Abstract
The short time series expression miner by Ernst et al. (Bioinformatics 21:i159–i168, 2005) assigns time series data to the closest of suitably selected prototypes followed by the selection of significant clusters and eventual grouping. We prove that the proposed dissimilarity measure 1 − ρ, with correlation coefficient ρ, can be interpreted as the distance of projected data onto the (d − 1)-dimensional unit sphere \({\mathcal{S}^{d-1}}\). The choice of prototypes is closely related to classical problems in optimization theory. Moreover, we propose a new functional, which has a data-driven component and connects the choice of prototypes to the theory of finite unit norm tight frames by Benedetto and Fickus (Adv Comput Math 18:357–385, 2003).
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Springer, T., Ickstadt, K. & Stöckler, J. Frame potential minimization for clustering short time series. Adv Data Anal Classif 5, 341–355 (2011). https://doi.org/10.1007/s11634-011-0097-4
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DOI: https://doi.org/10.1007/s11634-011-0097-4