Abstract
We propose and analyze a fast spectral clustering algorithm with computational complexity linear in the number of data points that is directly applicable to large-scale datasets. The algorithm combines two powerful techniques in machine learning: spectral clustering algorithms and Nyström methods commonly used to obtain good quality low rank approximations of large matrices. The proposed algorithm applies the Nyström approximation to the graph Laplacian to perform clustering. We provide theoretical analysis of the performance of the algorithm and show the error bound it achieves and we discuss the conditions under which the algorithm performance is comparable to spectral clustering with the original graph Laplacian. We also present empirical results.
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Belkin, M., Niyogi, P.: Convergence of Laplacian eigenmaps. In: NIPS 2006, pp. 129–136. MIT Press (2007)
Drineas, P., Mahoney, M.W.: On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning. Journal of Machine Learning Research 6, 2005 (2005)
Fowlkes, C., Belongie, S., Chung, F., Malik, J.: Spectral grouping using the nyström method. IEEE Trans. Pattern Anal. Mach. Intell. 26(2), 214–225 (2004)
Fung, W.S., Hariharan, R., Harvey, N.J., Panigrahi, D.: A general framework for graph sparsification. In: STOC (2011)
Kannan, R., Vempala, S.: Spectral algorithms. Foundations and Trends in Theoretical Computer Science 4(3-4), 157–288 (2009)
Kumar, S., Mohri, M., Talwalkar, A.: Sampling techniques for the nyström method. Journal of Machine Learning Research 5, 304–311 (2009)
Lashkari, D., Golland, P.: Convex clustering with exemplar-based models. In: NIPS 2007 (2007)
Li, M., Lian, X.-C., Kwok, J.T., Lu, B.-L.: Time and space efficient spectral clustering via column sampling. In: 24th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011, pp. 2297–2304. IEEE (2011)
Lloyd, S.P.: Least squares quantization in pcm. IEEE Transactions on Information Theory 28, 129–137 (1982)
Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: NIPS 2001, pp. 849–856. MIT Press (2001)
Spielman, D.A., Teng, S.-H.: Spectral sparsification of graphs. SIAM Journal on Computing 40(4), 981–1025 (2011)
Williams, C., Seeger, M.: Using the Nyström method to speed up kernel machines. In: NIPS 2000, pp. 682–688. MIT Press (2001)
Yan, D., Huang, L., Jordan, M.I.: Fast approximate spectral clustering. In: ACM SIGKDD, pp. 907–916. ACM (2009)
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Choromanska, A., Jebara, T., Kim, H., Mohan, M., Monteleoni, C. (2013). Fast Spectral Clustering via the Nyström Method. In: Jain, S., Munos, R., Stephan, F., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2013. Lecture Notes in Computer Science(), vol 8139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40935-6_26
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DOI: https://doi.org/10.1007/978-3-642-40935-6_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40934-9
Online ISBN: 978-3-642-40935-6
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