基于锚点图的低秩缺失多视图子空间聚类

doi:10.12141/j.issn.1000-565X.220069

摘要/Abstract

摘要：

经典的多视图聚类任务针对的是完整数据，然而实际任务中受限于信息的获取渠道，某些视图往往含有缺失数据，由此引出了缺失多视图聚类问题。针对此问题，现有的聚类模型大多基于非负矩阵分解或距离构造聚类图，存在着联合优化使解的性能得不到保障以及无法对全局结构进行充分刻画的不足。为了提升聚类图的性能，基于低秩子空间聚类和锚点图，文中提出了一种低秩缺失多视图子空间聚类算法ALIMSC。该算法先通过基于锚点图的缺失多视图聚类（APMC）算法得到数据的基准相似矩阵，将其嵌入低秩子空间聚类模型，通过升维对齐和加权融合的方法得到相似矩阵，再通过让相似矩阵与基准相似矩阵尽可能的一致来求得最终的聚类图。ALIMSC算法通过对每个视图的相似矩阵施加秩最小化约束来刻画高维数据的低维子空间分布，在原有锚点图的基础上进一步强调了数据的子空间算法结构，即聚类图中所体现的块对角性。在多个公开数据集上的实验结果表明，本文算法的聚类性能优于所对比的缺失多视图聚类算法。

关键词: 聚类算法, 低秩表示, 缺失多视图聚类, 子空间聚类

Abstract:

Traditional multi-view clustering task is for complete data. However, in practical tasks, due to the limitation of the information acquisition method, some views tend to contain missing data, and this leads to the problem of incomplete multi-view clustering. In view of this problem, most of the existing clustering models are based on non-negative matrix factorization or distance graph, and their co-optimization strategy can easily make the performance of the solution insecure and the global structure can’t be fully characterized. In order to improve the performance of clustering graph, this paper proposed an incomplete multi-view clustering algorithm ALIMSC based on low-rank subspace clustering and anchor graph. The algorithm first obtained the benchmark similarity matrix of data by incomplete multi-view subspace clustering algorithm APMC based on anchor graph, which was embedded in the low-rank subspace clustering model. The similarity matrix was obtained by dimensionality ascending alignment and weighted fusion, and the final clustering graph was obtained by making the similarity matrix as consistent as possible with the benchmark similarity matrix. ALIMSC algorithm characterized the low-dimensional subspace distribution of high-dimensional data by imposing rank minimization constraint on the similarity matrix of each view and emphasized the subspace structure of the data on the basis of the original anchor graph, that is, the block diagonality reflected in the cluster graph. Experimental results on several public datasets show that the proposed algorithm outperforms the classical incomplete multi-view algorithms.

Key words: clustering algorithm, low-rank representation, incomplete multi-view clustering, subspace clustering

中图分类号:

TP391

刘小兰, 石宗宇, 叶泽慧, 等. 基于锚点图的低秩缺失多视图子空间聚类[J]. 华南理工大学学报(自然科学版), 2022, 50(12): 60-70.

LIU Xiaolan, SHI Zongyu, YE Zehui, et al. Anchor Graph Based Low-Rank Incomplete Multi-View Subspace Clustering[J]. Journal of South China University of Technology(Natural Science Edition), 2022, 50(12): 60-70.

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数据集	样本数	视图数	类别数	样本维度
3Source	416	3	6	3 068，3 560，3 632
USPS-MNIST	500	2	10	784，256
UCI Digit	2 000	2	10	216，76
BBCSports	544	2	5	3 183，3 203
ORL	400	3	40	512，59，864
WebKB	203	3	4	1 703，230，230

数据集	算法	ACC					NMI
数据集	算法	r_PD=0.1	r_PD=0.3	r_PD=0.5	r_PD=0.7	r_PD=0.9	r_PD=0.1	r_PD=0.3	r_PD=0.5	r_PD=0.7	r_PD=0.9
USPS-MNIST	PVC	0.502	0.468	0.432	0.444	0.353	0.400	0.392	0.349	0.337	0.274
	MIC	0.832	0.810	0.734	0.690	0.610	0.759	0.695	0.615	0.574	0.569
	DAIMC	0.834	0.795	0.670	0.576	0.457	0.761	0.681	0.556	0.493	0.390
	IMSC_AGL	0.964	0.934	0.854	0.770	0.739	0.934	0.892	0.776	0.682	0.624
	OPIMC	0.580	0.502	0.486	0.438	0.354	0.603	0.487	0.461	0.422	0.293
	HCP-IMSC	0.949	0.938	0.887	0.810	0.662	0.900	0.881	0.800	0.734	0.576
	APMC	0.964	0.936	0.846	0.810	0.574	0.926	0.881	0.741	0.707	0.466
	ALIMSC	0.975	0.968	0.896	0.868	0.678	0.950	0.940	0.810	0.790	0.539
UCI Digit	PVC	0.605	0.537	0.566	0.522	0.554	0.580	0.531	0.544	0.482	0.510
	MIC	0.835	0.795	0.653	0.535	0.412	0.728	0.690	0.577	0.522	0.418
	DAIMC	0.739	0.674	0.566	0.491	0.453	0.647	0.589	0.530	0.469	0.429
	IMSC_AGL	0.891	0.890	0.899	0.849	0.731	0.819	0.813	0.819	0.757	0.663
	OPIMC	0.350	0.223	0.219	0.209	0.295	0.465	0.285	0.139	0.164	0.313
	HCP-IMSC	0.795	0.861	0.772	0.771	0.701	0.745	0.772	0.725	0.702	0.611
	APMC	0.817	0.814	0.811	0.826	0.794	0.832	0.820	0.814	0.714	0.682
	ALIMSC	0.921	0.915	0.902	0.856	0.828	0.874	0.849	0.831	0.763	0.726

算法	ACC				NMI
算法	BBC-Guardian	BBC-Reuters	Guardian-Reuters	3-Views	BBC-Guardian	BBC-Reuters	Guardian-Reuters	3-Views
PVC	0.662	0.578	0.001		0.569	0.569	0.642
MIC	0.731	0.772	0.654	0.817	0.551	0.639	0.538	0.675
DAIMC	0.540	0.564	0.512	0.596	0.426	0.448	0.381	0.473
IMSC_AGL	0.870	0.853	0.741	0.796	0.712	0.712	0.562	0.685
OPIMC	0.531	0.529	0.457	0.671	0.318	0.343	0.294	0.521
HCP-IMSC	0.818	0.877	0.813	0.899	0.654	0.743	0.614	0.781
APMC	0.837	0.845	0.849	0.851	0.680	0.687	0.706	0.702
ALIMSC	0.871	0.894	0.872	0.899	0.734	0.759	0.721	0.767

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