广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (4): 137-152.doi: 10.16088/j.issn.1001-6600.2023110202

• 研究论文 • 上一篇    下一篇

基于超图正则NMF的自适应半监督多视图聚类

李向利1,2,3*, 梅建平1,3, 莫元健1   

  1. 1.桂林电子科技大学 数学与计算科学学院, 广西 桂林 541004;
    2.广西高校数据分析与计算重点实验室(桂林电子科技大学), 广西 桂林 541004;
    3.广西应用数学中心(桂林电子科技大学), 广西 桂林 541004
  • 收稿日期:2023-11-02 修回日期:2024-01-19 出版日期:2024-07-25 发布日期:2024-09-05
  • 通讯作者: 李向利(1977—), 女, 陕西宝鸡人, 桂林电子科技大学教授, 博士。E-mail:lixiangli@guet.edu.cn
  • 基金资助:
    国家自然科学基金(11961010, 61967004); 桂林电子科技大学研究生创新项目(2023YCXS115)

Adaptive Semi-supervised Multi-view Clustering Based on Hypergraph Regular NMF

LI Xiangli1,2,3*, MEI Jianping1,3, MO Yuanjian1   

  1. 1. School of Mathematics & Computing Science, Guilin University of Electronic Techology, Guilin Guangxi 541004, China;
    2. Guangxi University Key Laboratory of Data Analysis and Calculation (Guilin University of Electronic Techology), Guilin Guangxi 541004, China;
    3. Center for Applied Mathematics of Guangxi (Guilin University of Electronic Techology), Guilin Guangxi 541004, China
  • Received:2023-11-02 Revised:2024-01-19 Online:2024-07-25 Published:2024-09-05

PDF (PC)

6

摘要： 图正则非负矩阵分解(GNMF)虽然已成为大量多视图聚类方法的基本框架,但其尝试用简单图融合来自不同视图的复杂数据关系,同时获得一致性判别表示,这无疑有很大挑战性。为了更好地应对多视图数据的聚类任务,本文提出一种基于超图正则非负矩阵分解的半监督多视图聚类方法ASMCHNMF。该方法通过构造超图,学习来自多个视图的数据高阶关系,为合理利用现实世界中可获取的标签信息,引入标签约束项进行半监督学习。此外,该方法同时考虑一致性信息和互补性信息的学习,采用自适应措施区分不同视图的贡献,并使用交替迭代算法来对主函数进行优化。在7个真实数据集上的对比实验表明,在其中6个数据集上,ASMCHNMF算法的ACC和NMI指标均优于经典算法和当前先进算法。

关键词: 超图, 非负矩阵分解, 多视图聚类, 半监督学习

Abstract: Although graph regularized non-negative matrix factorization (GNMF) has become the basic framework for a large number of multi-view clustering methods, it is undoubtedly a great challenge to fuse complex data relationships from different views with a simple graph and obtain a consistent discriminative representation at the same time. In order to better deal with the clustering task of multi-view data,a semi-supervised multi-view clustering method based on hypergraph regularized non-negative matrix factorization is proposed. Specifically,by constructing a hypergraph,this method learns the high-order relationships of data from multiple views. In order to make reasonable use of the label information available in the real world,the label constraint is introduced for semi-supervised learning. In addition,this method considers the learning of consistency information and complementarity information at the same time,adopts adaptive measures to distinguish the contributions of different views,and uses an alternating iterative algorithm to optimize the objective function. The comparative experimental results on 7 real datasets show that the proposed algorithm is superior to other classical algorithms and current advanced algorithms in ACC and NMI indicators on 6 datasets.

Key words: hypergraph, non-negative matrix factorization, multi-view clustering, semi-supervised learning

中图分类号:  TP391.1

[1] SHAHNAZ F,BERRY M W,PAUCA V P,et al. Document clustering using nonnegative matrix factorization[J]. Information Processing & Management,2006,42(2):373-386. DOI: 10.1016/j.ipm.2004.11.005.
[2] 王纯杰,董小刚,刁心薇. 基于免疫粒子群的K均值聚类算法[J]. 广西师范大学学报(自然科学版),2008,26(3):165-168. DOI: 10.3969/j.issn.1001-6600.2008.03.041.
[3] DING C,HE X F, SIMON H D. On the equivalence of nonnegative matrix factorization and spectral clustering[C] //Procceedings of the 2005 SIAM International Conference on Data Mining. Philadelphia, PA: SIAM, 2005: 606-610. DOI: 10.1137/1.9781611972757.70.
[4] GRONE R,MERRIS R. The Laplacian spectrum of a fraph II[J]. Siam Journal on Discrete Mathematics,1994,7(2):221-229. DOI: 10.1137/S0895480191222653.
[5] 张荣国,曹俊辉,胡静,等. 基于非负正交矩阵分解的多视图聚类图像分割算法[J]. 模式识别与人工智能,2023,36(6):556-571. DOI: 10.16451/j.cnki.issn1003-6059.202306006.
[6] CAI D,HE X F,HAN J W,et al. Graph regularized nonnegative matrix factorization for data representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(8):1548-1560. DOI: 10.1109/TPAMI.2010.231.
[7] YI Y G,WANG J Z,ZHOU W,et al. Non-negative matrix factorization with locality constrained adaptive graph[J]. IEEE Transactions on Circuits and Systems for Video Technology,2020,30(2):427-441. DOI: 10.1109/TCSVT.2019.2892971.
[8] SHU Z Q,WU X J,FAN H H,et al. Parameter-less auto-weighted multiple graph regularized nonnegative matrix factorization for data representation[J]. Knowledge-Based Systems,2017,131:105-112. DOI: 10.1016/j.knosys.2017.05.029.
[9] 刘威,邓秀勤,刘冬冬,等. 基于约束图正则的块稀疏对称非负矩阵分解[J]. 计算机科学,2023,50(7):89-97. DOI: 10.11896/jsjkx.220500050.
[10] 刘国庆,卢桂馥,张强. 一种稀疏图正则化的非负低秩矩阵分解算法[J]. 重庆邮电大学学报(自然科学版),2020,32(2):295-303. DOI: 10.3979/j.issn.1673-825X.2020.02.017.
[11] DING J M,FANG X J,JIA L Y,et al. Diversity multi-view clustering with subspace and NMF-based manifold learning[J]. IEEE Access,2023,11:37041-37051. DOI: 10.1109/ACCESS.2023.3264837.
[12] LIU J L, WANG C, GAO J,et al. Multi-view clustering via joint nonnegative matrix factorization[C] //Proceedings of the 2013 SIAM International Conference on Data Mining. Philadelphia, PA: SIAM, 2013: 252-260. DOI: 10.1137/1.9781611972832.28.
[13] BRUNO E,MARCHAND-MAILLET S. Multiview clustering:a late fusion approach using latent models[C] //Proceedings of the 32nd International ACM SIGIR Conference on Research and Development in Information Retrieval. New York, NY: Association for Computing Machinery,2009:736-737. DOI: 10.1145/1571941.1572103.
[14] ZHANG D P,LUO Y H,YU Y Y,et al. Semi-supervised multi-view clustering with dual hypergraph regularized partially shared non-negative matrix factorization[J]. Science China Technological Sciences,2022,65(6):1349-1365. DOI: 10.1007/s11431-021-1957-3.
[15] SHANG F H,JIAO L C,WANG F. Graph dual regularization non-negative matrix factorization for co-clustering[J]. Pattern Recognition,2012,45(6):2237-2250. DOI: 10.1016/j.patcog.2011.12.015.
[16] ZHANG P,LIU X W,XIONG J,et al. Consensus one-step multi-view subspace clustering[J]. IEEE Transactions on Knowledge and Data Engineering,2022,34(10):4676-4689. DOI: 10.1109/TKDE.2020.3045770.
[17] WANG Q,JIANG X,CHEN M L,et al. Autoweighted multiview feature selection with graph optimization[J]. IEEE Transactions on Cybernetics,2022,52(12):12966-12977. DOI: 10.1109/TCYB.2021.3094843.
[18] 刘相男,丁世飞,王丽娟. 基于深度图正则化矩阵分解的多视图聚类算法[J]. 智能系统学报,2022,17(1):158-169. DOI: 10.11992/tis.202104046.
[19] 宗林林,张宪超,赵乾利,等. 一种多流形正则化的多视图非负矩阵分解算法[J]. 南京大学学报(自然科学),2017,53(3):557-568. DOI: 10.13232/j.cnki.jnju.2017.03.020.
[20] HIDRU D,GOLDENBERG A. EquiNMF:graph regularized multiview nonnegative matrix factorization[EB/OL]. (2014-09-14)[2023-11-02]. https://arxir.org/abs/1409.4018. DOI: 10.48550/arXiv.1409.4018.
[21] LUONG K,NAYAK R,BALASUBRAMANIAM T,et al. Multi-layer manifold learning for deep non-negative matrix factorization-based multi-view clustering[J]. Pattern Recognition,2022,131:108815. DOI: 10.1016/j.patcog.2022.108815.
[22] LIU W Z,LIU L Y,ZHANG Y,et al. Adaptive multi-view multiple-means clustering via subspace reconstruction[J]. Engineering Applications of Artificial Intelligence,2022,114:104986. DOI: 10.1016/j.engappai.2022.104986.
[23] LI C L,CHE H J,LEUNG M F,et al. Robust multi-view non-negative matrix factorization with adaptive graph and diversity constraints[J]. Information Sciences,2023,634:587-607. DOI: 10.1016/j.ins.2023.03.119.
[24] WANG D,GAO X B,WANG X M. Semi-supervised nonnegative matrix factorization via constraint propagation[J]. IEEE Transactions on Cybernetics,2016,46(1):233-244. DOI: 10.1109/TCYB.2015.2399533.
[25] 于晓,刘慧,林毓秀,等. 一致性引导的自适应加权多视图聚类[J]. 计算机研究与发展,2022,59(7):1496-1508. DOI: 10.7544/issn1000-1239.20210126.
[26] 宋成宝,柳平增,刘兴华,等. 基于HSIC的日光温室温度传感器优化配置策略[J]. 农业工程学报,2022,38(8):200-208. DOI: 10.11975/j.issn.1002-6819.2022.08.023.
[27] 吴颖豪,刘虹,张岐山. 基于改进成对约束扩充的标签传播聚类算法[J]. 计算机应用研究,2022,39(12):3592-3597. DOI: 10.19734/j.issn.1001-3695.2022.05.0244.
[28] 肖成龙,张重鹏,王珊珊,等. 基于流形正则化与成对约束的深度半监督谱聚类算法[J]. 系统科学与数学,2020,40(8):1325-1341. DOI: 10.12341/jssms13926.
[29] LIU H F,WU Z H,LI X L,et al. Constrained nonnegative matrix factorization for image representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,34(7):1299-1311. DOI: 10.1109/TPAMI.2011.217.
[30] CAI H,LIU B,XIAO Y S,et al. Semi-supervised multi-view clustering based on constrained nonnegative matrix factorization[J]. Knowledge-Based Systems,2019,182:104798. DOI: 10.1016/j.knosys.2019.06.006.
[31] ZHOU H,YIN H P,LI Y X,et al. Multiview clustering via exclusive non-negative subspace learning and constraint propagation[J]. Information Sciences,2021,552:102-117. DOI: 10.1016/j.ins.2020.11.037.
[32] SHANG F H,JIAO L C,SHI J R,et al. Robust positive semidefinite L-Isomap ensemble[J]. Pattern Recognition Letters,2011,32(4):640-649. DOI: 10.1016/j.patrec.2010.12.005.
[33] 陈璐瑶,刘奇龙,许云霞,等. 基于超图正则化非负Tucker分解的图像聚类算法[J]. 计算机工程,2022,48(4):197-205. DOI: 10.19678/j.issn.1000-3428.0060601.
[34] LEE D D,SEUNG H S. Learning the parts of objects by non-negative matrix factorization[J]. Nature,1999,401(6755):788-791. DOI: 10.1038/44565.
[35] WANG C P,ZHANG J S,WU T J,et al. Semi-supervised nonnegative matrix factorization with positive and negative label propagations[J]. Applied Intelligence,2022,52(9):9739-9750. DOI: 10.1007/s10489-021-02940-z.
[36] WANG J,TIAN F,YU H C,et al. Diverse non-negative matrix factorization for multiview data representation[J]. IEEE Transactions on Cybernetics,2018,48(9):2620-2632. DOI: 10.1109/TCYB.2017.2747400.
[37] ZHOU P,YE F,DU L. Spectral clustering with distinction and consensus learning on multiple views data[J]. PLoS ONE,2018,13(12):e0208494. DOI: 10.1371/journal.pone.0208494.
[38] LUETHI H J. Convex optimization[J]. Journal of the American Statistical Association,2015,100(471):1097. DOI: 10.1198/jasa.2005.s41.
[39] 高海燕,刘万金,黄恒君. 鲁棒自适应对称非负矩阵分解聚类算法[J]. 计算机应用研究,2023,40(4): 1024-1029. DOI: 10.19734/j.issn.1001-3695.2022.08.0414.
[40] YANG B,ZHANG X T,CHEN B D,et al. Efficient correntropy-based multi-view clustering with anchor graph embedding[J]. Neural Networks,2022,146:290-302. DOI: 10.1016/j.neunet.2021.11.027.
[41] TANG C,LIU X W,ZHU X Z,et al. CGD:multi-view clustering via cross-view graph diffusion[J].Proceedings of the AAAI Conference on Artificial Intelligence,2020,34(4):5924-5931. DOI: 10.1609/aaai.v34i04.6052.
[42] LI B,SHU Z Q,LIU Y B,et al. Multi-view clustering via label-embedded regularized NMF with dual-graph constraints[J]. Neurocomputing,2023,551:126521. DOI: 10.1016/j.neucom.2023.126521.
[43] BAI L,WANG J B,LIANG J Y,et al. New label propagation algorithm with pairwise constraints[J]. Pattern Recognition,2022,106:107411. DOI: 10.1016/j.patcog.2020.107411.
[1] 玉婷英, 石长瑶, 李科赞. 牵制控制下含不确定耦合机制的超图同步[J]. 广西师范大学学报（自然科学版）, 2024, 42(2): 140-151.
[2] 杨烁祯, 张珑, 王建华, 张恒远. 声音事件检测综述[J]. 广西师范大学学报（自然科学版）, 2023, 41(2): 1-18.
[3] 赵红涛, 刘志伟. λ重完全二部3-一致超图λK(3)n,n分解为超图双三角锥[J]. 广西师范大学学报（自然科学版）, 2021, 39(4): 93-98.
[4] 陆广泉, 谢扬才, 刘星, 张师超. 一种基于KNN的半监督分类改进算法[J]. 广西师范大学学报（自然科学版）, 2012, 30(1): 45-49.
[5] 赵涛涛, 洪宇, 华震威, 赵明明, 姚建民. 基于Tri-training算法的中文短语翻译自由度计算[J]. 广西师范大学学报（自然科学版）, 2010, 28(3): 122-125.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 赵洁, 宋爽, 武斌. 图像USM锐化取证与反取证技术综述[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 1 -16 .
[2] 艾聪聪, 龚国利, 焦小雨, 田露, 盖中朝, 缑敬轩, 李慧. 毕赤酵母作为基础研究的新兴模式生物研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 17 -26 .
[3] 翟言豪, 王燕舞, 李强, 李景坤. 基于CiteSpace的三维荧光光谱技术对内陆水体中溶解性有机质研究的进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 34 -46 .
[4] 陈丽, 唐明珠, 郭胜辉. 智能汽车信息物理系统状态估计与执行器攻击重构[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 59 -69 .
[5] 李成乾, 石晨, 邓敏艺. 基于元胞自动机的Brugada综合征患者心电信号研究[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 86 -98 .
[6] 吕辉, 吕卫峰. 基于改进YOLOv5的眼底出血点检测算法[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 99 -107 .
[7] 易见兵, 彭鑫, 曹锋, 李俊, 谢唯嘉. 多尺度特征融合的点云配准算法研究[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 108 -120 .
[8] 李莉, 李昊泽, 李涛. 基于Raft的多主节点拜占庭容错共识机制[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 121 -130 .
[9] 赵小梅, 丁勇, 王海涛. 基于改进帝王蝶算法的最大似然DOA估计[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 131 -140 .
[10] 朱艳, 蔡静, 龙芳. 逐步Ⅰ型混合截尾下复合Rayleigh分布竞争失效产品部分步加寿命试验的统计分析[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 159 -169 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发