Abstract
Similarity based clustering, which is to find the extrinsic clusters in data by taking as input a collection of real-valued similarities between data points, has been playing an important role in data analysis and engineering. Lots of work had been done in this field. However, data clustering is an rather challenge problem as there is no labeled data available. We observe that an ideal similarity matrix should be close to an adjacency matrix up to a scale. Based on this idea, we develop a scaled adjacency matrix (SAM) clustering algorithm that could find an optimal adjacency matrix in some sense for a given similarity matrix. Based on the learnt adjacency matrix, clustering could be performed straightforwardly. Upon three assumptions on the similarity matrix, we prove that the performance of SAM is robust. Experimental results also show that SAM is effective.
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References
Shi, J.B., Malik, J.: Normalized cuts and image segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Hagen, L., Kahng, A.B.: New spectral methods for ratio cut partitioning and clustering. IEEE Transactions Computer Aided Design 11(9), 1074–1085 (1992)
Ding, C.H.Q., He, H.F., Zha, H.Y., Gu, M., Simon, H.D.: A min-max cut algorithm for graph partitioning and data clustering. In: Proceedings of IEEE International Conference on Data Mining, pp. 107–114 (2001)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and algorithm. In: Proceedings of NIPS, vol. 14, pp. 897–856 (2002)
Zelnik-Manor, L., Perona, P.: Self-Tuning Spectral Clustering. In: Proceedings of NIPS, vol. 17, pp. 1601–1608 (2004)
Li, X.B., Tian, Z.: Optimum cut-based clustering. Signal Processing 87(11), 2491–2502 (2007)
Chang, H., Yeung, D.Y.: obust Path-Based Spectral Clustering with Application to Image Segmentation. In: Proceedings of ICCV, pp. 278–285 (2005)
Qiu, H.J., Hancock, E.R.: Clustering and Embedding Using Commute Times. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 1873–1890 (2007)
Gower, J., Ross, G.: Minimum spanning trees and single linkage cluster analysis. Applied Statistics 18, 54–64 (1969)
Wu, Z.Y., Leahy, R.: An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence 15(11), 1101–1113 (1993)
Nene, S.K.N.S.A., Murase, H.: Columibia object image library (coil-20). Techinical Report CUCS-005-96 (1996)
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© 2011 Springer-Verlag Berlin Heidelberg
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Yu, J., Jia, C. (2011). Data Clustering by Scaled Adjacency Matrix. In: Xiong, H., Lee, W.B. (eds) Knowledge Science, Engineering and Management. KSEM 2011. Lecture Notes in Computer Science(), vol 7091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25975-3_18
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DOI: https://doi.org/10.1007/978-3-642-25975-3_18
Publisher Name: Springer, Berlin, Heidelberg
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