Tensor distance based multilinear multidimensional scaling for image and video analysis

This paper presents a novel dimensionality reduction technique named Tensor Distance based Multilinear Multidimensional Scaling (TD-MMDS). First, we propose a new distance metric called Tensor Distance (TD) to build a relationship graph of data points with high-order. Then we employ an iterative strategy to sequentially learn the transformation matrices that can best keep pair-wise TDs of the high-order data in the low-dimensional embedded space. By integrating both tensor distance and tensor embedding, TD-MMDS provides a uniform framework of tensor based dimensionality reduction, which preserves the intrinsic structure of high-order data through the whole learning procedure. Experiments on standard image and video datasets validate the effectiveness of the proposed TD-MMDS.