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.

Validating Co-Training Models for Web Image Classification

Co-training is a semi-supervised learning method that is designed to take advantage of the redundancy that is present when the object to be identified has multiple descriptions. Co-training is known to work well when the multiple descriptions are conditional independent given the class of the object. The presence of multiple descriptions of objects in the form of text, images, audio and video in multimedia applications appears to provide redundancy in the form that may be suitable for co-training. In this paper, we investigate the suitability of utilizing text and image data from the Web for co-training. We perform measurements to find indications of conditional independence in the texts and images obtained from the Web. Our measurements suggest that conditional independence is likely to be present in the data. Our experiments, within a relevance feedback framework to test whether a method that exploits the conditional independence outperforms methods that do not, also indicate that better performance can indeed be obtained by designing algorithms that exploit this form of the redundancy when it is present.