  In the domain of pattern recognition, using the SPD (Symmetric Positive
Definite) matrices to represent data and taking the metrics of resulting
Riemannian manifold into account have been widely used for the task of image
set classification. In this paper, we propose a new data representation
framework for image sets named CSPD (Component Symmetric Positive Definite).
Firstly, we obtain sub-image sets by dividing the image set into square blocks
with the same size, and use traditional SPD model to describe them. Then, we
use the results of the Riemannian kernel on SPD matrices as similarities of
corresponding sub-image sets. Finally, the CSPD matrix appears in the form of
the kernel matrix for all the sub-image sets, and CSPDi,j denotes the
similarity between i-th sub-image set and j-th sub-image set. Here, the
Riemannian kernel is shown to satisfy the Mercer's theorem, so our proposed
CSPD matrix is symmetric and positive definite and also lies on a Riemannian
manifold. On three benchmark datasets, experimental results show that CSPD is a
lower-dimensional and more discriminative data descriptor for the task of image
set classification.
