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Spectral Clustering with Sparse Graph Construction Based on Markov Random Walk
( Jiangzhong Cao ),( Pei Chen ),( Bingo Wing-kuen Ling ),( Zhijing Yang ),( Qingyun Dai ) 한국인터넷정보학회 2015 KSII Transactions on Internet and Information Syst Vol.9 No.7
Spectral clustering has become one of the most popular clustering approaches in recent years. Similarity graph constructed on the data is one of the key factors that influence the performance of spectral clustering. However, the similarity graphs constructed by existing methods usually contain some unreliable edges. To construct reliable similarity graph for spectral clustering, an efficient method based on Markov random walk (MRW) is proposed in this paper. In the proposed method, theMRW model is defined on the raw k-NN graph and the neighbors of each sample are determined by the probability of the MRW. Since the high order transition probabilities carry complex relationships among data, the neighbors in the graph determined by our proposed method are more reliable than those of the existing methods. Experiments are performed on the synthetic and real-world datasets for performance evaluation and comparison. The results show that the graph obtained by our proposed method reflects the structure of the data better than those of the state-of-the-art methods and can effectively improve the performance of spectral clustering.
A Max-Flow-Based Similarity Measure for Spectral Clustering
Jiangzhong Cao,Pei Chen,Yun Zheng,Qingyun Dai 한국전자통신연구원 2013 ETRI Journal Vol.35 No.2
In most spectral clustering approaches, the Gaussian kernel-based similarity measure is used to construct the affinity matrix. However, such a similarity measure does not work well on a dataset with a nonlinear and elongated structure. In this paper, we present a new similarity measure to deal with the nonlinearity issue. The maximum flow between data points is computed as the new similarity, which can satisfy the requirement for similarity in the clustering method. Additionally, the new similarity carries the global and local relations between data. We apply it to spectral clustering and compare the proposed similarity measure with other state-of-the-art methods on both synthetic and real-world data. The experiment results show the superiority of the new similarity: 1) The max-flow-based similarity measure can significantly improve the performance of spectral clustering; 2) It is robust and not sensitive to the parameters.