Discriminative Tensor Decomposition with Large Margin

Tensor decompositions have many application areas in several domains where one key application is revealing relational structure between multiple dimensions simultaneously and thus enabling the compression of relational data. In this paper, we propose the Discriminative Tensor Decomposition with Large Margin (shortly, Large Margin Tensor Decomposition, LMTD), which can be viewed as a tensor-to-tensor projection operation. It is a novel method for calculating the mutual projection matrices that map the tensors into a lower dimensional space such that the nearest neighbor classification accuracy is improved. The LMTD aims finding the mutual discriminative projection matrices which minimize the misclassification rate by minimizing the Frobenius distance between the same class instances (in-class neighbors) and maximizing the distance between different class instances (impostor neighbors). Two versions of LMTD are proposed, where the nearest neighbor classification error is computed in the feature (latent) or input (observations) space. We evaluate the proposed models on real data sets and provide a comparison study with alternative decomposition methods in the literature in terms of their classification accuracy and mean average precision.