Feature Selection for Linear SVM with Provable Guarantees

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised approach is based on sampling features from support vectors. We prove that the margin in the feature space is preserved to within $\epsilon$-relative error of the margin in the full feature space in the worst-case. In the unsupervised setting, we also provide worst-case guarantees of the radius of the minimum enclosing ball, thereby ensuring comparable generalization as in the full feature space and resolving an open problem posed in Dasgupta et al. We present extensive experiments on real-world datasets to support our theory and to demonstrate that our method is competitive and often better than prior state-of-the-art, for which there are no known provable guarantees.Comment: Appearing in Proceedings of 18th AISTATS, JMLR W&CP, vol 38, 201

Ensemble Learning for Free with Evolutionary Algorithms ?

Evolutionary Learning proceeds by evolving a population of classifiers, from which it generally returns (with some notable exceptions) the single best-of-run classifier as final result. In the meanwhile, Ensemble Learning, one of the most efficient approaches in supervised Machine Learning for the last decade, proceeds by building a population of diverse classifiers. Ensemble Learning with Evolutionary Computation thus receives increasing attention. The Evolutionary Ensemble Learning (EEL) approach presented in this paper features two contributions. First, a new fitness function, inspired by co-evolution and enforcing the classifier diversity, is presented. Further, a new selection criterion based on the classification margin is proposed. This criterion is used to extract the classifier ensemble from the final population only (Off-line) or incrementally along evolution (On-line). Experiments on a set of benchmark problems show that Off-line outperforms single-hypothesis evolutionary learning and state-of-art Boosting and generates smaller classifier ensembles

Support Vector Machines in High Energy Physics

This lecture will introduce the Support Vector algorithms for classification and regression. They are an application of the so called kernel trick, which allows the extension of a certain class of linear algorithms to the non linear case. The kernel trick will be introduced and in the context of structural risk minimization, large margin algorithms for classification and regression will be presented. Current applications in high energy physics will be discussed.Comment: 11 pages, 12 figures. Part of the proceedings of the Track 'Computational Intelligence for HEP Data Analysis' at iCSC 200

Customizing kernel functions for SVM-based hyperspectral image classification

Previous research applying kernel methods such as support vector machines (SVMs) to hyperspectral image classification has achieved performance competitive with the best available algorithms. However, few efforts have been made to extend SVMs to cover the specific requirements of hyperspectral image classification, for example, by building tailor-made kernels. Observation of real-life spectral imagery from the AVIRIS hyperspectral sensor shows that the useful information for classification is not equally distributed across bands, which provides potential to enhance the SVM's performance through exploring different kernel functions. Spectrally weighted kernels are, therefore, proposed, and a set of particular weights is chosen by either optimizing an estimate of generalization error or evaluating each band's utility level. To assess the effectiveness of the proposed method, experiments are carried out on the publicly available 92AV3C dataset collected from the 220-dimensional AVIRIS hyperspectral sensor. Results indicate that the method is generally effective in improving performance: spectral weighting based on learning weights by gradient descent is found to be slightly better than an alternative method based on estimating ";relevance"; between band information and ground trut