Local Linear Coding Based on Riemannian Kernel

DOI：10.13328/j.cnki.jos.004714

 作者 单位 E-mail 姜伟 辽宁师范大学 数学学院, 辽宁 大连 116029 swxxjw@aliyun.com 毕婷婷 辽宁师范大学 数学学院, 辽宁 大连 116029 李克秋 大连理工大学 计算机科学与技术学院, 辽宁 大连 116024 杨炳儒 北京科技大学 计算机与通信工程学院, 北京 100083

最近的研究表明:在许多计算机视觉任务中,将对称正定矩阵表示为黎曼流形上的点能够获得更好的识别性能.然而,已有大多数算法仅由切空间局部逼近黎曼流形,不能有效地刻画样本分布.受核方法的启发,提出了一种新的黎曼核局部线性编码方法,并成功地应用于视觉分类问题.首先,借助于最近所提出的黎曼核,把对称正定矩阵映射到再生核希尔伯特空间中,通过局部线性编码理论建立稀疏编码和黎曼字典学习数学模型;其次,结合凸优化方法,给出了黎曼核局部线性编码的字典学习算法;最后,构造一个迭代更新算法优化目标函数,并且利用最近邻分类器完成测试样本的鉴别.在3个视觉分类数据集上的实验结果表明,该算法在分类精度上获得了相当大的提升.

Recent research has shown that better recognition performance can be attained through representing symmetric positive definite matrices as points on Riemannian manifolds for many computer vision tasks. However, most existing algorithms only approximate the Riemannian manifold locally by its tangent space and are incapable of scaling effectively distribution of samples. Inspired by kernel methods, a novel method, called local linear coding based on Riemannian kernel (LLCRK), is proposed and applied successfully to vision classification issues. Firstly, with the aid of recently introduced Riemannian kernel, symmetric positive definite matrices are mapped into the reproducing kernel Hilbert space by kernel method and a mathematical model of sparse coding and Riemannian dictionary learning is constructed by local linear coding theory. Secondly, an efficient algorithm of LLCRK is presented for dictionary learning according to the convex optimization methods. Finally, an iterative updating algorithm is constructed to optimize the objective function, and the test samples are classified by nearest neighbor classifier. Experimental results on three visual classification data sets demonstrate that the proposed algorithm achieves considerable improvement in discrimination accuracy.
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