Spectral Clustering Based on Local Density Estimation and Neighbor Propagation
GE Hong-Wei, LI Zhi-Wei, YANG Jin-Long
Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, School of Internet of Things Engineering, Jiangnan University, Wuxi 214122
Neighbor propagation based spectral clustering can be used to cluster the dataset with inhomogeneous density. However, sometimes it propagates different clustering samples into the same subset with high similarity, which can not obtain the real similarity matrix and accurate clustering results. To solve this problem, a local density estimation and neighbor propagation based spectral clustering algorithm (LDENP-SC) is proposed. In this algorithm, the local density of the samples is firstly estimated and the dimensions of the datasets are increased. Then, the similarity matrix is updated by using neighbor propagation and the new dataset is clustered by spectral clustering. Also, a simple local density estimation method is proposed by with the local density of the samples can be estimated accurately and fast. Moreover, based on propagation algorithm, a method for updating the similarity of the samples in different subsets is adopted to get more actual similarity matrix. The experimental results show that LDENP-SC algorithm can obtain similarity matrix close to the ideal and accurate clustering results, has good generalization ability and is robust to a certain range ofparameter σ.
葛洪伟,李志伟,杨金龙. 基于局部密度估计和近邻关系传播的谱聚类*[J]. 模式识别与人工智能, 2014, 27(9): 856-864.
GE Hong-Wei, LI Zhi-Wei, YANG Jin-Long. Spectral Clustering Based on Local Density Estimation and Neighbor Propagation. , 2014, 27(9): 856-864.
[1] Luxburg U V. A Tutorial on Spectral Clustering. Technical Report, No.TR-149. Tübingen, Germany: Max Planck Institute for Biological Cybernetics, 2006 [2] Shi J B, Malik J. Normalized Cuts and Image Segmentation. IEEE Trans on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905 [3] Ng A Y, Jordan M I, Weiss Y. On Spectral Clustering: Analysis and an Algorithm // Dietterich T G, Becker S, Ghahramani Z, eds. Advances in Neural Information Processing Systems. Cambridge, USA: MIT Press, 2001: 849-856 [4] Fowlkes C, Belongie S, Chung F, et al. Spectral Grouping Using the Nystrm Method. IEEE Trans on Pattern Analysis and Machine Intelligence, 2004, 26(2): 214-225 [5] Sharon E, Galun M, Sharon D, et al. Hierarchy and Adaptivity in Segmenting Visual Scenes. Nature, 2006, 442(7104): 810-813 [6] Xia T, Cao J, Zhang Y D, et al. On Defining Affinity Graph for Spectral Clustering through Ranking on Manifolds. Neurocomputing, 2009, 72(13/14/15): 3203-3211 [7] Zhang X C, Li J W, Yu H. Local Density Adaptive Similarity Measurement for Spectral Clustering. Pattern Recognition Letters, 2011, 32(2): 352-358 [8] Li X Y, Guo L J. Constructing Affinity Matrix in Spectral Clustering Based on Neighbor Propagation. Neurocomputing, 2012, 97(15): 125-130 [9] Ozertem U, Erdogmus D, Jenssen R. Mean Shift Spectral Clustering. Pattern Recognition, 2008, 41(6): 1924-1938 [10] Song Y Q, Xie C H, Zhu Y Q, et al. Research on Medical Image Clustering Based on Approximate Density Function. Journal of Computer Research and Development, 2006, 43(11): 1947-1952 (in Chinese) (宋余庆,谢从华,朱玉全,等.基于近似密度函数的医学图像聚类分析研究.计算机研究与发展, 2006, 43(11): 1947-1952) [11] Meila M, Shi J B. A Random Walks View of Spectral Segmentation // Proc of the 8th International Workshop on Artificial Intelligence and Statistics. Florida, USA, 2001 [12] Meila M, Xu L. Multiway Cuts and Spectral Clustering. Technical Report, No.TR-217. Washington, USA: University of Washington, 2003 [13] Wang L, Bo L F, Jiao L C. Density-Sensitive Spectral Clustering. Acta Electronica Sinica, 2007, 35(8): 1577-1581 (in Chinese) (王 玲,薄列峰,焦李成.密度敏感的谱聚类.电子学报, 2007, 35(8): 1577-1581) [14] Meila M. Comparing Clusterings by the Variation of Information // Proc of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop. Washington, USA, 2003: 173-187 [15] Kong W Z, Sun Z H, Yang C, et al. Automatic Spectral Clustering Based on Eigengap and Orthogonal Eigenvector. Acta Electronica Sinica, 2010, 38(8): 1880-1885,1891 (in Chinese) (孔万增,孙志海,杨 灿,等.基于本征间隙与正交特征向量的自动谱聚类.电子学报, 2010, 38(8): 1880-1885,1891) [16] Tian Z, Li X B, Ju Y W. Spectral Matrix Perturbation Analysis. SCIENTIA SINICA Information, 2007, 37(4): 527- 543 (in Chinese) (田 铮,李小斌,句彦伟.谱聚阵的扰动分析.中国科学E辑:信息科学, 2007, 37(4): 527- 543) [17] Sun J G. Matrix Perturbation Analysis. Beijing, China: Science Press, 2001: 146-160 (in Chinese) (孙继广.矩阵扰动分析.北京:科学出版社, 2001: 146-160)