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Mixed Region Covariance Discriminative Learning for Image Classification on Riemannian Manifolds

机译：黎曼流形上图像分类的混合区域协方差判别学习

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摘要

Covariance matrices, known as symmetric positive definite (SPD) matrices, are usually regarded as points lying on Riemannian manifolds. We describe a new covariance descriptor, which could improve the discriminative learning ability of region covariance descriptor by taking into account the mean of feature vectors. Due to the specific geometry of Riemannian manifolds, classical learning methods cannot be directly used on it. In this paper, we propose a subspace projection framework for the classification task on Riemannian manifolds and give the mathematical derivation for it. It is different from the common technique used for Riemannian manifolds, which is to explicitly project the points from a Riemannian manifold onto Euclidean space based upon a linear hypothesis. Under the proposed framework, we define a Gaussian Radial Basis Function- (RBF-) based kernel with a Log-Euclidean Riemannian Metric (LERM) to embed a Riemannian manifold into a high-dimensional Reproducing Kernel Hilbert Space (RKHS) and then project it onto a subspace of the RKHS. Finally, a variant of Linear Discriminative Analyze (LDA) is recast onto the subspace. Experiments demonstrate the considerable effectiveness of the mixed region covariance descriptor and the proposed method.
机译：协方差矩阵（称为对称正定（SPD）矩阵）通常被视为位于黎曼流形上的点。我们描述了一种新的协方差描述符，它可以通过考虑特征向量的均值来提高区域协方差描述符的判别学习能力。由于黎曼流形的特定几何形状，经典的学习方法不能直接在其上使用。在本文中，我们为黎曼流形上的分类任务提出了一个子空间投影框架，并对其进行了数学推导。它与用于黎曼流形的常用技术不同，后者是基于线性假设将黎曼流形的点显式投影到欧几里得空间上的。在提出的框架下，我们定义了基于高斯径向基函数（RBF-）的内核，并使用对数-欧几里德黎曼度量（LERM）将黎曼流形嵌入到高维复制内核希尔伯特空间（RKHS）中，然后对其进行投影到RKHS的子空间上。最后，将线性判别分析（LDA）的变体重铸到子空间上。实验证明了混合区域协方差描述符和所提出方法的有效性。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第5期|1261398.1-1261398.11|共11页
  • 作者

    Liu Xi; Ma Zhengming; Niu Guo;

  • 作者单位

    Sun Yat Sen Univ, Sch Elect & Informat Technol, Guangzhou 510006, Guangdong, Peoples R China;

    Sun Yat Sen Univ, Sch Elect & Informat Technol, Guangzhou 510006, Guangdong, Peoples R China|Sun Yat Sen Univ, Nanfang Coll, Guangzhou 510275, Guangdong, Peoples R China;

    Foshan Univ, Sch Elect Informat Engn, Foshan 528000, Peoples R China;

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