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Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been on short time-series data composed of a few patterns exhibiting variabilities, while recently there have been attempts to focus on longer series composed of multiple local patrepeating with an arbitrary irregularity. The primary contribution of this paper relies on presenting a method which can detect local patterns in repetitive time-series via fitting local polynomial functions of a specified degree. We capture the repetitiveness degrees of time-series datasets via a new measure. Furthermore, our method approximates local polynomials in linear time and ensures an overall linear running time complexity. The coefficients of the polynomial functions are converted to symbolic words via equi-area discretizations of the coefficients' distributions. The symbolic polynomial words enable the detection of similar local patterns by assigning the same word to similar polynomials. Moreover, a histogram of the frequencies of the words is constructed from each time-series' bag of words. Each row of the histogram enables a new representation for the series and symbolizes the occurrence of local patterns and their frequencies. In an experimental comparison against state-of-the-art baselines on repetitive datasets, our method demonstrates significant improvements in terms of prediction accuracy.

Scalable Classification of Repetitive Time Series Through Frequencies of Local Polynomials