Dimensionality Reduction for Tensor Data Based on Local Decision Margin Maximization.

In machine learning, the idea of maximizing the margin between two classes is widely used in classifier design. Enlighted by the idea, this paper proposes a novel supervised dimensionality reduction method for tensor data based on local decision margin maximization. The proposed method seeks to preserve and protect the local discriminant information of the original data in the low-dimensional data space. Firstly, we depart the original tensor dataset into overlapped localities with discriminant information. Then, we extract the similarity and anti-similarity coefficients of each high-dimensional locality and preserve these coefficients in the embedding data space via the multilinear projection scheme. Under the combined effect of these coefficients, each dimension-reduced locality tends to be a convex set where strongly correlated intraclass points gather. Simultaneously, the local decision margin, which is defined as the shortest distance from the boundary of each locality to the nearest point of each side, will be maximized. Therefore, the local discriminant structure of the original data could be well maintained in the low-dimensional data space. Moreover, a simple iterative scheme is proposed to solve the final optimization problem. Finally, the experiment results on 6 real-world datasets demonstrate the effectiveness of the proposed method.