Positive-definite matrix-variate data is becoming popular in computer vision. The computer vision data descriptors in the form of Region Covariance Descriptors (RCD) are positive definite matrices, which extract the key features of the images. The RCDs are extensively used in image set classification. Some classification methods treating RCDs as Wishart distributed random matrices are being proposed. However, the majority of the current methods preclude the potential correlation among the RCDs caused by the so-called auxiliary information (e.g., subjects’ ages and nose widths, etc). Modeling correlated Wishart matrices is difficult since the joint density function of correlated Wishart matrices is difficult to be obtained. In this paper, we propose an Expectation-Maximization composite likelihoodbased algorithm of Wishart matrices to tackle this issue. Given the numerical studies based on the synthetic data and the real data (Chicago face data-set), our proposed algorithm performs better than the alternative methods which do not consider the correlation caused by the so-called auxiliary information.

中文翻译：

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通过基于期望最大化复合似然的算法进行相关 Wishart 矩阵分类

正定矩阵变量数据在计算机视觉中变得越来越流行。区域协方差描述符（RCD）形式的计算机视觉数据描述符是正定矩阵，用于提取图像的关键特征。RCD 广泛用于图像集分类。一些将 RCD 视为 Wishart 分布式随机矩阵的分类方法正在被提出。然而，目前的大多数方法排除了由所谓的辅助信息（例如，受试者的年龄和鼻子宽度等）引起的RCD之间的潜在相关性。对相关 Wishart 矩阵进行建模很困难，因为相关 Wishart 矩阵的联合密度函数很难获得。在本文中，我们提出了一种基于 Wishart 矩阵的期望最大化复合似然算法来解决这个问题。鉴于基于合成数据和真实数据（芝加哥人脸数据集）的数值研究，我们提出的算法比不考虑所谓辅助信息引起的相关性的替代方法表现得更好。