Time-Series Classification Through Histograms of Symbolic Polynomials

Abstract: 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 unique pattern with intraclass pattern distortions and variations, while recently there have been attempts to focus on longer series composed of various local patterns. This study presents a novel method which can detect local patterns in long time-series via fitting local polynomial functions of arbitrary degrees. The coefficients of the polynomial functions are converted to symbolic words via equivolume discretizations of the coefficients' distributions. The symbolic polynomial words enable the detection of similar local patterns by assigning the same words 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 symbolize the existence of local patterns and their frequencies. Experimental evidence demonstrates outstanding results of our method compared to the state-of-art baselines, by exhibiting the best classification accuracies in all the datasets and having statistically significant improvements in the absolute majority of experiments.