of these early visual areas is. Here we will concentrate on this neuro-computational aspect of vision. Experts from neurobiology, psychophysics and computational neuroscience will present studies which approach this question from different viewpoints and promote a critical discussion of whether we actually understand what early areas contribute to the processing and perception of visual information.

PDF [BibTex]

PDF [BibTex]


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Implicit Wiener Series for Estimating Nonlinear Receptive Fields

Franz, MO., Macke, JH., Saleem, A., Schultz, SR.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 1199, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


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Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach

Chiappa, S., Barber, D.

(161), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, March 2007 (techreport)

Abstract
We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes.

PDF [BibTex]

PDF [BibTex]


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3D Reconstruction of Neural Circuits from Serial EM Images

Maack, N., Kapfer, C., Macke, J., Schölkopf, B., Denk, W., Borst, A.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 1195, March 2007 (poster)

PDF [BibTex]

PDF [BibTex]


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Identifying temporal population codes in the retina using canonical correlation analysis

Bethge, M., Macke, J., Gerwinn, S., Zeck, G.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 359, March 2007 (poster)

PDF PDF [BibTex]

PDF PDF [BibTex]


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Bayesian Neural System identification: error bars, receptive fields and neural couplings

Gerwinn, S., Seeger, M., Zeck, G., Bethge, M.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 360, March 2007 (poster)

PDF PDF [BibTex]

PDF PDF [BibTex]


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Modeling data using directional distributions: Part II

Sra, S., Jain, P., Dhillon, I.

(TR-07-05), University of Texas, Austin, TX, USA, February 2007 (techreport)

Abstract
High-dimensional data is central to most data mining applications, and only recently has it been modeled via directional distributions. In [Banerjee et al., 2003] the authors introduced the use of the von Mises-Fisher (vMF) distribution for modeling high-dimensional directional data, particularly for text and gene expression analysis. The vMF distribution is one of the simplest directional distributions. TheWatson, Bingham, and Fisher-Bingham distributions provide distri- butions with an increasing number of parameters and thereby commensurately increased modeling power. This report provides a followup study to the initial development in [Banerjee et al., 2003] by presenting Expectation Maximization (EM) procedures for estimating parameters of a mixture of Watson (moW) distributions. The numerical challenges associated with parameter estimation for both of these distributions are significantly more difficult than for the vMF distribution. We develop new numerical approximations for estimating the parameters permitting us to model real- life data more accurately. Our experimental results establish that for certain data sets improved modeling power translates into better results.

PDF [BibTex]

PDF [BibTex]


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About the Triangle Inequality in Perceptual Spaces

Jäkel, F., Schölkopf, B., Wichmann, F.

Proceedings of the Computational and Systems Neuroscience Meeting 2007 (COSYNE), 4, pages: 308, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


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Automatic 3D Face Reconstruction from Single Images or Video

Breuer, P., Kim, K., Kienzle, W., Blanz, V., Schölkopf, B.

(160), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, February 2007 (techreport)

Abstract
This paper presents a fully automated algorithm for reconstructing a textured 3D model of a face from a single photograph or a raw video stream. The algorithm is based on a combination of Support Vector Machines (SVMs) and a Morphable Model of 3D faces. After SVM face detection, individual facial features are detected using a novel regression-and classification-based approach, and probabilistically plausible configurations of features are selected to produce a list of candidates for several facial feature positions. In the next step, the configurations of feature points are evaluated using a novel criterion that is based on a Morphable Model and a combination of linear projections. Finally, the feature points initialize a model-fitting procedure of the Morphable Model. The result is a high-resolution 3D surface model.

PDF [BibTex]

PDF [BibTex]


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Center-surround filters emerge from optimizing predictivity in a free-viewing task

Kienzle, W., Wichmann, F., Schölkopf, B., Franz, M.

Proceedings of the Computational and Systems Neuroscience Meeting 2007 (COSYNE), 4, pages: 207, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


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Nonlinear Receptive Field Analysis: Making Kernel Methods Interpretable

Kienzle, W., Macke, J., Wichmann, F., Schölkopf, B., Franz, M.

Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 16, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


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Estimating Population Receptive Fields in Space and Time

Macke, J., Zeck, G., Bethge, M.

Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 44, February 2007 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


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Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract
This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

PDF link (url) [BibTex]

PDF link (url) [BibTex]

2003


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Natural Actor-Critic

Peters, J., Vijayakumar, S., Schaal, S.

NIPS Workshop " Planning for the Real World: The promises and challenges of dealing with uncertainty", December 2003 (poster)

PDF Web [BibTex]

2003

PDF Web [BibTex]


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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.

PDF Web [BibTex]

PDF Web [BibTex]


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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.

Web DOI [BibTex]

Web DOI [BibTex]


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Technical report on Separation methods for nonlinear mixtures

Jutten, C., Karhunen, J., Almeida, L., Harmeling, S.

(D29), EU-Project BLISS, October 2003 (techreport)

PDF [BibTex]

PDF [BibTex]


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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)

PDF [BibTex]

PDF [BibTex]


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Technical report on implementation of linear methods and validation on acoustic sources

Harmeling, S., Bünau, P., Ziehe, A., Pham, D.

EU-Project BLISS, September 2003 (techreport)

PDF [BibTex]

PDF [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.

PDF [BibTex]

PDF [BibTex]


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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.

PDF [BibTex]

PDF [BibTex]


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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.

[BibTex]

[BibTex]


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The Metric Nearness Problem with Applications

Dhillon, I., Sra, S., Tropp, J.

Univ. of Texas at Austin, June 2003 (techreport)

GZIP [BibTex]

GZIP [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.

PDF [BibTex]

PDF [BibTex]


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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.

PDF [BibTex]

PDF [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.

PDF [BibTex]

PDF [BibTex]


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A unifying computational framework for optimization and dynamic systemsapproaches to motor control

Mohajerian, P., Peters, J., Ijspeert, A., Schaal, S.

10th Joint Symposium on Neural Computation (JSNC 2003), 10, pages: 1, May 2003 (poster)

PDF Web [BibTex]

PDF Web [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.

PostScript [BibTex]

PostScript [BibTex]


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A Unifying Computational Framework for Optimization and Dynamic Systems Approaches to Motor Control

Mohajerian, P., Peters, J., Ijspeert, A., Schaal, S.

13th Annual Neural Control of Movement Meeting 2003, 13, pages: 1, April 2003 (poster)

[BibTex]

[BibTex]


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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.

Web [BibTex]

Web [BibTex]


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Expectation Maximization for Clustering on Hyperspheres

Banerjee, A., Dhillon, I., Ghosh, J., Sra, S.

Univ. of Texas at Austin, February 2003 (techreport)

GZIP [BibTex]

GZIP [BibTex]