Side-information-induced reweighted sparse subspace clustering

Hua Huang; Weiwei Wang; Chengwu Lu; Xiangchu Feng; Ruiqiang He

doi:10.3934/jimo.2020019

Article Contents

2021, Volume 17, Issue 3: 1235-1252. Doi: 10.3934/jimo.2020019

This issue Previous Article Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion Next Article Maximizing reliability of the capacity vector for multi-source multi-sink stochastic-flow networks subject to an assignment budget

Side-information-induced reweighted sparse subspace clustering

1.
School of Mathematics and Statistics, Xidian University, Xi'an 710171, Shaanxi, China
2.
Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, China

^* Corresponding author: Weiwei Wang
^* Corresponding author: Weiwei Wang

Received: February 28, 2019

Revised: June 30, 2019

Early access: January 2020

Published: May 2021

The first author is supported by National Natural Science Foundation of China (Grants 61472303, 61772389)

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Abstract

Subspace clustering segments a collection of data from a union of several subspaces into clusters with each cluster corresponding to one subspace. The geometric information of the dataset reflects its intrinsic structure and can be utilized to assist the segmentation. In this paper, we propose side-information-induced reweighted sparse subspace clustering (SRSSC) for high-dimensional data clustering. In our method, the geometric information of the high-dimensional data points in a target space is utilized to induce subspace clustering as side-information. We solve the method by iterating the reweighted $ l_1 $-norm minimization to obtain the self-representation coefficients of the data and segment the data using the spectral clustering framework. We compare the performance of our proposed algorithm with some state-of-the-art algorithms using synthetic data and three famous real datasets. Our proposed SRSSC algorithm is the simplest but the most effective. In the experiments, the results of these clustering algorithms verify the effectiveness of our proposed algorithm.

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Mathematics Subject Classification: Primary: 62H30, 68T10; Secondary: 90C26.

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Figure 1. Illustration of a simple instance of subspace clustering

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Figure 2. Angles of pairs of data in the databases

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Figure 3. Convergence of SRSSC on the Extended YaleB dataset

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Figure 4. Visualization of the similarity matrices that were obtained by the different methods

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Figure 5. Some sample images from the Extended Yale B database

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Figure 6. The average computation times of the different algorithms using the Yale B dataset

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Figure 7. Some sample images from the COIL 20 database (top) and the images that belong to the same object (bottom)

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Figure 8. Some sample images from the USPS database

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Table 1. Performance comparison of the different algorithms using the synthetic data

Algorithms		LSR	SMR	LRR	SSC	StrSSC	RSSC	Ours
Accuracy	Mean	93.57%	94.35%	92.46%	94.04%	94.08%	96.60%	97.00%
Accuracy	Median	92.85%	94.07%	92.13%	93.60%	93.70%	96.10%	96.90%

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Table 2. The clustering errors (%) of some different algorithms using the Extended Yale B dataset

No. of subject	Algorithms	LSR	SMR	LRR	SSC	StrSSC	RSSC	Ours
2 Subjects	Mean	7.35	1.75	2.13	1.87	1.23	0.57	0.48
2 Subjects	Median	7.03	0.78	0.78	0	0	0	0
3 Subjects	Mean	9.92	3.03	3.49	3.29	2.84	1.08	0.78
3 Subjects	Median	10.41	2.08	2.08	0.52	0.52	0	0.52
4 Subjects	Mean	13.66	3.25	4.86	3.80	2.95	1.65	1.07
4 Subjects	Median	14.07	2.34	3.91	1.95	0.78	0.39	0.39
5 Subjects	Mean	17.56	3.91	5.92	4.33	3.31	2.21	1.40
5 Subjects	Median	17.81	2.50	4.99	2.50	1.25	0.62	0.62
6 Subjects	Mean	20.95	5.28	6.83	4.87	3.73	2.79	1.68
6 Subjects	Median	21.07	2.86	5.99	3.39	2.08	1.30	1.04
7 Subjects	Mean	24.31	6.38	7.75	5.40	4.01	3.43	2.03
7 Subjects	Median	24.10	3.13	7.14	4.46	2.68	1.79	1.34
8 Subjects	Mean	27.52	6.83	11.05	5.92	4.38	3.98	2.59
8 Subjects	Median	27.83	3.71	7.42	4.69	3.13	1.86	1.56
9 Subjects	Mean	31.01	7.14	10.32	6.46	4.56	4.55	2.84
9 Subjects	Median	31.42	4.51	7.81	4.77	3.65	2.43	1.65
10 Subjects	Mean	33.49	7.81	16.95	7.40	4.74	4.90	3.33
10 Subjects	Median	32.81	7.03	18.91	5.63	4.22	3.59	2.03

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Table 3. The clustering errors (%) of some comparative algorithms using the COIL 20 dataset

No. of subject	Algorithms	LSR	SMR	LRR	SSC	StrSSC	RSSC	Ours
2 Subjects	Mean	15.05	13.75	14.86	8.13	0.76	1.35	0.43
2 Subjects	Median	13.91	10.42	13.07	0	0	0	0
3 Subjects	Mean	22.16	21.97	21.81	10.87	1.86	1.37	0.72
3 Subjects	Median	20.22	19.44	19.65	1.85	0	0	0
20 Subjects	Mean(Mdian)	25.49	24.72	24.67	20.07	15.73	16.32	7.78

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Table 4. The clustering errors (%) of some comparative algorithms using the USPS dataset

No. of subject	Algorithms	LSR	SMR	LRR	SSC	StrSSC	RSSC	Ours
2 Subjects	Mean	15.49	15.25	14.76	11.80	11.48	10.90	10.80
2 Subjects	Median	13.91	13.42	13.07	9.00	8.50	9.50	7.00
3 Subjects	Mean	29.13	28.91	28.81	27.59	27.88	27.44	26.67
3 Subjects	Median	27.02	16.34	26.37	21.83	25.67	23.82	21.33
10 Subjects	Mean(Median)	46.25	45.97	45.53	44.89	44.25	44.03	43.95

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