Abstract
In this paper we develop an information-theoretic approach for pairwise clustering. The Laplacian of the pairwise similarity matrix can be used to define a Markov random walk on the data points. This view forms a probabilistic interpretation of spectral clustering methods. We utilize this probabilistic model to define a novel clustering cost function that is based on maximizing the mutual information between consecutively visited clusters of states of the Markov chain defined by the graph Laplacian matrix. The algorithm complexity is linear on sparse graphs. The improved performance and the reduced computational complexity of the proposed algorithm are demonstrated on several standard datasets.
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References
Chung, F.: Spectral graph theory. CBMS Regional Conference Series in Mathematics, vol. 92 (1997)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Interscience (1991)
Dhillon, I., Guan, Y., Kulis, B.: Weighted graph cuts without eigenvectors: A multilevel approach. In: IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), pp. 1944–1957 (2007)
Dhillon, I., Mallela, S., Kumar, R.: A divisive information-theoretic feature clustering algorithm for text classification. Journal of Machine Learning Research 3, 1265–1287 (2003)
Dhillon, I.S., Mallela, S., Modha, D.S.: Information-theoretic co-clustering. In: ACM SIGKDD (2003)
Dubnov, S., El-Yaniv, R., Gdalyahu, Y., Schneidman, E., Tishby, N., Yona, G.: A new nonparametric pairwise clustering algorithm based on iterative estimation of distance profiles. Macine Learning 47(1), 35–61 (2002)
Goldberger, J., Erez, K., Abeles, M.: A Markov clustering method for analyzing movement trajectories. In: IEEE Machine Learning for Signal Processing Workshop, MLSP (2007)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer (2001)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Scientific Computing, 359–392 (1999)
Lin, F., Cohen, W.: Power iteration clustering. In: Int. Conf. on Machine Learning (2010)
Manning, C., Raghavan, P., Schutze, H.: Introduction to information retrieval. Cambridge University Press (2008)
Meila, M., Shi, J.: A random walks view of spectral segmentation. In: AISTATS (2001)
Mitchell, T.: Machine learning. McGraw Hill (1997)
Ng, A.Y., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems 14 (2002)
Samaria, F., Harter, A.: Parameterisation of a stochastic model for human face identification. In: IEEE Workshop on Applications of Computer Vision (1994)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. pattern Anal. Machine Intell. 22(8), 888–905 (2000)
Slonim, N., Friedman, N., Tishby, N.: Unsupervised document classification using sequential information maximization. In: Int. ACM SIGIR Conf. on Research and Development in Information Retrieval (2002)
Slonim, N., Tishby, N.: Document clustering using word clusters via the information bottleneck method. In: Int. ACM SIGIR Conf. on Research and Development in Information Retrieval (2000)
Tishby, N., Pereira, F., Bialek, W.: The information bottleneck method. In: Allerton Conf. on Communication, Control and Computing (1999)
von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing, 395–416 (2007)
Yu, S.X., Shi, J.: Multiclass spectral clustering. In: Int’l Conf. Computer Vision (2003)
Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: Advances in Neural Information Processing Systems 17 (2005)
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Friedman, A., Goldberger, J. (2013). Information Theoretic Pairwise Clustering. In: Hancock, E., Pelillo, M. (eds) Similarity-Based Pattern Recognition. SIMBAD 2013. Lecture Notes in Computer Science, vol 7953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39140-8_7
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DOI: https://doi.org/10.1007/978-3-642-39140-8_7
Publisher Name: Springer, Berlin, Heidelberg
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