Training Support Vector Machines Using Frank-Wolfe Optimization Methods

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of Core Vector Machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a Minimal Enclosing Ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs and can thus be used for a wider set of problems

Support Vector Machines in a real time tracking architecture

The standard approach to tracking an object of interest in a video stream is to use an object detector, a classifier and a tracker in sequential order. This work investigates the use of Support Vector Machines (SVM) as classifiers for real-time tracking systems, combining them with Kalman Filter predictors. Support Vector Machines have been proved successful in a variety of classification tasks such as recognizing faces, cars, handwriting and others. However their use has been hampered by the complexity and computational time involved in the training and classification stages. In recent years new methods and techniques for training and classification of Support Vector Machines have been discovered making possible their utilization in real-time applications. These methods have been explored and improved resulting in a framework for fast prototyping and development of real-time tracking systems. New optimal and sub-optimal methods for parallel SVM training based on biased and unbiased versions of the Sequential Minimal Optimization algorithm are presented. They provide a trade-off between time performance and accuracy. Time performance in the classification stage is significantly improved by reducing the number of support vectors with almost no loss in accuracy. New methods to allow the reduction with different kernels are presented. The effectiveness of the approach developed is demonstrated in a face tracking problem where the objective is to track the lips and eyes of a subject in a video stream in real-time