Translational Symmetry in Subsequence Time-Series Clustering

  • Tsuyoshi Idé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4384)

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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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Tsuyoshi Idé
    • 1
  1. 1.IBM Research, Tokyo Research Laboratory, 1623-14 Shimotsuruma, Yamato, 242-8502 KanagawaJapan

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