| Several pattern recognition problems in computer vision and medical diagnosis can be posed in the general framework of supervised learning. However, the high-dimensionality of the samples in these domains makes the direct application of off-the-shelf learning techniques problematic. Moreover, in certain cases the cost of collecting large number of samples can be prohibitive.;In this dissertation, we present a novel concept class that is particularly designed to suit high-dimensional sparse datasets. Each member class in the dataset is assigned a prototype conic section in the feature space, that is parameterized by a focus (point), a directrix (hyperplane) and an eccentricity value. The focus and directrix from each class attribute an eccentricity to any given data point. The data points are assigned to the class to which they are closest in eccentricity value. In a two-class classification problem, the resultant boundary turns out to be a pair of degree 8 polynomial described by merely four times the parameters of a linear discriminant.;The learning algorithm involves arriving at appropriate class conic section descriptors. We describe three geometric learning algorithms that are tractable and preferably pursue simpler discriminants so as to improve their performance on unseen test data. We demonstrate the efficacy of the learning techniques by comparing their classification performance to several state-of-the-art classifiers on multiple public domain datasets. |
