A Least Squares Regression Framework on Manifolds and Its Application to Gesture Recognition

Abstract

Least squares regression is a basic approach for statistical analysis. However, its simplicity has often led to researchers overlooking it for complex recognition problems. In this paper, we present a nonlinear regression framework on manifolds for gesture recognition. Our method is developed based upon two key attributes: underlying geometry and least squares fitting. The former attribute is vital since geometry characterizes the space for classification while the latter exhibits a simple estimation model. Considering geometric properties, we formulate least squares regression as a composite function. This gives a natural extension from Euclidean space to manifolds. Our experiments show that the proposed framework achieves state-of-the-art results on the standard hand gesture and body gesture datasets. Our method also generalizes well on the one-shot-learning CHALEARN gesture challenge.