Learning on Fisher-Bingham Model Based on Normalizing Constant

Abstract

Our focus in this work is on the practical applicability of matrix variate Fisher-Bingham model for statistical inferences via Maximum Likelihood Estimation (MLE) technique using simple Bayesian classifier. The practicability of such parametric models on high dimensional data (e.g., via manifold valued data) remained a big hurdle since long i.e., mainly due to the difficult normalising constant naturally appear with them. We applied the method of Saddle Point Approximation (SPA) for calculating the corresponding normalising constant and then tested the validity and performance of the proposed algorithm on two datasets against the state of the art existing techniques and observed that the proposed technique is more suitable for recognition on Grassmann manifolds via a simple Bayesian classifier.