基于加权锚点的多视图聚类算法

刘溯源; 王思为; 唐厂; 周思航; 王思齐; 刘新旺

doi:10.16383/j.aas.c220531

基于加权锚点的多视图聚类算法

doi: 10.16383/j.aas.c220531

1.
国防科技大学计算机学院长沙 410073
2.
中国地质大学计算机学院武汉 430074
3.
国防科技大学智能科学学院长沙 410073
4.
国防科技大学计算机学院高性能计算国家重点实验室长沙 410073

基金项目: 国家自然科学基金(61922088, 62006236, 62006237), 国防科技大学科研计划项目(ZK21-23, ZK20-10), 高性能计算国家重点实验室自主课题(202101-15)资助

详细信息

作者简介:
刘溯源：国防科技大学计算机学院硕士研究生.主要研究方向为多视图学习. E-mail: suyuanliu@nudt.edu.cn

王思为：国防科技大学计算机学院博士研究生.主要研究方向为无监督多视图学习, 大规模聚类和深度无监督学习. E-mail: wangsiwei13@nudt.edu.cn

唐厂：中国地质大学计算机学院教授.主要研究方向为多视图学习. E-mail: tangchang@cug.edu.cn

周思航：国防科技大学智能科学学院讲师.主要研究方向为机器学习, 医学图像分析. E-mail: sihangjoe@gmail.com

王思齐：国防科技大学计算机学院高性能计算国家重点实验室助理研究员.主要研究方向为机器学习, 异常检测.本文通信作者. E-mail: wangsiqi10c@gmail.com

刘新旺：国防科技大学计算机学院教授.主要研究方向为核学习, 无监督特征学习. E-mail: xinwangliu@nudt.edu.cn

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出版历程
- 收稿日期: 2022-06-27
- 录用日期: 2022-11-12
- 网络出版日期: 2022-12-19

Multi-view Clustering With Weighted Anchors

1.
College of Computer, National University of Defence Technology, Changsha 410073
2.
College of Computer, China University of Geosciences, Wuhan 430074
3.
College of Intelligent Science and Technology, National University of Defence Technology, Changsha 410073
4.
State Key Laboratory of High performance Computing, College of Computer, National University of Defence Technology, Changsha 410073

Funds: Supported by National Natural Science Foundation of China (61922088, 62006236, 62006237), Research Project of National University of Defense Technology (ZK21-23, ZK20-10) and Autonomous Project of State Key Laboratory of High performance Computing (202101-15)

More Information

Author Bio:
LIU Su-Yuan　Master student at the College of Computer, National University of Defence Technology. His main research interest is multi-view learning

WANG Si-Wei　Ph. D. candidate at the College of Computer, National University of Defence Technology. His research interest covers unsupervised multi-view learning, scalable clustering, and deep unsupervised learning

TANG Chang　Professor at the College of Computer, China University of Geosciences. His research interest is multi-view learning

ZHOU Si-Hang　Lecturer at the College of Intelligent Science and Technology, National University of Defence Technology. His research interest covers machine learning and medical image analysis

WANG Si-Qi　Assistant professor at State Key Laboratory of High performance Computing, the College of Computer, National University of Defence Technology. His research interest covers machine learning and soutlier/anomaly detection. Corresponding author of this paper

LIU Xin-Wang　Professor at the College of Computer, National University of Defence Technology. His research interest covers kernel learning and unsupervised feature learning

摘要

摘要: 大规模多视图聚类旨在解决传统多视图聚类算法中计算速度慢、空间复杂度高以致无法扩展到大规模数据的问题.其中, 基于锚点的多视图聚类方法通过使用整体数据集合的锚点集构建后者对于前者的重构矩阵, 利用重构矩阵进行聚类, 有效地降低了算法的时间和空间复杂度.然而, 现有的方法忽视了锚点之间的差异, 均等地看待所有锚点, 导致聚类结果受到低质量锚点的限制.为了定位更具有判别性的锚点, 加强高质量锚点对聚类的影响, 提出了一种基于加权锚点的大规模多视图聚类算法(Multi-view Clustering With Weighted Anchors, MVC-WA).通过引入自适应锚点加权机制, 所提方法在统一框架下确定锚点的权重, 进行锚图的构建.同时, 为了增加锚点的多样性, 根据锚点之间的相似度进一步调整锚点的权重.在9个基准数据集上与现有最先进的大规模多视图聚类算法的对比实验结果验证了所提方法的高效性与有效性.
- 多视图聚类 /
- 大规模聚类 /
- 锚点 /
- 权重学习
Abstract: Large-scale multi-view clustering aims to solve the problem that traditional methods cannot scale to large-scale data due to slow computational speed and high complexity. Among them, the anchor-based multi-view clustering methods construct the reconstruction matrix of the latter for the former by using the anchor point set of the overall data set. Clustering with the reconstruction matrix effectively reduces the time and space complexity of the algorithm. However, existing methods ignore the differences among anchor points and treat them equally, resulting in clustering results limited by low-quality anchor points. In order to identify more discriminative anchor points and enhance the influence of high-quality anchors on clustering, a large-scale multi-view clustering algorithm based on weighted anchors (MVC-WA) was proposed. By introducing an adaptive anchor weighting mechanism, the proposed method determine the weights of anchors in a unified framework for the construction of anchor graphs. Meanwhile, in order to increase the diversity among anchors, the weights of anchors was further adjusted according to the similarity between them. Experimental results comparing with existing state-of-the-art large-scale multi-view clustering algorithms on nine benchmark datasets validate the efficiency and effectiveness of the proposed method.
- Multi-view clustering /
- large-scale clustering /
- anchor /
- weight learning
注释:

1) ¹ http://mkl.ucsd.edu/dataset/protein-fold-prediction/² http://archive.ics.uci.edu/ml/datasets/Multiple+Features³ https://www.fruitfly.org/⁴ http://svcl.ucsd.edu/projects/crossmodal/⁵ https://www.ee.columbia.edu/ln/dvmm/CCV/⁶ http://staff.science.uva.nl/aloi/⁷ https://www.cs.tau.ac.il/wolf/ytfaces/

2) http://archive.ics.uci.edu/ml/datasets/Multiple+Features

3) https://www.fruitfly.org/

4) http://svcl.ucsd.edu/projects/crossmodal/

5) https://www.ee.columbia.edu/ln/dvmm/CCV/

6) http://staff.science.uva.nl/aloi/

7) https://www.cs.tau.ac.il/wolf/ytfaces/

HTML全文

图 1 4个数据集上学习到的锚点权重

Fig. 1 Learned anchor weights on four datasets

下载: 全尺寸图片幻灯片

图 2 目标函数值随迭代次数增长的变化曲线

Fig. 2 The curve of the objective function value with the increase of the number of iterations

下载: 全尺寸图片幻灯片

图 3 参数调整对聚类性能的影响

Fig. 3 The influence of parameter tuning on clustering performance

下载: 全尺寸图片幻灯片

表 1 本文使用的主要符号

Table 1 Summary of notations

符号	定义
$n$	数据点数量
$k$	类别数
$v$	视图数
$m$	锚点数
$d^{(p)}$	第$p$个视图上数据的维度
${\boldsymbol{X}}^{(p)} \in \mathbf{R}^{d^{(p)} \times n}$	第$p$个视图的数据矩阵
${\boldsymbol{A}}^{(p)} \in \mathbf{R}^{d^{(p)} \times m}$	第$p$个视图的锚点矩阵
${\boldsymbol{Z}}^{(p)} \in \mathbf{R}^{m \times n}$	第$p$个视图上的锚图
${\boldsymbol{W}}^{(p)} \in \mathbf{R}^{m \times m}$	第$p$个视图上的权重矩阵
${\boldsymbol{M}}^{(p)} \in \mathbf{R}^{m \times m}$	第$p$个视图上锚点的相关性矩阵

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表 2 实验中使用的数据集

Table 2 Description of datasets

数据集	样本数	视图数	类别数
ProteinFold	694	12	27
Mfeat	2 000	6	10
BDGP	2 500	3	5
Wiki	2 866	2	10
CCV	6 773	3	20
ALOI	10 800	4	100
YTF10	38 654	4	10
YTF20	63 896	4	20
YTF50	126 054	4	50

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表 3 对比算法在所有数据集上的聚类性能 (%)

Table 3 Clustering performance of compared methods on all datasets (%)

Datasets	MSC—IAS	PMSC	MVSC	FMR	SFMC	MLRSSC	AMGL	RMKM	BMVC	LMVSC	SMVSC	FPMVS	Proposed
ACC
ProteinFold	28.45±1.31	12.06±0.41	24.83±1.35	32.85±1.75	26.22±0	11.10±0	10.96±1.23	23.63±0	26.22±0	28.29±1.57	29.26±1.52	30.03±1.06	32.57±1.88
Mfeat	85.95±6.81	32.48±2.11	45.40±3.03	59.63±3.21	85.85±0	20±0	83.08±7.58	67.10±0	58.45±0	81.50±5.30	67.64±3.86	46.34±3.11	88.97±6.42
BDGP	52.10±4.59	26.44±0.19	35.36±2.45	24.93±0.28	20.08±0	36.12±0	32.33±1.82	41.44±0	29.48±0	50.16±0.29	37.22±2.03	32.62±0.71	60.04±1.89
Wiki	23.91±0.58	49.93±3.46	20.99±0.50	41.97±1.26	35.45±0	15.77±0	12.21±0.16	17.34±0	15.11±0	56.05±2.65	52.47±3.53	51.18±2.54	56.55±2.03
CCV	—	—	—	11.93±0.26	12.52±0	10.44±0	13.71±0.31	11.94±0	15.50±0	20.28±0.60	22.98±0.58	22.88±0.74	22.60±0.67
ALOI	—	—	—	—	—	1.01±0	60.26±1.69	33.74±0	59.67±0	40.27±1.55	48.34±1.49	21.72±0.65	71.29±1.80
YTF10	—	—	—	—	—	—	—	75.68±0	60.43±0	66.74±3.69	72.93±3.96	67.09±2.80	79.15±8.39
YTF20	—	—	—	—	—	—	—	57.62±0	60.09±0	60.64±4.18	67.13±4.20	63.08±2.39	68.16±4.82
YTF50	—	—	—	—	—	—	—	—	66.00±0	68.32±2.45	67.13±3.68	64.24±2.97	66.97±3.08
NMI
ProteinFold	36.91±0.89	6.71±0.58	34.45±1.58	40.69±1.13	31.02±0	0±0	20.02±2.19	34.83±0	29.53±0	37.43±1.14	39.94±1.40	37.75±0.99	43.34±1.19
Mfeat	87.68±2.85	40.14±2.76	42.49±3.30	49.19±1.37	91.77±0	28.63±0	87.29±3.84	65.33±0	68.88±0	79.35±1.95	62.18±1.77	56.46±1.81	86.74±2.26
BDGP	33.07±2.81	3.70±0.20	10.25±2.15	0.99±0.08	2.25±0	26.33±0	13.42±2.29	28.12±0	4.60±0	25.41±0.15	9.85±1.22	10.02±0.38	33.78±0.43
Wiki	8.65±0.27	52.01±1.51	7.28±0.67	33.09±1.09	34.18±0 0.00	0.08±0	0.82±0.10	4.34±0	2.46±0	51.57±2.17	50.05±3.79	49.34±2.95	49.47±1.77
CCV	—	—	—	7.04±0.32	5.44±0	0±0	12.52±0.40	7.76±0	11.70±0	16.28±0.46	17.55±0.32	16.96±0.68	17.02±0.49
ALOI	—	—	—	—	—	0.02±0	75.29±0.90	63.55±0	75.67±0	54.38±1.88	72.51±0.50	55.39±0.29	83.15±0.53
YTF10	—	—	—	—	—	—	—	80.22±0	58.91±0	73.75±2.25	78.57±4.61	76.11±5.78	83.15±4.01
YTF20	—	—	—	—	—	—	—	73.84±0	71.67±0	75.57±1.88	78.36±3.96	74.30±5.99	78.63±1.90
YTF50	—	—	—	—	—	—	—	—	81.90±0	82.43±0.78	82.56±1.42	82.08±1.07	83.19±0.90
Purity
ProteinFold	32.99±1.37	14.37±0.41	31.26±1.19	38.46±1.60	28.96±0	11.10±0	11.71±1.20	33.86±0	28.53±0	35.90±1.63	36.00±1.16	34.95±0.66	39.21±1.56
Mfeat	87.20±6.10	33.27±2.29	47.92±3.08	60.99±2.47	88.25±0	20±0	83.94±6.13	75.95±0	74.98±0	82.08±4.59	68.80±2.87	49.44±2.92	89.97±5.26
BDGP	53.52±3.70	28.59±0.23	35.67±3.06	25.17±0.21	21.12±0	36.12±0	33.46±2.10	51.00±0	29.48±0	50.17±0.23	37.80±1.17	34.82±1.33	60.13±1.24
Wiki	26.68±0.76	51.85±2.91	24.03±0.94	46.06±1.31	37.68±0	15.77±0	12.46±0.19	24.08±0	17.62±0	60.45±2.69	57.63±4.19	55.97±3.30	59.54±1.68
CCV	—	—	—	15.92±0.31	13.04±0	10.44±0	14.12±0.33	17.04±0	19.18±0	23.62±0.47	25.91±0.51	25.09±0.78	25.34±0.67
ALOI	—	—	—	—	—	1.01±0	63.92±1.26	64.02±0	62.35±0	42.32±1.55	51.46±1.41	23.67±0.72	73.81±1.42
YTF10	—	—	—	—	—	—	—	80.70±0	60.43±0	71.52±3.25	77.35±5.70	69.43±3.06	83.57±5.78
YTF20	—	—	—	—	—	—	—	68.78±0	64.83±0	68.20±3.02	72.40±3.79	64.92±1.95	74.40±3.32
YTF50	—	—	—	—	—	—	—	—	73.64±0	73.21±2.18	70.09±3.61	66.84±3.02	73.65±2.50
Fscore
ProteinFold	14.07±0.62	9.44±0.01	14.28±0.85	18.57±1.38	11.68±0	9.64±0	7.84±0.79	12.92±0	16.41±0	15.58±1.17	16.76±0.96	17.09±0.94	19.61±1.62
Mfeat	83.66±6.35	26.94±1.09	37.46±2.69	41.49±1.51	85.52±0	27.39±0	81.39±7.35	59.22±0	62.59±0	74.42±4.13	56.50±2.45	46.57±1.33	85.05±5.09
BDGP	40.44±2.22	29.55±0.10	29.08±0.61	21.00±0.07	33.15±0	41.19±0	32.62±0.81	36.28±0	26.51±0	37.81±0.06	28.81±1.23	28.79±0.58	45.31±0.50
Wiki	15.44±0.25	41.83±2.91	14.91±0.54	30.34±0.78	21.38±0	19.46±0	12.48±0.69	13.04±0	11.15±0	48.71±2.18	45.76±4.69	44.91±3.43	47.17±1.64
CCV	—	—	—	7.50±0.07	10.81±0	10.84±0	10.93±0.41	8.66±0	9.79±0	11.43±0.31	12.93±0.21	13.16±0.31	12.51±0.30
ALOI	—	—	—	—	—	1.96±0	13.58±2.28	28.82±0	48.29±0	29.91±1.49	31.22±0.85	10.21±0.13	61.96±1.48
YTF10	—	—	—	—	—	—	—	73.27±0	53.15±0	62.24±3.70	68.34±5.88	66.10±5.06	75.78±8.28
YTF20	—	—	—	—	—	—	—	53.89±0	48.06±0	55.39±4.25	61.68±3.83	57.81±4.00	63.66±4.34
YTF50	—	—	—	—	—	—	—	—	57.09±0	62.49±2.45	57.97±5.08	56.89±3.18	60.54±3.26

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表 4 对比算法在所有数据集上的运行时间 (s)

Table 4 Running time of compared methods on all datasets (s)

Datasets	MSC—IAS	PMSC	MVSC	FMR	SFMC	MLRSSC	AMGL	RMKM	BMVC	LMVSC	SMVSC	FPMVS	Proposed
ProteinFold	2.44	1 512.10	408.89	16.43	6.86	2.12	1.66	1.21	12.64	2.55	2.82	3.97	6.91
Mfeat	16.81	3 300.30	11 528.00	251.03	88.62	27.94	19.62	3.95	0.43	2.96	1.38	1.43	9.20
BDGP	13.26	15 215.00	34 800.00	1 070.40	39.00	26.89	73.71	7.53	0.35	2.86	1.63	3.38	7.18
Wiki	15.92	14 386.00	9 991.70	1 068.80	9.84	30.72	180.62	6.27	0.11	3.57	3.15	20.16	4.89
CCV	—	—	—	10 287.00	39.51	486.68	1 250.00	25.00	0.88	20.46	13.79	10.54	47.37
ALOI	—	—	—	—	—	3 358.90	10 594.00	202.32	8.41	68.53	66.24	61.46	581.28
YTF10	—	—	—	—	—	—	—	675.42	108.22	196.70	253.21	998.23	495.83
YTF20	—	—	—	—	—	—	—	1 780.50	80.53	513.52	720.15	1 680.34	1 516.70
YTF50	—	—	—	—	—	—	—	—	65.71	3 535.72	2 254.48	9 175.31	4 868.40

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表 5 消融实验结果 (%)

Table 5 Results of ablation experiments (%)

聚类指标	对比方法	数据集
聚类指标	对比方法	ProteinFold	Mfeat	BDGP	Wiki	CCV	ALOI	YTF10	YTF20
ACC	最优单视图	31.48±1.22	77.62±5.85	49.98±2.95	52.01±3.70	20.03±0.32	55.79±1.40	72.08±5.27	63.52±3.80
	未加权	27.83±1.66	82.55±6.64	46.32±3.19	52.05±2.38	18.10±0.53	70.14±2.04	70.72±8.29	66.36±4.72
	无正则化项	30.57±1.57	86.54±7.40	47.37±2.16	47.49±2.35	21.75±0.74	66.26±1.82	68.95±8.83	62.18±4.49
	所提出的方法	32.57±1.88	88.97±6.42	60.04±1.89	56.55±2.03	22.60±0.67	71.29±1.80	79.15±8.39	68.16±4.82
NMI	最优单视图	41.08±0.82	74.73±2.25	27.61±2.33	50.01±3.12	16.67±0.40	73.59±0.44	74.87±2.52	69.70±1.55
	未加权	36.98±1.18	84.10±2.64	24.28±3.34	49.25±1.88	13.90±0.36	83.17±0.51	76.34±4.74	75.09±1.74
	无正则化项	42.10±1.08	87.26±2.59	26.89±2.87	36.51±2.07	16.83±0.49	79.91±0.51	76.77±4.39	75.65±1.70
	所提出的方法	43.34±1.19	86.74±2.26	33.78±0.43	49.47±1.77	17.02±0.49	83.15±0.53	83.15±4.01	78.63±1.90
Purity	最优单视图	36.97±0.97	79.67±4.38	51.69±2.83	57.39±3.90	23.59±0.32	58.86±1.22	76.85±3.66	68.07±2.33
	未加权	35.17±1.46	84.32±5.43	47.12±3.11	58.34±2.52	21.10±0.40	72.77±1.71	76.89±6.26	71.52±3.27
	无正则化项	38.73±1.27	88.55±5.55	47.45±2.04	50.37±1.98	24.76±0.63	69.02±1.47	76.11±6.23	70.25±3.64
	所提出的方法	39.21±1.56	89.97±5.26	60.13±1.24	59.54±1.68	25.34±0.67	73.81±1.42	83.57±5.78	74.40±3.32
Fscore	最优单视图	19.63±1.10	69.72±4.28	37.83±2.14	45.07±3.62	11.50±0.20	43.10±1.38	67.00±4.92	52.49±3.96
	未加权	15.68±1.38	78.80±5.59	35.78±2.64	44.79±2.01	10.64±0.23	60.72±1.60	66.43±8.78	58.07±4.43
	无正则化项	18.65±1.24	83.90±5.96	38.61±2.13	37.17±1.75	12.06±0.32	54.92±1.47	67.00±8.70	54.88±3.74
	所提出的方法	19.61±1.62	85.05±5.09	45.31±0.50	47.17±1.64	12.51±0.30	61.96±1.48	75.78±8.28	63.66±4.34

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