Localized subspace pattern classification

Subspace classifiers assume that different output classes primarily lie in different subspaces of the original feature space. Hence, associated with each output class is a projection subspace. The class discriminant function is then the projected distance of a given input vector onto these subspaces (each subspace can be uniquely specified by a projection matrix), the input vector being classified into that class on whose subspace it gives maximal projection. We extend this basic model of a subspace classifier allowing different submanifolds to be associated with a single class. We define a new cost function which incorporates the notion of local manifolds. To obtain the different local submanifolds for each class, we 'cluster' the input space and then compute the projection submanifolds for each class in each cluster. The clustering in the feature space is dependent on the associated class labels of the training examples and proceeds to minimize the overall cost function. Simulation results on standard data sets are used to demonstrate the efficacy of the proposed method.