基于黎曼流形的稀疏图保持投影的特征提取

doi:10.13229/j.cnki.jdxbgxb20200589

摘要/Abstract

摘要：

为了解决流形学习算法在欧式空间提取的特征不够显著的问题，提出了一种基于黎曼流形的稀疏图保持投影算法，并用于轴承的故障诊断。首先，计算原始数据的对称正定矩阵，构造对称正定流形（SPD流形）。其次，利用正则技术探索SPD流形中的稀疏结构，在此基础上分别建立样本的类内内在图和类间惩罚图，并通过图嵌入的方法实现数据的特征提取。实验结果表明，基于黎曼流形的稀疏图保持投影算法能提取到显著的特征。

关键词: 控制科学与工程, 黎曼流形, 稀疏表示, 图嵌入, 特征提取

Abstract:

To solve the problem that the feature extracted by the manifold learning algorithm in Euclidean space is not significant enough, this paper proposes a sparse graph preserving projection algorithm based on Riemannian manifold and applies it to bearing fault diagnosis. Firstly, the symmetric positive definite matrix of the original data is calculated to construct the Symmetric Positive Definite manifold (SPD manifold). Secondly, the sparse structure of the SPD manifold is explored by using the regularization technique. On this basis, the intrinsic graph of within-class and the penalty graph of the between-class of the sample are established respectively. Finally, the feature extraction of the data is realized by the method of graph embedding. Experimental results show that the sparse graph preserving projection algorithm based on Riemannian manifold can extract significant features.

Key words: control science and engineering, Riemannian manifold, sparse representation, graph embedding, feature extraction

中图分类号:

TP273

刘远红,郭攀攀,张彦生,李鑫. 基于黎曼流形的稀疏图保持投影的特征提取[J]. 吉林大学学报(工学版), 2021, 51(6): 2268-2279.

Yuan-hong LIU,Pan-pan GUO,Yan-sheng ZHANG,Xin LI. Feature extraction of sparse graph preserving projection based on Riemannian manifold[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(6): 2268-2279.

图/表 13

图1

图2

图3

图4

表1

不同算法在CWRU数据集上的Fisher度量"

算法	$t r (S b)$	$t r (S w)$	$F$
SPP	0.0913	1.3848	0.0659
LPP	3.18×10^-4	3.74×10^-5	8.5185
DSCPE	6.9762	0.2502	27.8793
黎曼SPP	4.73×10^-28	2.40×10^-27	0.1968
黎曼LPP	8.38×10^-28	2.97×10^-29	28.2356
SGPPRM	3.07×10^-29	5.38×10^-31	56.9958

表1

表2

不同算法在OL数据子集1上的Fisher度量"

算法	$t r (S b)$	$t r (S w)$	$F$
SPP	1.17×10^-6	1.42×10^-5	0.0820
LPP	3.10×10^-4	2.27×10^-5	13.7130
DSCPE	1.27×10^-4	7.63×10^-6	16.6818
黎曼SPP	1.16×10^-28	1.51×10^-26	0.0077
黎曼LPP	1.19×10^-30	2.18×10^-30	0.5450
SGPPRM	1.04×10^-21	7.98×10^-25	1300.0665

表2

表3

不同算法在OL数据子集2上的Fisher度量"

算法	$t r (S b)$	$t r (S w)$	$F$
SPP	3.02×10^-7	1.70×10^-5	0.0178
LPP	1.34×10^-4	8.54×10^-35	1.5740
DSCPE	1.73×10^-3	1.15×10^-4	15.0967
黎曼SPP	1.80×10^-30	5.18×10^-29	0.0347
黎曼LPP	1.99×10^-27	1.28×10^-28	15.5541
SGPPRM	2.62×10^-30	5.62×10^-32	46.6698

表3

图5

图6

图7

图8

图9

图10

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