Unsupervised Discovery of Motifs under Amplitude Scaling and Shifting in Time Series Databases

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Abstract

We introduce an algorithm, MD-RP, for unsupervised discovery of frequently occurring patterns, or motifs, in time series databases. Unlike prior approaches that can handle pattern distortion in the time dimension only, MD-RP is robust at finding pattern instances with amplitude shifting and with amplitude scaling. Using an established discretization method, SAX, we augment the existing real-valued time series representation with additional features to capture shifting and scaling. We evaluate our representation change on the modified randomized projection algorithm on synthetic data with planted, known motifs and on real-world data with known motifs (e.g., GPS). The empirical results demonstrate the effectiveness of MD-RP at discovering motifs that are undiscoverable by prior approaches. Finally, we show that MD-RP can be used to find subsequences of time series that are the least similar to all other subsequences.