Gaëlle Loosli

Learning SVM in Kreĭn Spaces

This paper presents a theoretical foundation for an SVM solver in Kreĭn spaces. Up to now, all methods are based either on the matrix correction, or on non-convex minimization, or on feature-space embedding. Here we justify and evaluate a solution that uses the original (indefinite) similarity measure, in the original Kreĭn space. This solution is the result of a stabilization procedure. We establish the correspondence between the stabilization problem (which has to be solved) and a classical SVM based on minimization (which is easy to solve). We provide simple equations to go from one to the other (in both directions). This link between stabilization and minimization problems is the key to obtain a solution in the original Kreĭn space. Using KSVM, one can solve SVM with usually troublesome kernels (large negative eigenvalues or large numbers of negative eigenvalues). We show experiments showing that our algorithm KSVM outperforms all previously proposed approaches to deal with indefinite matrices in SVM-like kernel methods.

Boîte à outils SVM simple et rapide

If SVM (Support Vector Machines) are now considered as one of the best learning methods, they are still considered as slow. Here we propose a Matlab toolbox that enables the usage of SVM in a fast and simple way. This is done thanks to the projected gradient method which is well adapted to the problem : SimpleSVM (VIS 03). We chose to implement this algorithm with Matlab environment since it is user-friendly and efficient - it uses the ATLAS (Automatically Tuned Linear Algebra Software) library. The comparison to the state of the art in this field, SMO (Sequential Minimal Optimization) shows that in some cases, our solution is faster and less complex. In order to point out how fast and simple our method is, we give here results on the MNITS database. It was possible to compute a satisfying solution in a quite short time (one hour and a half on a PC with Linux distribution to compute 45 binary classifiers, with

Regularization Paths for ν -SVM and ν -SVR

This paper presents the ν-SVM and theν-SVR full regularization paths along with aleave-one-out inspired stopping criterion and an efficientimplementation. In the ν-SVR method, two parameters areprovided by the user: the regularization parameter Candνwhich settles the width of the ν-tube. Inthe classical ν-SVM method, parameter νisan lower bound on the number of support vectors in the solution.Based on the previous works of [1,2], extensions of regularizationpaths for SVM and SVR are proposed and permit to automaticallycompute the solution path by varying νor theregularization parameter.

Handling missing weak classifiers in boosted cascade: application to multiview and occluded face detection

We propose a generic framework to handle missing weak classifiers at testing stage in a boosted cascade. The main contribution is a probabilistic formulation of the cascade structure that considers the uncertainty introduced by missing weak classifiers. This new formulation involves two problems: (1) the approximation of posterior probabilities on each level and (2) the computation of thresholds on these probabilities to make a decision. Both problems are studied, and several solutions are proposed and evaluated. The method is then applied to two popular computer vision applications: detecting occluded faces and detecting faces in a pose different than the one learned. Experimental results are provided using conventional databases to evaluate the proposed strategies related to basic ones.

Improving existing cascaded face classifier by adding occlusion handling

Recent face detectors used in human robot interaction are boosted cascades. These cascades can detect upright faces but are very sensible to occlusions. We propose a generic framework to handle occlusions at prediction time in a boosted cascade. The contribution is a probabilistic formulation of the cascade structure that considers the uncertainty introduced by missing weak classifiers. This new formulation involves two problems: (1) the approximation of posterior probabilities on each level and (2) the computation of thresholds on these probabilities to make a decision. Both problems are studied and solutions are proposed and evaluated. The method is then applied on the problem of occluded faces detection. Experimental results are provided on classic databases to evaluate the proposed solution related to the basic one.