Qualitative approximation to Dynamic TimeWarping similarity between time series data

Dynamic time warping (DTW) is a method for calculating the similarity between two time series which can occur at different times or speeds. Although its effectiveness made it very popular in several disciplines, its time complexity of O(N2) makes it useful only for relatively short time series. In this paper, we propose a qualitative approximation Qualitative Dynamic Time Warping (QDTW) to DTW. QDTW reduces a time series length by transforming it to qualitative time series. DTW is later calculated between qualitative time series. As qualitative time series are normally much shorter than their corresponding numerical time series, time to compute their similarity is significantly reduced. Experimental results have shown improved running time of up to three orders of magnitude, while prediction accuracy only slightly decreased.