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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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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