mSIMPAD: Efficient and Robust Mining of Successive Similar Patterns of Multiple Lengths in Time Series

A successive similar pattern (SSP) is a series of similar sequences that occur consecutively at non-regular intervals in time series. Mining SSPs could provide valuable information without a priori knowledge, which is crucial in many applications ranging from health monitoring to activity recognition. However, most existing work is computationally expensive, focuses only on periodic patterns occurring in regular time intervals, and is unable to recognize patterns containing multiple periods. Here we investigate a more general problem of finding similar patterns occurring successively, in which the similarity between patterns is measured by the z-normalized Euclidean distance. We propose a linear time, robust method, called Multiple-length Successive sIMilar PAtterns Detector (mSIMPAD), that mines SSPs of multiple lengths, making no assumptions regarding periodicity. We apply our method on the detection of repetitive movement using a wearable inertial measurement unit. The experiments were conducted on three public datasets, two of which contain simple walking and idle data, whereas the third is more complex and contains multiple activities. mSIMPAD achieved F-score improvements of 3.2% and 6.5%, respectively, over the simple and complex datasets compared to the state-of-the-art walking detector. In addition, mSIMPAD is scalable and applicable to real-time applications since it operates in linear time complexity.