Elliptical Wishart distributions: information geometry, maximum likelihood estimator, performance analysis and statistical learning
This work addresses statistical modeling challenges in signal processing and machine learning, offering incremental improvements for domain-specific applications like EEG and hyperspectral analysis.
The paper tackles the problem of generalizing Wishart distributions to elliptical Wishart distributions for signal processing and machine learning, proposing two maximum likelihood estimation algorithms and deriving their statistical properties, with results showing improved performance on EEG and hyperspectral data.
This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the $t$-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.