王雷,杜亮,周芃,吴鹏

• 1:山西大学计算机与信息技术学院
• 2:山西大学大数据科学与产业研究院
• 3:安徽大学计算机科学与技术学院

摘要(Abstract)：

提出一种基于自步学习的对称非负矩阵分解算法，通过误差驱动的方式使模型更好地区分正常样本与异常样本，进而提高模型的聚类性能。该方法为所有样本赋予了一个可以衡量其难易程度的权重变量，并采用硬加权与软加权两种策略分别对此变量进行约束以保证模型的合理性。在图像、文本等多个数据集上进行聚类分析，实验结果表明了所提算法的有效性。

关键词(KeyWords)： 无监督学习;对称非负矩阵分解;误差驱动;自步学习;聚类

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(61502289,61806003);; 山西省重点研发项目(201803D31199);; 山西省自然科学基金项目(201801D221163,201801D221173)

作者(Author): 王雷,杜亮,周芃,吴鹏

DOI: 10.13705/j.issn.1671-6841.2021227

参考文献(References)：

• [1] 朱威威，赵岩松，李艳灵.一种基于集合划分的鲁棒性自适应模糊聚类分割算法[J].信阳师范学院学报(自然科学版),2019,32(1):146-152.ZHU W W,ZHAO Y S,LI Y L.A robust adaptive fuzzy clustering segmentation algorithm based on set partition[J].Journal of Xinyang normal university (natural science edition),2019,32(1):146-152.
• [2] 朱恒东，马盈仓，张要，等.基于L21范数和回归正则项的半监督聚类算法[J].郑州大学学报(理学版),2020,52(4):67-74.ZHU H D,MA Y C,ZHANG Y,et al.Semi-supervised clustering algorithm based on L21 norm and regression regular term[J].Journal of Zhengzhou university (natural science edition),2020,52(4):67-74.
• [3] LEE D D,SEUNG H S.Learning the parts of objects by non-negative matrix factorization[J].Nature,1999,401(6755):788-791.
• [4] MACQUEEN J.Some methods for classification and analysis of multivariate observations[C]//Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability.Berkeley:University of California Press,1967:281-297.
• [5] KUANG D,YUN S,PARK H.SymNMF:nonnegative low-rank approximation of a similarity matrix for graph clustering[J].Journal of global optimization,2015,62(3):545-574.
• [6] HE Z S,XIE S L,ZDUNEK R,et al.Symmetric nonnegative matrix factorization:algorithms and applications to probabilistic clustering[J].IEEE transactions on neural networks,2011,22(12):2117-2131.
• [7] LIN C J.Projected gradient methods for nonnegative matrix factorization[J].Neural computation,2007,19(10):2756-2779.
• [8] VANDAELE A,GILLIS N,LEI Q,et al.Efficient and non-convex coordinate descent for symmetric nonnegative matrix factorization[J].IEEE transactions on signal processing,2016,64(21):5571-5584.
• [9] HSIEH C J,DHILLON I S.Fast coordinate descent methods with variable selection for non-negative matrix factorization[C]//Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.New York:ACM Press,2011:1064-1072.
• [10] KIM J,PARK H.Toward faster nonnegative matrix factorization:a new algorithm and comparisons[C]//Proceedings of the 8th IEEE International Conference on Data Mining.Piscataway:IEEE Press,2008:353-362.
• [11] KUMAR M,PACKER B,KOLLER D.Self-paced learning for latent variable models[J].Advances in neural information processing systems,2010,23:1189-1197.
• [12] BENGIO Y,LOURADOUR J,COLLOBERT R,et al.Curriculum learning[C]//Proceedings of the 26th Annual International Conference on Machine Learning.New York:ACM Press,2009:41-48.
• [13] ZHAO Q,MENG D,JIANG L,et al.Self-paced learning for matrix factorization[C]//Proceedings of the AAAI Conference on Artificial Intelligence.Palo Alto:AAAI Press,2015:3196-3202.
• [14] ZHOU P,DU L,LIU X W,et al.Self-paced clustering ensemble[J].IEEE transactions on neural networks and learning systems,2021,32(4):1497-1511.
• [15] ZHENG W,ZHU X F,WEN G Q,et al.Unsupervised feature selection by self-paced learning regularization[J].Pattern recognition letters,2020,132:4-11.
• [16] JIANG L,MENG D Y,MITAMURA T,et al.Easy samples first:self-paced reranking for zero-example multimedia search[C]//Proceedings of the 22nd ACM International Conference on Multimedia.New York:ACM Press,2014:547-556.
• [17] ZHU Z,LI X,LIU K,et al.Dropping symmetry for fast symmetric nonnegative matrix factorization[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems.Cambridge:MIT Press,2018:5154-5164.
• [18] SHI J B,MALIK J.Normalized cuts and image segmentation[J].IEEE transactions on pattern analysis and machine intelligence,2000,22(8):888-905.
• [19] DU L,LI X,SHEN Y D.Robust nonnegative matrix factorization via half-quadratic minimization[C]//Proceedings of the 12th IEEE International Conference on Data Mining.Piscataway:IEEE Press,2012:201-210.
• [20] KONG D G,DING C,HUANG H.Robust nonnegative matrix factorization using L21-norm[C]//Proceedings of the 20th ACM International Conference on Information and Knowledge Management.New York:ACM Press,2011:673-682.
• [21] HUANG S D,ZHAO P,REN Y Z,et al.Self-paced and soft-weighted nonnegative matrix factorization for data representation[J].Knowledge-based systems,2019,164:29-37.
• [22] GUAN N Y,LIU T L,ZHANG Y,et al.Truncated cauchy non-negative matrix factorization[J].IEEE transactions on pattern analysis and machine intelligence,2019,41(1):246-259.