Multilinear Isometric Embedding for Visual Pattern Analysis

Abstract

This paper proposes a novel tensor based dimensionality reduction algorithm called Multilinear Isometric Embedding (MIE) based on a representative manifold learning algorithm Isomap. Unlike Isomap that unfolds input data to the vector form, MIE directly works on more general tensor representation and utilizes iterative strategy to seek the low-dimensional equivalence, which best preserves the global geometry. By avoiding the problems caused by data vectorization, MIE reduces the data analysis difficulty and computational cost. More importantly, MIE keeps the intrinsic tensor structure of the data in low-dimensional representation. Meanwhile, MIE inherits the merits of Isomap, i.e., the ability of uncovering the global geometry of high-dimensional observations. By providing explicit embedding function, MIE makes the embedding of new data points to the low-dimensional space straightforward. Experiments on various datasets validate the effectiveness of proposed method.