Learning object material categories via pairwise discriminant analysis

In this paper, we investigate linear discriminant analysis (LDA) methods for multiclass classification problems in hyperspectral imaging. We note that LDA does not consider pairwise relations between different classes, it rather assumes equal within and between-class scatter matrices. As a result, we present a pairwise discriminant analysis algorithm for learning class categories. Our pairwise linear discriminant analysis measures the separability of two classes making use of the class centroids and variances. Our approach is based upon a novel cost function with unitary constraints based on the aggregation of pairwise costs for binary classes. We view the minimisation of this cost function as an unconstrained optimisation problem over a Grassmann manifold and solve using a projected gradient method. Our approach does not require matrix inversion operations and, therefore, does not suffer of stability problems for small training sets. We demonstrate the utility of our algorithm for purposes of learning material catergories in hyperspectral images.