Learning on probabilistic modelling using Grassmann Manifolds

Probabilistic models are playing an important role as building blocks in more sophisticated geometric parametric models. Although probabilistic or parametric models are seemingly very straightforward for making Bayesian inferences from data that are assumed to be drawn from some model into consideration, the barrier to the Bayesian approach is the normalising constants naturally appearing with them. Our main focus in this paper is to make inferences on matrix variate parametric models via Maximum Likelihood Estimation (MLE) using a simple Bayesian approach. For calculating the value of the matrix based normalising constant we propose the Taylor expansion method for very high concentrated parameter. For inferences we have considered the matrix variate Bingham model on Grassman manifolds. The model is then tested for validity and performance on real World databases with best accuracy estimates.