Non-linear sparse and group sparse classifier

Recently there has been an interest in a new classification model, where it is assumed that the training samples for a particular class form a linear basis for any new test sample belonging to that class. This assumption led to two successful classification methods called the Sparse Classifier (SC) and the Group Sparse Classifier (GSC). This work generalizes the previous linearity assumption and accounts for non-linear functional relationship between the training samples of a class and a new test sample belonging to that class. Such a generalization requires solving sparse/group-sparse optimization problems with non-linear constraints. We develop exact optimization based algorithms as well as approximate (fast) algorithms to solve such hitherto un-addressed optimization problem. Results show that significant improvement can be achieved by the proposed Non-Linear Sparse Classifiers compared to previous Sparse/Group Sparse Classifiers.