Header logo is ei


2018


no image
A virtual reality environment for experiments in assistive robotics and neural interfaces

Bustamante, S.

Graduate School of Neural Information Processing, Eberhard Karls Universität Tübingen, Germany, 2018 (mastersthesis)

PDF [BibTex]

2018

PDF [BibTex]


no image
Optimal Trajectory Generation and Learning Control for Robot Table Tennis

Koc, O.

Technical University Darmstadt, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
Distribution-Dissimilarities in Machine Learning

Simon-Gabriel, C. J.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
Domain Adaptation Under Causal Assumptions

Lechner, T.

Eberhard Karls Universität Tübingen, Germany, 2018 (mastersthesis)

[BibTex]

[BibTex]


no image
Probabilistic Approaches to Stochastic Optimization

Mahsereci, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


no image
Reinforcement Learning for High-Speed Robotics with Muscular Actuation

Guist, S.

Ruprecht-Karls-Universität Heidelberg , 2018 (mastersthesis)

[BibTex]

[BibTex]


no image
Probabilistic Ordinary Differential Equation Solvers — Theory and Applications

Schober, M.

Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]


no image
A machine learning approach to taking EEG-based computer interfaces out of the lab

Jayaram, V.

Graduate Training Centre of Neuroscience, IMPRS, Eberhard Karls Universität Tübingen, Germany, 2018 (phdthesis)

[BibTex]

[BibTex]

2009


no image
Learning an Interactive Segmentation System

Nickisch, H., Kohli, P., Rother, C.

Max Planck Institute for Biological Cybernetics, December 2009 (techreport)

Abstract
Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.

Web [BibTex]

2009

Web [BibTex]


no image
Detection of objects in noisy images and site percolation on square lattices

Langovoy, M., Wittich, O.

(2009-035), EURANDOM, Technische Universiteit Eindhoven, November 2009 (techreport)

Abstract
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.

PDF [BibTex]

PDF [BibTex]


no image
An Incremental GEM Framework for Multiframe Blind Deconvolution, Super-Resolution, and Saturation Correction

Harmeling, S., Sra, S., Hirsch, M., Schölkopf, B.

(187), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract
We develop an incremental generalized expectation maximization (GEM) framework to model the multiframe blind deconvolution problem. A simplistic version of this problem was recently studied by Harmeling etal~cite{harmeling09}. We solve a more realistic version of this problem which includes the following major features: (i) super-resolution ability emph{despite} noise and unknown blurring; (ii) saturation-correction, i.e., handling of overexposed pixels that can otherwise confound the image processing; and (iii) simultaneous handling of color channels. These features are seamlessly integrated into our incremental GEM framework to yield simple but efficient multiframe blind deconvolution algorithms. We present technical details concerning critical steps of our algorithms, especially to highlight how all operations can be written using matrix-vector multiplications. We apply our algorithm to real-world images from astronomy and super resolution tasks. Our experimental results show that our methods yield improve d resolution and deconvolution at the same time.

PDF [BibTex]

PDF [BibTex]


no image
Efficient Filter Flow for Space-Variant Multiframe Blind Deconvolution

Hirsch, M., Sra, S., Schölkopf, B., Harmeling, S.

(188), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)

Abstract
Ultimately being motivated by facilitating space-variant blind deconvolution, we present a class of linear transformations, that are expressive enough for space-variant filters, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on astronomical imaging through atmospheric turbulences and on noisy magnetic resonance images of constantly moving objects demonstrate the practical significance of our approach.

PDF [BibTex]

PDF [BibTex]


no image
Algebraic polynomials and moments of stochastic integrals

Langovoy, M.

(2009-031), EURANDOM, Technische Universiteit Eindhoven, October 2009 (techreport)

PDF [BibTex]

PDF [BibTex]


no image
Kernel Learning Approaches for Image Classification

Gehler, PV.

Biologische Kybernetik, Universität des Saarlandes, Saarbrücken, Germany, October 2009 (phdthesis)

Abstract
This thesis extends the use of kernel learning techniques to specific problems of image classification. Kernel learning is a paradigm in the field of machine learning that generalizes the use of inner products to compute similarities between arbitrary objects. In image classification one aims to separate images based on their visual content. We address two important problems that arise in this context: learning with weak label information and combination of heterogeneous data sources. The contributions we report on are not unique to image classification, and apply to a more general class of problems. We study the problem of learning with label ambiguity in the multiple instance learning framework. We discuss several different image classification scenarios that arise in this context and argue that the standard multiple instance learning requires a more detailed disambiguation. Finally we review kernel learning approaches proposed for this problem and derive a more efficient algorithm to solve them. The multiple kernel learning framework is an approach to automatically select kernel parameters. We extend it to its infinite limit and present an algorithm to solve the resulting problem. This result is then applied in two directions. We show how to learn kernels that adapt to the special structure of images. Finally we compare different ways of combining image features for object classification and present significant improvements compared to previous methods.

PDF [BibTex]

PDF [BibTex]


no image
A PAC-Bayesian Approach to Structure Learning

Seldin, Y.

Biologische Kybernetik, The Hebrew University of Jerusalem, Israel, September 2009 (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Expectation Propagation on the Maximum of Correlated Normal Variables

Hennig, P.

Cavendish Laboratory: University of Cambridge, July 2009 (techreport)

Abstract
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

Web [BibTex]

Web [BibTex]


no image
Consistent Nonparametric Tests of Independence

Gretton, A., Györfi, L.

(172), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2009 (techreport)

Abstract
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. Two kinds of tests are provided. Distribution-free strong consistent tests are derived on the basis of large deviation bounds on the test statistcs: these tests make almost surely no Type I or Type II error after a random sample size. Asymptotically alpha-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value alpha, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.

PDF [BibTex]

PDF [BibTex]


no image
Semi-supervised subspace analysis of human functional magnetic resonance imaging data

Shelton, J., Blaschko, M., Bartels, A.

(185), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2009 (techreport)

Abstract
Kernel Canonical Correlation Analysis is a very general technique for subspace learning that incorporates PCA and LDA as special cases. Functional magnetic resonance imaging (fMRI) acquired data is naturally amenable to these techniques as data are well aligned. fMRI data of the human brain is a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single- and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.

PDF [BibTex]

PDF [BibTex]


no image
Kernel Methods in Computer Vision:Object Localization, Clustering,and Taxonomy Discovery

Blaschko, MB.

Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, March 2009 (phdthesis)

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Model selection, large deviations and consistency of data-driven tests

Langovoy, M.

(2009-007), EURANDOM, Technische Universiteit Eindhoven, March 2009 (techreport)

Abstract
We consider three general classes of data-driven statistical tests. Neyman's smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penalties, derived in statistical literature, can be used in our tests. We prove general consistency theorems for the tests from those classes. Our proofs make use of large deviations inequalities for deterministic and random quadratic forms. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Applications to testing in statistical inverse problems and statistics for stochastic processes are also presented..

PDF [BibTex]

PDF [BibTex]


no image
Motor Control and Learning in Table Tennis

Mülling, K.

Eberhard Karls Universität Tübingen, Gerrmany, 2009 (diplomathesis)

[BibTex]

[BibTex]


no image
Hierarchical Clustering and Density Estimation Based on k-nearest-neighbor graphs

Drewe, P.

Eberhard Karls Universität Tübingen, Germany, 2009 (diplomathesis)

[BibTex]

[BibTex]


no image
Learning with Structured Data: Applications to Computer Vision

Nowozin, S.

Technische Universität Berlin, Germany, 2009 (phdthesis)

PDF [BibTex]

PDF [BibTex]

2005


no image
Popper, Falsification and the VC-dimension

Corfield, D., Schölkopf, B., Vapnik, V.

(145), Max Planck Institute for Biological Cybernetics, November 2005 (techreport)

PDF [BibTex]

2005

PDF [BibTex]


no image
Extension to Kernel Dependency Estimation with Applications to Robotics

BakIr, G.

Biologische Kybernetik, Technische Universität Berlin, Berlin, November 2005 (phdthesis)

Abstract
Kernel Dependency Estimation(KDE) is a novel technique which was designed to learn mappings between sets without making assumptions on the type of the involved input and output data. It learns the mapping in two stages. In a first step, it tries to estimate coordinates of a feature space representation of elements of the set by solving a high dimensional multivariate regression problem in feature space. Following this, it tries to reconstruct the original representation given the estimated coordinates. This thesis introduces various algorithmic extensions to both stages in KDE. One of the contributions of this thesis is to propose a novel linear regression algorithm that explores low-dimensional subspaces during learning. Furthermore various existing strategies for reconstructing patterns from feature maps involved in KDE are discussed and novel pre-image techniques are introduced. In particular, pre-image techniques for data-types that are of discrete nature such as graphs and strings are investigated. KDE is then explored in the context of robot pose imitation where the input is a an image with a human operator and the output is the robot articulated variables. Thus, using KDE, robot pose imitation is formulated as a regression problem.

PDF PDF [BibTex]

PDF PDF [BibTex]


no image
Geometrical aspects of statistical learning theory

Hein, M.

Biologische Kybernetik, Darmstadt, Darmstadt, November 2005 (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Implicit Surfaces For Modelling Human Heads

Steinke, F.

Biologische Kybernetik, Eberhard-Karls-Universität, Tübingen, September 2005 (diplomathesis)

[BibTex]

[BibTex]


no image
Machine Learning Methods for Brain-Computer Interdaces

Lal, TN.

Biologische Kybernetik, University of Darmstadt, September 2005 (phdthesis)

Web [BibTex]

Web [BibTex]


no image
A Combinatorial View of Graph Laplacians

Huang, J.

(144), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, August 2005 (techreport)

Abstract
Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence for the normalized Laplacian. In this paper, we analyze different variants of graph Laplacians directly from the ways solving the original graph partitioning problem. The graph partitioning problem is a well-known combinatorial NP hard optimization problem. The spectral solutions provide evidence that normalized Laplacian encodes more reasonable considerations for graph partitioning. We also provide some examples to show their differences.

[BibTex]

[BibTex]


no image
Beyond Pairwise Classification and Clustering Using Hypergraphs

Zhou, D., Huang, J., Schölkopf, B.

(143), Max Planck Institute for Biological Cybernetics, August 2005 (techreport)

Abstract
In many applications, relationships among objects of interest are more complex than pairwise. Simply approximating complex relationships as pairwise ones can lead to loss of information. An alternative for these applications is to analyze complex relationships among data directly, without the need to first represent the complex relationships into pairwise ones. A natural way to describe complex relationships is to use hypergraphs. A hypergraph is a graph in which edges can connect more than two vertices. Thus we consider learning from a hypergraph, and develop a general framework which is applicable to classification and clustering for complex relational data. We have applied our framework to real-world web classification problems and obtained encouraging results.

PDF [BibTex]

PDF [BibTex]


no image
Liver Perfusion using Level Set Methods

Nowozin, S.

Biologische Kybernetik, Shanghai JiaoTong University, Shanghai, China, July 2005 (diplomathesis)

PDF [BibTex]

PDF [BibTex]


no image
Generalized Nonnegative Matrix Approximations using Bregman Divergences

Sra, S., Dhillon, I.

Univ. of Texas at Austin, June 2005 (techreport)

[BibTex]

[BibTex]


no image
Measuring Statistical Dependence with Hilbert-Schmidt Norms

Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.

(140), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2005 (techreport)

Abstract
We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

PDF [BibTex]

PDF [BibTex]


no image
Consistency of Kernel Canonical Correlation Analysis

Fukumizu, K., Bach, F., Gretton, A.

(942), Institute of Statistical Mathematics, 4-6-7 Minami-azabu, Minato-ku, Tokyo 106-8569 Japan, June 2005 (techreport)

PDF [BibTex]

PDF [BibTex]


no image
Discriminative Methods for Label Sequence Learning

Altun, Y.

Brown University, Providence, RI, USA, May 2005 (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Efficient Adaptive Sampling of the Psychometric Function by Maximizing Information Gain

Tanner, TG.

Biologische Kybernetik, Eberhard-Karls University Tübingen, Tübingen, Germany, May 2005 (diplomathesis)

Abstract
A common task in psychophysics is to measure the psychometric function. A psychometric function can be described by its shape and four parameters: offset or threshold, slope or width, false alarm rate or chance level and miss or lapse rate. Depending on the parameters of interest some points on the psychometric function may be more informative than others. Adaptive methods attempt to place trials on the most informative points based on the data collected in previous trials. A new Bayesian adaptive psychometric method placing trials by minimising the expected entropy of the posterior probabilty dis- tribution over a set of possible stimuli is introduced. The method is more flexible, faster and at least as efficient as the established method (Kontsevich and Tyler, 1999). Comparably accurate (2dB) threshold and slope estimates can be obtained after about 30 and 500 trials, respectively. By using a dynamic termination criterion the efficiency can be further improved. The method can be applied to all experimental designs including yes/no designs and allows acquisition of any set of free parameters. By weighting the importance of parameters one can include nuisance parameters and adjust the relative expected errors. Use of nuisance parameters may lead to more accurate estimates than assuming a guessed fixed value. Block designs are supported and do not harm the performance if a sufficient number of trials are performed. The method was evaluated by computer simulations in which the role of parametric assumptions, its robustness, the quality of different point estimates, the effect of dynamic termination criteria and many other settings were investigated.

[BibTex]

[BibTex]


no image
Support Vector Classification of Images with Local Features

Blaschko, MB.

Biologische Kybernetik, University of Massachusetts, Amherst, May 2005 (diplomathesis)

[BibTex]

[BibTex]


no image
Efficient Pattern Selection for Support Vector Classifiers and its CRM Application

Shin, H.

Biologische Kybernetik, Seoul National University, Seoul, Korea, February 2005 (phdthesis)

PDF [BibTex]

PDF [BibTex]


no image
Kernels: Regularization and Optimization

Ong, CS.

Biologische Kybernetik, The Australian National University, Canberra, Australia, 2005 (phdthesis)

PDF GZIP [BibTex]

PDF GZIP [BibTex]


no image
Approximate Inference for Robust Gaussian Process Regression

Kuss, M., Pfingsten, T., Csato, L., Rasmussen, C.

(136), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectation-propagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling.

PDF [BibTex]

PDF [BibTex]


no image
Maximum-Margin Feature Combination for Detection and Categorization

BakIr, G., Wu, M., Eichhorn, J.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
In this paper we are concerned with the optimal combination of features of possibly different types for detection and estimation tasks in machine vision. We propose to combine features such that the resulting classifier maximizes the margin between classes. In contrast to existing approaches which are non-convex and/or generative we propose to use a discriminative model leading to convex problem formulation and complexity control. Furthermore we assert that decision functions should not compare apples and oranges by comparing features of different types directly. Instead we propose to combine different similarity measures for each different feature type. Furthermore we argue that the question: ”Which feature type is more discriminative for task X?” is ill-posed and show empirically that the answer to this question might depend on the complexity of the decision function.

PDF [BibTex]

PDF [BibTex]


no image
Towards a Statistical Theory of Clustering. Presented at the PASCAL workshop on clustering, London

von Luxburg, U., Ben-David, S.

Presented at the PASCAL workshop on clustering, London, 2005 (techreport)

Abstract
The goal of this paper is to discuss statistical aspects of clustering in a framework where the data to be clustered has been sampled from some unknown probability distribution. Firstly, the clustering of the data set should reveal some structure of the underlying data rather than model artifacts due to the random sampling process. Secondly, the more sample points we have, the more reliable the clustering should be. We discuss which methods can and cannot be used to tackle those problems. In particular we argue that generalization bounds as they are used in statistical learning theory of classification are unsuitable in a general clustering framework. We suggest that the main replacements of generalization bounds should be convergence proofs and stability considerations. This paper should be considered as a road map paper which identifies important questions and potentially fruitful directions for future research about statistical clustering. We do not attempt to present a complete statistical theory of clustering.

PDF [BibTex]

PDF [BibTex]


no image
Approximate Bayesian Inference for Psychometric Functions using MCMC Sampling

Kuss, M., Jäkel, F., Wichmann, F.

(135), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2005 (techreport)

Abstract
In psychophysical studies the psychometric function is used to model the relation between the physical stimulus intensity and the observer's ability to detect or discriminate between stimuli of different intensities. In this report we propose the use of Bayesian inference to extract the information contained in experimental data estimate the parameters of psychometric functions. Since Bayesian inference cannot be performed analytically we describe how a Markov chain Monte Carlo method can be used to generate samples from the posterior distribution over parameters. These samples are used to estimate Bayesian confidence intervals and other characteristics of the posterior distribution. In addition we discuss the parameterisation of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generate d data and in a case study for real experimental data. Furthermore, we compare our approach with traditional methods based on maximum-likelihood parameter estimation combined with bootstrap techniques for confidence interval estimation. The appendix provides a description of an implementation for the R environment for statistical computing and provides the code for reproducing the results discussed in the experiment section.

PDF [BibTex]

PDF [BibTex]

2002


no image
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Schölkopf, B., Smola, A.

pages: 644, Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, USA, December 2002, Parts of this book, including an introduction to kernel methods, can be downloaded here. (book)

Abstract
In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs-kernels—for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics. Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

Web [BibTex]

2002

Web [BibTex]


no image
Kernel Dependency Estimation

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

(98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)

Abstract
We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images.

PDF [BibTex]

PDF [BibTex]


no image
Global Geometry of SVM Classifiers

Zhou, D., Xiao, B., Zhou, H., Dai, R.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)

Abstract
We construct an geometry framework for any norm Support Vector Machine (SVM) classifiers. Within this framework, separating hyperplanes, dual descriptions and solutions of SVM classifiers are constructed by a purely geometric fashion. In contrast with the optimization theory used in SVM classifiers, we have no complicated computations any more. Each step in our theory is guided by elegant geometric intuitions.

PDF PostScript [BibTex]

PDF PostScript [BibTex]