  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 non-voxel 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 likelihood-based
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 non-voxel information. All
these above demonstrate our algorithm's compelling potential in image set
classification in the coming future.
