Clustering of Time Series Subsequences is Meaningless: Implications for Previous and Future Research
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Kernel k-means: spectral clustering and normalized cuts
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
K-means clustering via principal component analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Pairwise Symmetry Decomposition Method for Generalized Covariance Analysis
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Why does subsequence time-series clustering produce sine waves?
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
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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.