提出椭圆威沙特分布的高效估计与学习方法，适用于脑电与遥感数据建模。
Elliptical Wishart distributions: information geometry, maximum likelihood estimator, performance analysis and statistical learning
- 基于信息几何设计两种最大似然估计算法，保证收敛性与唯一性。
- 证明估计量具一致性、渐近正态性及内在费雪效率，理论完备。
- 在真实脑电与高光谱数据上验证分类聚类性能，适合信号处理场景。
本文研究椭圆威沙特分布——一种推广的威沙特分布——在信号处理与机器学习中的应用。提出了两种最大似然估计（MLE）算法：固定点法和基于所推导信息几何的黎曼优化法。分析了MLE的存在性、唯一性及两种算法的收敛性。进一步研究了MLE的统计性质，包括一致性、渐近正态性和内在费雪效率。在统计学习方面，设计了新的分类与聚类方法。针对t-威沙特分布，在模拟数据及真实的脑电（EEG）与高光谱数据上评估了MLE与学习算法的性能，展示了所提方法的实际价值。
原文摘要 · Abstract (English)
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.
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