Maximum Discriminant Difference Criterion for Dimensionality Reduction of Tensor Data

Discriminant analysis is an important tool in machine learning. One of the motivations of this paper is to judge whether a dataset is suitable for discriminant analysis. At present, tensor data are becoming more and more popular in machine learning. Another motivation is to propose a dimensionality reduction algorithm of tensor data which facilitates discriminant analysis of tensor data. The first contribution of this paper is to propose a criterion to measure the potential ability of discriminant analysis of a dataset, and the criterion is called Maximum Discriminant Difference (MDD). The second contribution is to propose a dimensionality reduction algorithm of tensor data based on the mode product of tensor and MDD, called MDD-TDR for short. The first innovation of this paper is that, although MDD is inspired by Linear discriminant analysis (LDA), MDD is a criterion, not an algorithm. MDD can be applied to many applications, not just dimensionality reduction. Furthermore, MDD can be applied to both supervised and unsupervised learning. The second innovation is that, unlike many other tenor dimensionality reduction algorithms that are linear and align tenor into a vector for processing, MDD-TDR is nonlinear and iterative, and in each iteration, each dimension of a tensor is dimensionally reduced separately. The experimental results on 5 widely-used landmark datasets show MDD-TDR outperforms 7 related algorithms published in top academic journals in recent years.