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

Xi Liu,Zhengming Ma,Peng Yang,Zehui Zhan

doi:10.1155/2021/6663710

Abstract

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.

Highlights

A growing number of non-Euclidean data, such as symmetric positive definite (SPD) manifolds [1] and Grassmann manifolds [2], are often encountered in vision recognition tasks
We construct a new image descriptor by directly incorporating the mean feature information into the RCD. e new image descriptor is called the hybrid region covariance descriptor (HRCD). e HRCD inherits the advantages of the RCD, and it is more discriminable than the RCD. e images represented by the HRCD are SPD matrices that lie on SPD manifolds
The performance of the RCD and HRCD and the effectiveness of HilbertSchmidt independence criterion subspace learning (HSIC-SL) and the other algorithms were compared. e following observations were made: (1) e classification accuracy in the image feature space represented by the HRCD was better than that by the RCD regardless of which classifier was used (i.e., KNN classifier without feature extraction or the proposed Hilbert–Schmidt independence criterion (HSIC)-SL). e result showed that the proposed image descriptor HRCD outperformed the RCD

Summary

Introduction

A growing number of non-Euclidean data, such as symmetric positive definite (SPD) manifolds [1] and Grassmann manifolds [2], are often encountered in vision recognition tasks. We mainly discuss the image classification on SPD manifolds. E RCD has been proved to be an effective descriptor in a variety of applications [10,11,12]. It captures the correlation between different features of an image and represents the image with a covariance matrix. The mean vector of features has been proved to be significant in image recognition tasks [13, 14]. We construct a new image descriptor by directly incorporating the mean feature information into the RCD. Given the non-Euclidean geometry of Riemannian manifolds, directly using most of the conventional machine learning methods on Riemannian manifolds is inadequate [15, 16]. erefore, the classification of the points on Riemannian manifolds has become a hot research topic

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