The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation withvarious interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

The theoretical understanding of support vector machines (SVMs) and related kernel-based methods has been substantially improved in recent years.

We consider the task of tuning hyperparameters in SVM models based on minimizing a smooth performance validation function, e.g., smoothed k-fold cross-validation error, using nonlineaI optimization techniques.

VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimizationproblem is non-convex.

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.

A geometric framework for understanding multi-category classification is introduced, through which many existing 'all-together' algorithms can be understood. The structure enables parsimonious optimisation, through a direct extension of the binary methodology. The focus is on Support Vector Classification, with parallels drawn to related methods. The ability of the framework to compare algorithms is illustrated by a brief discussion of Fisher consistency. Its utility in improving understanding of multi-category analysis is demonstrated through a derivation of improved generalisation bounds. It is also described how this architecture provides insights regarding how to further improve on the speed of existing multi-category classification algorithms. An initial example of how this might be achieved is developed in the formulation of a straightforward multi-category Sequential Minimal Optimisation algorithm. Proof-of-concept experimental results have shown that this, combined with the mapping of pairwise results, is comparable with benchmark optimisation speeds.

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind these two types of methods, namely how to transform linear algorithms into nonlinear ones by using kernel functions, and how to make predictions with an ensemble or a collection of models rather than a single model. I also share my personal perspectives on how these ideas have influenced and shaped my own research. In particular, I present two recent algorithms that I have invented with my collaborators: LAGO, a fast kernel algorithm for unbalanced classification and rare target detection; and Darwinian evolution in parallel universes, an ensemble method for variable selection.

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the set of posterior probability measures, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We then discuss relative bounds, comparing the generalization error of two classification rules, showing how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model.We show how to associate to any posterior distribution an effective temperature relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate converges according to the best possible power of the sample size adaptively under any margin and parametric complexity assumptions. We describe and study an alternative selection scheme based on relative bounds between estimators, and present a two step localization technique which can handle the selection of a parametric model from a family of those. We show how to extend systematically all the results obtained in the inductive setting to transductive learning, and use this to improve Vapnik's generalization bounds, extending them to the case when the sample is made of independent non-identically distributed pairs of patterns and labels. Finally we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through the value of the transductive or inductive margin.

This has been made possible by advancements in satellite sensor technology thus enabling the acquisition of land cover information over large areas at various spatial, temporal spectral and radiometric resolutions. The process of relating pixels in a satellite image to known land cover is called image classification and the algorithms used to effect the classification process are called image classifiers (Mather, 1987). The extraction of land cover information from satellite images using image classifiers has been the subject of intense interest and research in the remote sensing community (Foody and Mathur, 2004b). Some of the traditional classifiers that have been in use in remote sensing studies include the maximum likelihood, minimum distance to means and the box classifier. As technology has advanced, new classification algorithms have become part of the main stream image classifiers such as decision trees and artificial neural networks. Studies have been made to compare these new techniques with the traditional ones and they have been observed to post improved classification accuracies (Peddle et al. 1994; Rogan et al. 2002; Li et al. 2003; Mahesh and Mather, 2003).

Data collection often results in records that have missing values or variables. This investigation compares 3 different data imputation models and identifies their merits by using accuracy measures. Autoencoder Neural Networks, Principal components and Support Vector regression are used for prediction and combined with a genetic algorithm to then impute missing variables. The use of PCA improves the overall performance of the autoencoder network while the use of support vector regression shows promising potential for future investigation. Accuracies of up to 97.4 % on imputation of some of the variables were achieved.