Large-Scale Sonar Target Detection with l1-Norm SV Regression based on Unfeasible Interior Point Methods

Support Vector Machines (SVMs) have become one of the most popular supervised learning-machines in the statistical pattern recognition area. They are used for classification (i.e. SVM) and regression analysis (i.e. Support Vector Regression, SVR). However, when the number of samples available to model an SVM/SVR problem supersedes the computational resources (i.e. large-scale problems where the number of dimensions or samples are in the order of millions) the traditional methods fail in finding the optimal solution to a classification problem based on regression models. The reason for the typical failures is that the solution finding process involves high-dimensional vector operations. The aim of this research is to overcome the natural limitation of largescale problems particular to SVR using an efficient convex linear programming framework. We propose a sequential decomposition method based on a linear programming support vector regression (SLP-SVR) approach. The proposed scheme uses an interior point method (IPM) to solve a sequence of smaller LP optimization sub-problems given by the proposed decomposition strategy. Then we perform chunking (preserve the the support vectors) of the sub-problem at each iterate. We take advantage of the quadratic rate of convergence of IPM on the proposed LP-SVR method to finds the global solution to the regression/classification problem in few iterates. Experiments were performed to solve the large-scale sonar mine-rocks detection problem show fast rate of convergence, and very good performance when compared to other approaches such as neural networks and PCA-based methods. The proposed linear programming formulation is efficient from the mathematical point of view and the sequential decomposition strategy using IPM poses fast rate of convergence to make the proposed model also efficient from the computational point of view.