Abstract
We treat the problem of subsequence time-series clustering (STSC) from a group-theoretical perspective. First, we show that the sliding window technique introduces a mathematical artifact to the problem, which we call the pseudo-translational symmetry. Second, we show that the resulting cluster centers are necessarily governed by irreducible representations of the translational group. As a result, the cluster centers necessarily forms sinusoids, almost irrespective of the input time-series data. To the best of the author’s knowledge, this is the first work which demonstrates the interesting connection between STSC and group theory.
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References
Das, G., Lin, K.-I., Mannila, H., Renganathan, G., Smyth, P.: Rule discovery from time series. In: Proc. ACM SIGKDD Intl. Conf. Knowledge Discovery and Data Mining, ACM Press, New York (1998)
Dhillon, I.S., Guan, Y., Kulis, B.: Kernel k-means, spectral clustering and normalized cuts. In: Proc. ACM SIGKDD Intl. Conf. Knowledge Discovery and Data Mining, pp. 551–556. ACM Press, New York (2004)
Ding, C., He, X.: K-means clustering via principal component analysis. In: Proc. Intl. Conf. Machine Learning, pp. 225–232 (2004)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley Interscience, Chichester (2000)
Idé, T.: Pairwise symmetry decomposition method for generalized covariance analysis. In: Proc. IEEE Intl. Conf. Data Mining, pp. 657–660. IEEE Computer Society Press, Los Alamitos (2005)
Idé, T.: Why does subsequence time-series clustering produce sine waves? In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 311–322. Springer, Heidelberg (2006)
Inui, T., Tanabe, Y., Onodera, Y.: Group Theory and Its Applications in Physics, 2nd edn. Springer, Heidelberg (1996)
Keogh, E., Folias, T.: The UCR time series data mining archive (2002), http://www.cs.ucr.edu/~eamonn/TSDMA/index.html
Keogh, E., Lin, J., Truppel, W.: Clustering of time series subsequences is meaningless: Implications for previous and future research. In: Proc. IEEE Intl. Conf. Data Mining, pp. 115–122. IEEE Computer Society Press, Los Alamitos (2003)
Kondor, R., Jebara, T.: A kernel between sets of vectors. In: Proc. the 20th Intl. Conf. Machine Learning, pp. 361–368 (2003)
Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems, 14, pp. 849–856 (2001)
Sakurai, J.J.: Modern Quantum Mechanics, 2nd edn. Addison-Wesley, Reading (1994)
Zha, H., Ding, C., Gu, M., He, X., Simon, H.D.: Spectral relaxation for k-means clustering. In: Advances in Neural Information Processing Systems, 14, pp. 1057–1064 (2001)
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Idé, T. (2007). Translational Symmetry in Subsequence Time-Series Clustering. In: Washio, T., Satoh, K., Takeda, H., Inokuchi, A. (eds) New Frontiers in Artificial Intelligence. JSAI 2006. Lecture Notes in Computer Science(), vol 4384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69902-6_2
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DOI: https://doi.org/10.1007/978-3-540-69902-6_2
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