Kernelised orthonormal random projection on grassmann manifolds with applications to action and gait-based gender recognition

Abstract

Video surveillance systems require both accurate and efficient operations for biometric classification tasks. Recent research has shown that modelling video data on manifold space leads to significant improvement on classification accuracy. However, processing manifold points directly often requires computationally expensive operations since manifolds are non-Euclidean. In this work, we tackle this problem by projecting the manifold points into a random projection space constructed by orthonormal hyperplanes. As the projection notion in manifold space is generally not well defined, the random projection is done indirectly via the Reproducing Kernel Hilbert Space (RKHS). There are at least two reasons that make random projection for manifold points attractive: (1) by random projection, manifold points can be projected into lower dimensional space while preserving most of the structure in the RKHS; and (2) after random projection, the classification of manifold points can be solved via scalable linear classifiers. Our formulation is novel compared to the previous work in the way that we use an orthogonality constraint in the hyperplane generation. By orthogonalising the hyperplanes, the mutual information between the dimensions in the projected space is maximised; a desirable property for addressing classification problems. Experimental results in two biometric applications such as action and gait-based gender recognition, show that we can achieve better accuracy than the state-of-the-art random projection method for manifold points. Further, comparisons with kernelised classifiers show that our method achieves nearly 3-fold speed up on average whilst maintaining the accuracy.