Abstract: Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.

Abstract: This book is an introduction to support vector machines and related kernel methods in supervised learning, whose task is to estimate an input-output functional relationship from a training set of examples. A learning problem is referred to as classification if its output take discrete values in a set of possible categories and regression if it has continuous real-valued output.

Abstract: We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin-based binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with error-correcting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms. The scheme and the corresponding bounds apply to many popular classification learning algorithms including support-vector machines, AdaBoost, regression, logistic regression and decision-tree algorithms. We also give a multiclass generalization error analysis for general output codes with AdaBoost as the binary learner. Experimental results with SVM and AdaBoost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms.

Abstract: Wahba's classical representer theorem states that the solutions of certain risk minimization problems involving an empirical risk term and a quadratic regularizer can be written as expansions in terms of the training examples. We generalize the theorem to a larger class of regularizers and empirical risk terms, and give a self-contained proof utilizing the feature space associated with a kernel. The result shows that a wide range of problems have optimal solutions that live in the finite dimensional span of the training examples mapped into feature space, thus enabling us to carry out kernel algorithms independent of the (potentially infinite) dimensionality of the feature space.

Abstract: This article presents a Support Vector Machine (SVM) like learning system to handle multi-label problems. Such problems are usually decomposed into many two-class problems but the expressive power of such a system can be weak [5, 7]. We explore a new direct approach. It is based on a large margin ranking system that shares a lot of common properties with SVMs. We tested it on a Yeast gene functional classification problem with positive results.

Abstract: This textbook provides a thorough introduction to the field of learning from experimental data and soft computing. Support vector machines (SVM) and neural networks (NN) are the mathematical structures, or models, that underlie learning, while fuzzy logic systems (FLS) enable us to embed structured human knowledge into workable algorithms. The book assumes that it is not only useful, but necessary, to treat SVM, NN, and FLS as parts of a connected whole. Throughout, the theory and algorithms are illustrated by practical examples, as well as by problem sets and simulated experiments. This approach enables the reader to develop SVM, NN, and FLS in addition to understanding them. The book also presents three case studies: on NN-based control, financial time series analysis, and computer graphics. A solutions manual and all of the MATLAB programs needed for the simulated experiments are available.

Abstract: This paper deals with the application of a novel neural network technique, support vector machine (SVM), in financial time series forecasting. The objective of this paper is to examine the feasibility of SVM in financial time series forecasting by comparing it with a multi-layer back-propagation (BP) neural network. Five real futures contracts that are collated from the Chicago Mercantile Market are used as the data sets. The experiment shows that SVM outperforms the BP neural network based on the criteria of normalized mean square error (NMSE), mean absolute error (MAE), directional symmetry (DS) and weighted directional symmetry (WDS). Since there is no structured way to choose the free parameters of SVMs, the variability in performance with respect to the free parameters is investigated in this study. Analysis of the experimental results proved that it is advantageous to apply SVMs to forecast financial time series.

Abstract: Instead of a standard support vector machine (SVM) that classifies points by assigning them to one of two disjoint half-spaces, points are classified by assigning them to the closest of two parallel planes (in input or feature space) that are pushed apart as far as possible. This formulation, which can also be interpreted as regularized least squares and considered in the much more general context of regularized networks [8, 9], leads to an extremely fast and simple algorithm for generating a linear or nonlinear classifier that merely requires the solution of a single system of linear equations. In contrast, standard SVMs solve a quadratic or a linear program that require considerably longer computational time. Computational results on publicly available datasets indicate that the proposed proximal SVM classifier has comparable test set correctness to that of standard SVM classifiers, but with considerably faster computational time that can be an order of magnitude faster. The linear proximal SVM can easily handle large datasets as indicated by the classification of a 2 million point 10-attribute set in 20.8 seconds. All computational results are based on 6 lines of MATLAB code.

Abstract: Motivation: Protein fold recognition is an important approach to structure discovery without relying on sequence similarity. We study this approach with new multi-class classification methods and examined many issues important for a practical recognition system. Results: Most current discriminative methods for protein fold prediction use the one-against-others method, which has the well-known ‘False Positives’ problem. We investigated two new methods: the unique one-against-others and the all-against-all methods. Both improve prediction accuracy by 14‐110% on a dataset containing 27 SCOP folds. We used the Support Vector Machine (SVM) and the Neural Network (NN) learning methods as base classifiers. SVMs converges fast and leads to high accuracy. When scores of multiple parameter datasets are combined, majority voting reduces noise and increases recognition accuracy. We examined many issues involved with large number of classes, including dependencies of prediction accuracy on the number of folds and on the number of representatives in a fold. Overall, recognition systems achieve 56% fold prediction accuracy on a protein test dataset, where most of the proteins have below 25% sequence identity with the proteins used in training. Supplementary information: The protein parameter datasets used in this paper are available online (http://www.nersc.gov/∼cding/protein).

Abstract: Relevance feedback schemes using linear/quadratic estimators have been applied in content-based image retrieval to improve retrieval performance significantly. One major difficulty in relevance feedback is to estimate the support of target images in high dimensional feature space with a relatively small number of training samples. We develop a novel scheme based on one-class SVM, which fits a tight hyper-sphere in the nonlinearly transformed feature space to include most of the target images based on positive examples. The use of a kernel provides us an elegant way to deal with nonlinearity in the distribution of the target images, while the regularization term in SVM provides good generalization ability. To validate the efficacy of the proposed approach, we test it on both synthesized data and real-world images. Promising results are achieved in both cases.

Abstract: An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset is used as a constraint in an optimization problem with very few variables corresponding to the 1% of the data kept. The remainder of the data can be thrown away after solving the optimization problem. This is achieved by making use of a rectangular m×m kernel K(A, Ā) that greatly reduces the size of the quadratic program to be solved and simplifies the characterization of the nonlinear separating surface. Here, the m rows of A represent the original m data points while the m rows of Ā represent a greatly reduced m data points. Computational results indicate that test set correctness for the reduced support vector machine (RSVM), with a nonlinear separating surface that depends on a small randomly selected portion of the dataset, is better than that of a conventional support vector machine (SVM) with a nonlinear surface that explicitly depends on the entire dataset, and much better than a conventional SVM using a small random sample of the data. Computational times, as well as memory usage, are much smaller for RSVM than that of a conventional SVM using the entire dataset.

Abstract: Support vector machines (SVMs) have become a popular tool for machine learning with large amounts of high dimensional data. In this paper an approach for incremental learning with support vector machines is presented, that improves the existing approach of Syed et al. (1999). An insight into the interpretability of support vectors is also given.

Abstract: This chapter presents a summary of the issues discussed during the one day workshop on “Support Vector Machines (SVM) Theory and Applications” organized as part of the Advanced Course on Artificial Intelligence (ACAI ’99) in Chania, Greece [19]. The goal of the chapter is twofold: to present an overview of the background theory and current understanding of SVM, and to discuss the papers presented as well as the issues that arose during the workshop.

Abstract: The rapid advance in information processing systems in recent decades had directed engineering research towards the development of intelligent systems that can evolve models of natural phenomena automatically—“by themselves,” so to speak. In this respect, a wide range of machine learning techniques like decision trees, artificial neural networks (ANNs), Bayesian methods, fuzzy-rule based systems, and evolutionary algorithms have been successfully applied to model different civil engineering systems. In this study, the possibility of using yet another machine learning paradigm that is firmly based on the theory of statistical learning, namely that of the support vector machine (SVM), is investigated. An interesting property of this approach is that it is an approximate implementation of a structural risk minimization (SRM) induction principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing only the mean square error over the data set. In this paper, the basic ...

Abstract: Algorithms that produce classifiers with large margins, such as support vector machines (SVMs), AdaBoost, etc, are receiving more and more attention in the literature. A real application of SVMs for synthetic aperture radar automatic target recognition (SAR/ATR) is presented and the result is compared with conventional classifiers. The SVMs are tested for classification both in closed and open sets (recognition). Experimental results showed that SVMs outperform conventional classifiers in target classification. Moreover, SVMs with the Gaussian kernels are able to form a local "bounded" decision region around each class that presents better rejection to confusers.

Abstract: The Bayesian evidence framework is applied in this paper to least squares support vector machine (LS-SVM) regression in order to infer nonlinear models for predicting a financial time series and the related volatility. On the first level of inference, a statistical framework is related to the LS-SVM formulation which allows one to include the time-varying volatility of the market by an appropriate choice of several hyper-parameters. The hyper-parameters of the model are inferred on the second level of inference. The inferred hyper-parameters, related to the volatility, are used to construct a volatility model within the evidence framework. Model comparison is performed on the third level of inference in order to automatically tune the parameters of the kernel function and to select the relevant inputs. The LS-SVM formulation allows one to derive analytic expressions in the feature space and practical expressions are obtained in the dual space replacing the inner product by the related kernel function using Mercer's theorem. The one step ahead prediction performances obtained on the prediction of the weekly 90-day T-bill rate and the daily DAX30 closing prices show that significant out of sample sign predictions can be made with respect to the Pesaran-Timmerman test statistic.

Abstract: This chapter presents a summary of the issues discussed during the one day workshop on “Support Vector Machines (SVM) Theory and Applications” organized as part of the Advanced Course on Artificial Intelligence (ACAI ’99) in Chania, Greece [19]. The goal of the chapter is twofold: to present an overview of the background theory and current understanding of SVM, and to discuss the papers presented as well as the issues that arose during the workshop.

Abstract: We present a component-based method and two global methods for face recognition and evaluate them with respect to robustness against pose changes. In the component system we first locate facial components, extract them and combine them into a single feature vector which is classified by a Support Vector Machine (SVM). The two global systems recognize faces by classifying a single feature vector consisting of the gray values of the whole face image. In the first global system we trained a single SVM classifier for each person in the database. The second system consists of sets of viewpoint-specific SVM classifiers and involves clustering during training. We performed extensive tests on a database which included faces rotated up to about 40/spl deg/ in depth. The component system clearly outperformed both global systems on all tests.

Abstract: A number of linear classification methods such as the linear least squares fit (LLSF), logistic regression, and support vector machines (SVM's) have been applied to text categorization problems. These methods share the similarity by finding hyperplanes that approximately separate a class of document vectors from its complement. However, support vector machines are so far considered special in that they have been demonstrated to achieve the state of the art performance. It is therefore worthwhile to understand whether such good performance is unique to the SVM design, or if it can also be achieved by other linear classification methods. In this paper, we compare a number of known linear classification methods as well as some variants in the framework of regularized linear systems. We will discuss the statistical and numerical properties of these algorithms, with a focus on text categorization. We will also provide some numerical experiments to illustrate these algorithms on a number of datasets.

Abstract: Support Vector Machines (SVMs) are currently the state-of-the-art models for many classification problems but they suffer from the complexity of their training algorithm which is at least quadratic with respect to the number of examples, Hence, it is hopeless to try to solve real-life problems having more than a few hundreds of thousands examples with SVMs. The present paper proposes a new mixture of SVMs that can be easily implemented in parallel and where each SVM is trained on a small subset of the whole dataset. Experiments on a large benchmark dataset (Forest) as well as a difficult speech database, yielded significant time improvement (time complexity appears empirically to locally grow linearly with the number of examples). In addition, and that is a surprise, a significant improvement in generalization was observed on Forest.

Abstract: The use of Support Vector Machines (SVMs) is studied in financial forecasting by comparing it with a multi-layer perceptron trained by the Back Propagation (BP) algorithm. SVMs forecast better than BP based on the criteria of Normalised Mean Square Error (NMSE), Mean Absolute Error (MAE), Directional Symmetry (DS), Correct Up (CP) trend and Correct Down (CD) trend. S&P 500 daily price index is used as the data set. Since there is no structured way to choose the free parameters of SVMs, the generalisation error with respect to the free parameters of SVMs is investigated in this experiment. As illustrated in the experiment, they have little impact on the solution. Analysis of the experimental results demonstrates that it is advantageous to apply SVMs to forecast the financial time series.

Abstract: Neural networks such as multilayer perceptrons and radial basis function networks have been very successful in a wide range of problems. In this paper we give a short introduction to some new developments related to support vector machines (SVM), a new class of kernel based techniques introduced within statistical learning theory and structural risk minimization. This new approach lends to solving convex optimization problems and also the model complexity follows from this solution. We especially focus on a least squares support vector machine formulation (LS-SVM) which enables to solve highly nonlinear and noisy black-box modelling problems, even in very high dimensional input spaces. While standard SVMs have been basically only applied to static problems like classification and function estimation, LS-SVM models have been extended to recurrent models and use in optimal control problems. Moreover, using weighted least squares and special pruning techniques, LS-SVMs can be employed for robust nonlinear estimation and sparse approximation. Applications of (LS)-SVMs to a large variety of artificial and real-life data sets indicate the huge potential of these methods.

Abstract: A new class of Support Vector Machine (SVM) that is applicable to sequential-pattern recognition such as speech recognition is developed by incorporating an idea of non-linear time alignment into the kernel function. Since the time-alignment operation of sequential pattern is embedded in the new kernel function, standard SVM training and classification algorithms can be employed without further modifications. The proposed SVM (DTAK-SVM) is evaluated in speaker-dependent speech recognition experiments of hand-segmented phoneme recognition. Preliminary experimental results show comparable recognition performance with hidden Markov models (HMMs).