计算机科学 ›› 2020, Vol. 47 ›› Issue (11): 80-87.doi: 10.11896/jsjkx.190900144
王丽星1, 曹付元1,2
WANG Li-xing1, CAO Fu-yuan1,2
摘要: 非负矩阵分解( Nonnegative Matrix Factorization)算法能为原始数据找到非负的、线性的矩阵表示且保留了数据的本质特征,已被成功应用于多个领域。经典的NMF算法及其变体算法大部分使用均方误差函数来度量重建误差,在许多任务中已经显示出其有效性,但它在处理含有噪声的数据时仍然面临一些困难。Huber损失函数对较小的残差执行的惩罚与均方误差损失函数相同,对较大的残差执行的惩罚是线性增长的,因此与均方误差损失函数相比,Huber损失函数具有更强的鲁棒性;已有研究证明L2,1范数稀疏正则项在机器学习的分类和聚类模型中具有特征选择作用。结合两者的优点,文中提出了一种基于Huber损失函数且融入L2,1范数正则项的非负矩阵分解聚类模型,并给出了基于投影梯度更新规则的优化过程。在多组数据集上将所提算法与经典的多种聚类算法进行对比,实验结果验证了所提算法的有效性。
中图分类号:
[1] LU H T,FU Z Y,SHU X.Non-negative and sparse spectralclustering [J].Pattern Recognition,2014,47(1):418-426. [2] LEE D D,SEUNG H S.Learning the parts of objects by non-negative matrix factorization [J].Nature,1999,401:788-791. [3] LEE D D,SEUNG H S.Algorithms for non-negative matrix factorization[C]//NIPS.2000:535-541. [4] LI M J,XIE Q,DING Q L.Orthogonal Non-negative Matrix Factorization for K-means Clustering [J].Computer Science,2016,43(5):204-208. [5] LIN C J.Projected gradient methods for non-negative matrixfactorization [J].Neural Computation,2007,19(10):2756-2779. [6] HOYER P O.Non-negative matrix factorization with sparseness constraints [J].Journal of Machine Learning Research,2004,5(9):1457-1469. [7] CAI D,HE H,HAN J.Graph regularized nonnegative matrixfactorization for data representation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(8):1548-1560. [8] JIANG W,LI H,YU X,et al.Graph Regularized Non-negative Matrix Factorization with Sparseness Constraints [J].Computer Science,2013,40(1):218-220,256. [9] LIU H,WU Z,LI X.Constrained nonnegative matrix factorization for image representation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,34(7):1299-1311. [10] KONG D,DING C,HUANG H.Robust nonnegative matrix factorization using L21-norm[C]//Proceedings of the 20th ACM CIKM.2011:673-682. [11] DU L,LI X,SHEN Y D.Robust nonnegative matrix factorization via half-quadratic minimization[C]//IEEE.ICDM,2012:201-210. [12] YANG S,HOU C,ZHANG C,et al.Robust non-negative matrix factorization via joint sparse and graph regularization[C]//International Joint Conference on Neural Networks.2013:1-5. [13] KONG D,DING C,HUANG H.Robust nonnegative matrix factorization using l21-norm[C]//The 20th ACM International Conference on Information and Knowledge Management.2011:673-682. [14] NIE F P,HUANG H,CAI X,et al.Efficient and robust feature selection via L2,1-norms minimization [C]//Proceedings of International Conference on Neural Information Processing Systems.British,ACM,2010:1813-1821. [15] CALAMAI P H,MORÈ J J.Projected gradient methods for linearly constrained problems [J].Mathematical Programming,1987,39(1):93-116. [16] HUBER P J.Robust Statistics (second edition) [M].NewJersey:John Wiley & Sons,2009:1-5. [17] ANDREW S,TSOCHANTARIDIS I T.HOFMANN. Supportvector machines for multiple-instance learning[C]//Advances in Neural Information Processing Systems.USA:The MIT Press,2003:577-584. [18] TOLIC D,ANTULOV F N,KOPRVIA I.A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering [J].Pattern Recognition,2018,82(10):40-55. [19] NIE F P,WANG X Q,HUANG H.Clustering and projectedclustering with adaptive neighbors[C]//ACM SIGKDD Conference on Knowledge Discovery and Data Mining.New York,ACM,2014:977-986. [20] DUA D,GRAFF C.UCI Machine Learning Repository[OL].http://archive.ics.uci.edu/ml. |
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