MLE-Based learning on Grassmann manifolds

In this paper we focus on Maximum Likelihood Estimation (MLE) technique for classification on Grassmann manifolds using matrix variate Bingham density function. Unlike the conventional techniques for multivariate distributions in the existing literature e.g., Markov chain Monte Carlo (MCMC) sampling methods, non-parametric methods, Expectation Maximisation (EM) iterative methods or exact methods, we demonstrate a new way of parametric modelling for classification that is strictly based on normalising constant. The evaluation of normalising constant is based on the matrix-variate Saddle Point Approximation (SPA). The Maximum Likelihood Estimation (MLE) is directly employed on the proposed manifold based Bingham density function via simple Bayesian classifier. For numerical experiments a 3-class classification example is considered by using real world Caltech 101 and DynTex++ database. We have compared our average classification accuracy rate with the baseline results taken from the existing state of the art techniques, and found that our method outperforms or at least best comparable.