Progress in Vision and Robotics

The Vision Flashes are informal working papers intended primarily to stimulate internal interaction among participants in the A.I. Laboratory's Vision and Robotics group. Many of them report highly tentative conclusions or incomplete work. Others deal with highly detailed accounts of local equipment and programs that lack general interest. Still others are of great importance, but lack the polish and elaborate attention to proper referencing that characterizes the more formal literature. Nevertheless, the Vision Flashes collectively represent the only documentation of an important fraction of the work done in machine vision and robotics. The purpose of this report is to make the findings more readily available, but since they are not revised as presented here, readers should keep in mind the original purpose of the papers!

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.