基于黎曼核的多核集成计算机视觉分类方法  

A Multi Core Integrated Computer Vision Classification Method Based on Riemann Kernel

作　　者：夏伟 沈玉琳[2] 张仲荣 

机构地区：[1]兰州交通大学数理学院,甘肃 兰州 [2]甘肃省计算中心,甘肃 兰州

出　　处：《应用数学进展》2023年第11期4789-4797,共9页Advances in Applied Mathematics

摘　　要：在计算机视觉领域,使用空间协方差矩阵作为基础的简单分类应用已经被广泛研究和应用。然而,传统的方法在处理非线性问题时存在一定的局限性。为了克服这些局限性,本文提出了一种新的方法,即通过建立与对称正定矩阵的黎曼流形的连接,构建一个新的核——黎曼核。黎曼核是基于黎曼流形的核方法,它能够更好地处理非线性问题。通过将黎曼核与支持向量机相结合,我们可以得到一种更加强大的分类器。我们在常用的计算机视觉数据集上进行了一系列的实验。在实验中,我们使用了不同的内核结合支持向量机的方法,并采用了多核学习和RFE特征筛选方法来进一步提升分类性能。实验结果表明,使用黎曼核的方法在各个数据集上都取得了明显优于改进前算法的结果。这说明黎曼核方法能够有效地取代传统的多核SVM方法,提供更好的分类性能。In the field of computer vision, simple classification applications based on spatial covariance matri-ces have been widely studied and applied. However, traditional methods have certain limitations when dealing with nonlinear problems. To overcome these limitations, this article proposes a new method of constructing a new kernel—the Riemannian kernel—by establishing a connection with the Riemannian manifold of a symmetric positive definite matrix. Riemannian kernel is a kernel method based on Riemannian manifolds, which can better handle nonlinear problems. By combin-ing Riemann kernels with support vector machines, we can obtain a more powerful classifier. We conducted a series of experiments on commonly used computer vision datasets. In the experiment, we used different kernels combined with support vector machines, and adopted multi kernel learning and RFE feature filtering methods to further improve classification performance. The ex-perimental results show that the method using Riemannian kernels has achieved significantly bet-ter results than the improved algorithm on all datasets. This indicates that the Riemann kernel method can effectively replace traditional multi-core SVM methods and provide better classification performance.

关 键 词：黎曼流形 计算机视觉 对称正定矩阵 空间协方差矩阵 多核学习 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]