Translational Symmetry in Subsequence Time-Series Clustering
- Cite this paper as:
- 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
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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