A method is presented for deriving an optimal basis for features classified with a support vector machine. The method is based on minimizing the leave-one-out error which is approximated by the radius-margin bound. A gradient descent method provides a learning rule for the basis in an outer loop of an iteration. The inner loop performs support vector machine training and provides support vector coefficients on which the gradient descent depends. In this way, the derivation of a basis for feature extraction and the support vector machine are jointly optimized. The efficacy of the method is illustrated with examples from multi-dimensional synthetic data sets

An algorithm that discovers a compact data representation for support vector classification is presented. The algorithm finds a basis which reduces the volume occupied by the coefficients in subspace. This volume reduction is driven by the support vectors of a support vector machine. A compact support vector representation (CSVR) of this form is shown to exhibit good generalization in the form of large margin and a small number of support vectors, while achieving low classification error rates. The compact nature of the data representation is shown to be particularly effective in representing correlated image sets such as those found in databases where faces and objects are imaged under varying lighting or pose.

A method employing independent component analysis (ICA) to measure the position of a camera and the pose of an object from images in the presence of occlusion is presented. ICA is used to provide a low-dimensional representation of a set of images taken throughout a range of camera positions and object poses. Using the low-dimensional independent component subspace arbitrary camera locations or object poses can then be determined. The ICA technique is compared with principal component analysis (PCA) in the presence of varying degrees of occlusion. Occlusions of translation, pan and pose images were experimentally applied to provide a demonstration of the performance of this method. The independent component subspace is shown to provide more accurate position and pose information than PCA.