Enhanced Grassmann discriminant analysis with randomized time warping for motion recognition

Abstract

This paper proposes a framework for classifying motion sequences, by extending the framework of Grassmann discriminant analysis (GDA). A problem of GDA is that its discriminant space is not necessarily optimal. This limitation becomes even more prominent when utilizing the subspace representation of randomized time warping (RTW). RTW is a sequence representation that can effectively model a motion’s temporal information by a low-dimensional subspace, simplifying the problem of comparing two sequences to that of comparing two subspaces. The key idea of the proposed enhanced GDA is projecting class subspaces onto a generalized difference subspace before mapping them on a Grassmann manifold. The GDS projection can remove overlapping components of the subspaces in the vector space, nearly orthogonalizing them. Consequently, a dictionary of orthogonalized class subspaces produces a set of more discriminant data points in the Grassmann manifold, in comparison with the original set. This set of data points can further enhance the discriminant ability of GDA. We demonstrate the validity of the proposed framework, RTW+eGDA, through experiments on motion recognition using the publicly available Cambridge gesture, KTH action, and UCF sports datasets.