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

Abstract

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

CLC Number:

TP273

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.

Figures/Tables 13

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Table 1

Fisher measure of different algorithms on CWRU data set"

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

Table 1

Table 2

Fisher measure of different algorithms on OL data subset1"

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

Table 2

Table 3

Fisher measure of different algorithms on OL data subset2"

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

Table 3

Fig.5

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Feature extraction of sparse graph preserving projection based on Riemannian manifold

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