Depth-Adaptive Discriminant Projection with Optimal Transport

Discriminant projection is a key technique for dimensionality reduction, especially in many classification tasks of high-dimensional, small-sample datasets. In this paper, we propose a Depth-Adaptive Discriminant Projection (DADP) method to improve the discriminability of the projection subspace. First, we propose a novel single-layer discriminant projection by adjusting projected points with nonlinear transformation. Second, the single-layer structure is extended to multiple-layer ones according to the proposed Adaptive Depth Determination Criterion (ADDC), naturally constructing a deep projection model with adaptive depth, which makes DADP allow for the avoidance of over-fitting problem for small-scale datasets. Furthermore, the regularized optimal transport (OT) is introduced to learn the optimal weights for pairwise data, which balances the local and global information incorporated in scatter estimation. Experimental results on several high-dimensional, small-scale datasets show the effectiveness of our algorithm both in terms of visualization and classification prediction.