Tensor distance based multilinear globality preserving embedding: A unified tensor based dimensionality reduction framework for image and video classification

Image and video classification tasks often suffer from the problem of high-dimensional feature space. How to discover the meaningful, low-dimensional representations of such high-order, high-dimensional observations remains a fundamental challenge. In this paper, we present a unified framework for tensor based dimensionality reduction including a new tensor distance (TD) metric and a novel multilinear globality preserving embedding (MGPE) strategy. Different with the traditional Euclidean distance, which is constrained by orthogonality assumption, TD measures the distance between data points by considering the relationships among different coordinates of high-order data. To preserve the natural tensor structure in low-dimensional space, MGPE directly works on the high-order form of input data and employs an iterative strategy to learn the transformation matrices. To provide faithful global representation for datasets, MGPE intends to preserve the distances between all pairs of data points. According to the proposed TD metric and MGPE strategy, we further derive two algorithms dubbed tensor distance based multilinear multidimensional scaling (TD-MMDS) and tensor distance based multilinear isometric embedding (TD-MIE). TD-MMDS finds the transformation matrices by keeping the TDs between all pairs of input data in the embedded space, while TD-MIE intends to preserve all pairwise distances calculated according to TDs along shortest paths in the neighborhood graph. By integrating tensor distance into tensor based embedding, TD-MMDS and TD-MIE perform tensor based dimensionality reduction through the whole learning procedure and achieve obvious performance improvement on various standard datasets.