Hilbert–Schmidt Independence Criterion Subspace Learning on Hybrid Region Covariance Descriptor for Image Classification

The region covariance descriptor (RCD), which is known as a symmetric positive definite (SPD) matrix, is commonly used in image representation. As SPD manifolds have a non-Euclidean geometry, Euclidean machine learning methods are not directly applicable to them. In this work, an improved covariance descriptor called the hybrid region covariance descriptor (HRCD) is proposed. The HRCD incorporates the mean feature information into the RCD to improve the latter’s discriminative performance. To address the non-Euclidean properties of SPD manifolds, this study also proposes an algorithm called the Hilbert-Schmidt independence criterion subspace learning (HSIC-SL) for SPD manifolds. The HSIC-SL algorithm is aimed at improving classification accuracy. This algorithm is a kernel function that embeds SPD matrices into the reproducing kernel Hilbert space and further maps them to a linear space. To make the mapping consider the correlation between SPD matrices and linear projection, this method introduces global HSIC maximization to the model. The proposed method is compared with existing methods and is proved to be highly accurate and valid by classification experiments on the HRCD and HSIC-SL using the COIL-20, ETH-80, QMUL, face data FERET, and Brodatz datasets.