Large margin pursuit for a Conic Section classifier

Learning a discriminant becomes substantially more difficult when the datasets are high-dimensional and the available samples are few. This is often the case in computer vision and medical diagnosis applications. A novel conic section classifier (CSC) was recently introduced in the literature to handle such datasets, wherein each class was represented by a conic section parameterized by its focus, directrix and eccentricity. The discriminant boundary was the locus of all points that are equi-eccentric relative to each class-representative conic section. Simpler boundaries were preferred for the sake of generalizability. In this paper, we improve the performance of the two-class classifier via a large margin pursuit. When formulated as a non-linear optimization problem, the margin computation is demonstrated to be hard, especially due to the high dimensionality of the data. Instead, we present a geometric algorithm to compute the distance of a point to the non-linear discriminant boundary generated by the CSC in the input space. We then introduce a large margin pursuit in the learning phase so as to enhance the generalization capacity of the classifier. We validate the algorithm on real datasets and show favorable classification rates in comparison to many existing state-of-the-art binary classifiers as well as the CSC without margin pursuit.