Abstract
This paper presents a general framework for time series clustering based on spectral decomposition of the affinity matrix. We use the Gaussian function to construct the affinity matrix and develop a gradient based method for self-tuning the variance of the Gaussian function. The feasibility of our method is guaranteed by the theoretical inference in this paper. And our approach can be used to cluster both constant and variable length time series. Further our analysis shows that the cluster number is governed by the eigenstructure of the normalized affinity matrix. Thus our algorithm is able to discover the optimal number of clusters automatically. Finally experimental results are presented to show the effectiveness of our method.
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References
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. John Wiley & Sons, Inc., New York (2001)
Smyth, P.: Clustering Sequences with Hidden Markov Models. In: Advances in Neural Information Processing 9 (NIPS 1997). MIT Press, Cambridge (1997)
Zhong, S., Ghosh, J.: A Unified Framework for Model-based Clustering. Journal of Machine Learning Research 4, 1001–1037 (2003)
Porikli, F.M.: Clustering Variable Length Sequences by Eigenvector Decomposition Using Hmm. In: International Workshop on Structural and Syntactic Pattern Recognition, SSPR 2004 (2004)
Zha, H., He, X., Ding, C., Simon, H., Gu, M.: Spectral Relaxation for K-means Clustering. In: Advances in Neural Information Processing Systems 14 (NIPS 2001), Vancouver, Canada, pp. 1057–1064 (2001)
Golub, G.H., Van Loan, C.F.: Matrix Computation, 2nd edn. Johns Hopkins University Press, Baltimore (1989)
Das, G., Gunopulos, D., Mannila, H.: Finding Similar Time Series. In: Komorowski, J., Żytkow, J.M. (eds.) PKDD 1997. LNCS, vol. 1263, pp. 88–100. Springer, Heidelberg (1997)
Maila, M., Shi, J.: A Random Walks View of Spectral Segmentation. In: International Workshop on AI and STATISTICS, AISTATS (2001)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On Spectral Clustering: Analysis and an Algorithm. In: Advances in Neural Information Processing Systems 14 (NIPS 2001), Vancouver, Canada, pp. 849–856. MIT Press, Cambridge (2001)
Huang, J., Yuen, P.C., Chen, W.S., Lai, J.H.: Kernel Subspace LDA with Optimized Kernel Parameters on Face Recognition. In: Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition, (FGR 2004) (2004)
Panuccio, A., Bicego, M., Murino, V.: A Hidden Markov Model-based approach to sequential data clustering. In: Caelli, T.M., Amin, A., Duin, R.P.W., Kamel, M.S., de Ridder, D. (eds.) SPR 2002 and SSPR 2002. LNCS, vol. 2396, p. 734. Springer, Heidelberg (2002)
Wang, F., Zhang, C.: Boosting GMM and Its Two Applications. In: Oza, N.C., Polikar, R., Kittler, J., Roli, F. (eds.) MCS 2005. LNCS, vol. 3541, pp. 12–21. Springer, Heidelberg (2005)
Lin, Z., Zhang, C.: Enhancing Classification by Perceptual Characteristic for the P300 Speller Paradigm. In: Proceedings of the 2nd International IEEE EMBS Special Topic Conference on Neural Engineering, NER 2005 (2005)
Agrawal, R., Faloutsos, C., Swami, A.: Efficient Similarity Search in Sequence Databases. In: Lomet, D.B. (ed.) FODO 1993. LNCS, vol. 730. Springer, Heidelberg (1993)
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Wang, F., Zhang, C. (2005). Spectral Clustering for Time Series. In: Singh, S., Singh, M., Apte, C., Perner, P. (eds) Pattern Recognition and Data Mining. ICAPR 2005. Lecture Notes in Computer Science, vol 3686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551188_37
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DOI: https://doi.org/10.1007/11551188_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28757-5
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