Structural Laplacian Eigenmaps for Modeling Sets of Multivariate Sequences

A novel embedding-based dimensionality reduction approach, called structural Laplacian Eigenmaps, is proposed to learn models representing any concept that can be defined by a set of multivariate sequences. This approach relies on the expression of the intrinsic structure of the multivariate sequences in the form of structural constraints, which are imposed on dimensionality reduction process to generate a compact and data-driven manifold in a low dimensional space. This manifold is a mathematical representation of the intrinsic nature of the concept of interest regardless of the stylistic variability found in its instances. In addition, this approach is extended to model jointly several related concepts within a unified representation creating a continuous space between concept manifolds. Since a generated manifold encodes the unique characteristic of the concept of interest, it can be employed for classification of unknown instances of concepts. Exhaustive experimental evaluation on different datasets confirms the superiority of the proposed methodology to other state-of-the-art dimensionality reduction methods. Finally, the practical value of this novel dimensionality reduction method is demonstrated in three challenging computer vision applications, i.e., view-dependent and view-independent action recognition as well as human-human interaction classification.