The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.

/pdf/a-tutorial-on-support-vector-machines-for-pattern-5cn6x20psd.pdf

A Tutorial on Support Vector Machines for Pattern Recognition

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

/pdf/a-tutorial-on-support-vector-regression-10mfvogjkf.pdf

A tutorial on support vector regression

In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM‘s. The approach is illustrated on a two-spiral benchmark classification problem.

/pdf/least-squares-support-vector-machine-classifiers-4wyga3yhf5.pdf

Least Squares Support Vector Machine Classifiers

The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

/pdf/statistical-pattern-recognition-a-review-1kz1b0tte4.pdf

Statistical pattern recognition: a review

Introduction to support vector learning roadmap. Part 1 Theory: three remarks on the support vector method of function estimation, Vladimir Vapnik generalization performance of support vector machines and other pattern classifiers, Peter Bartlett and John Shawe-Taylor Bayesian voting schemes and large margin classifiers, Nello Cristianini and John Shawe-Taylor support vector machines, reproducing kernel Hilbert spaces, and randomized GACV, Grace Wahba geometry and invariance in kernel based methods, Christopher J.C. Burges on the annealed VC entropy for margin classifiers - a statistical mechanics study, Manfred Opper entropy numbers, operators and support vector kernels, Robert C. Williamson et al. Part 2 Implementations: solving the quadratic programming problem arising in support vector classification, Linda Kaufman making large-scale support vector machine learning practical, Thorsten Joachims fast training of support vector machines using sequential minimal optimization, John C. Platt. Part 3 Applications: support vector machines for dynamic reconstruction of a chaotic system, Davide Mattera and Simon Haykin using support vector machines for time series prediction, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel. Part 4 Extensions of the algorithm: reducing the run-time complexity in support vector machines, Edgar E. Osuna and Federico Girosi support vector regression with ANOVA decomposition kernels, Mark O. Stitson et al support vector density estimation, Jason Weston et al combining support vector and mathematical programming methods for classification, Bernhard Scholkopf et al.

Advances in kernel methods: support vector learning

The support vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights, and threshold that minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by X-means clustering, and the weights are computed using error backpropagation. We consider three machines, namely, a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the United States postal service database of handwritten digits, the SV machine achieves the highest recognition accuracy, followed by the hybrid system. The SV approach is thus not only theoretically well-founded but also superior in a practical application.

/pdf/comparing-support-vector-machines-with-gaussian-kernels-to-49hb3251zf.pdf

Comparing support vector machines with Gaussian kernels to radial basis function classifiers

A face detection system (100) includes an imaging device, a computer having a pattern prototype synthetizer and an image classifier, and an output display device. Face and non-face pattern prototypes are synthesized by a network training process using a number of example images. A new applied image is analysed by taking a distance from the applied image to each of the prototypes, and a decision is made as to whether the applied image contains a face based on the distances thus obtained. The system and method may be applied to various other detection tasks.

Network-based system and method for detection of faces and the like

In certain real-world learning scenarios where there are enormous amounts of training data, the training process can become computationally intractable. Researchers have attempted to address this problem by performing instance selection, which is to automatically identify and preserve a sufficiently small but highly informative data sample for training. In most classical formulations of example-based learning, the learner passively receives randomly drawn training examples from which it recovers the unknown target function. Active Learning describes a different example-based learning paradigm where the learner explicitly seeks for new training examples of high utility, and can thus be viewed as a form of instance selection. This chapter presents a Bayesian formulation for active learning within a classical function approximation learning framework, and shows how one can derive precise example selection algorithms for learning some simple target function classes more accurately with less training data. We then present a real-world learning scenario on object (face) detection, and show how our active learning formulation leads to a useful instance selection heuristic for identifying and retaining high utility training data.

An active learning formulation for instance selection with applications to object detection

In most classical formulations of learning from examples. a passive learner is presented with examples randomly drawn. Here we discuss an e-focusing strategy that actively chooses examples for concept learning. We describe the local focused property that functions must have for such a strategy to work. Finally, we develop an example selection heuristic, motivated by e-focusing for training a computer vision system to perform a human Mace detection task.

Kah-Kay Sung

Papers

Comparing support vector machines with Gaussian kernels to radial basis function classifiers

Network-based system and method for detection of faces and the like

An active learning formulation for instance selection with applications to object detection

Epsilon focusing—a strategy for active example selection