Modular discriminant analysis and its applications

摘要

We propose a multi-linear algebra based subspace learning approach for finding linear projection which preserves some implicit structural or locally-spatial information among the original feature space. Our method uses a new tensor data representation model, in which, each group of data points are partitioned into several equal-sized sub-groups with its neighbors affiliated to them, and all sub-groups are concatenated to represent as the tensor space product of the original feature space. Then, a new optimization algorithm called Lagrangian multiplier mode (L-mode) is presented for computing the optimal linear projections. We show that our method has three ways for resolving the Small Sample Size problem: by applying the fuzzy matrix model to avoid the disturbance from non-interested determinant, by a quadratic sample correlation model, and by projecting the samples into a manifold using linear programming. Extensive experimental results conducted on two benchmark face biometrics datasets i.e. Yale-B and CMU-PIE, and a nutrition surveillance dataset demonstrate that our method is effective and robust than the state-of-the-arts such as Principal Component Analysis, Linear Discriminant Analysis, Locality Preserving Projections and their variations on both classification accuracies and computational expenses.