Tensor distance based multilinear locality-preserved maximum information embedding

This brief paper presents a unified framework for tensor-based dimensionality reduction (DR) with a new tensor distance (TD) metric and a novel multilinear locality-preserved maximum information embedding (MLPMIE) algorithm. Different from traditional Euclidean distance, which is constrained by the orthogonality assumption, TD measures the distance between data points by considering the relationships among different coordinates. To preserve the natural tensor structure in low-dimensional space, MLPMIE directly works on the high-order form of input data and iteratively learns the transformation matrices. In order to preserve the local geometry and to maximize the global discrimination simultaneously, MLPMIE keeps both local and global structures in a manifold model. By integrating TD into tensor embedding, TD-MLPMIE performs tensor-based DR through the whole learning procedure, and achieves stable performance improvement on various standard datasets.