Robust Scale-Invariant Normalization and Similarity Measurement for Time Series Data

Abstract

Classification is one of the most prevalent tasks in time series mining. Dynamic Time Warping and Longest Common Subsequence are well-known and widely used algorithms to measure similarity between two time series sequences using non-linear alignment. However, these algorithms work at its best when the time series pair has similar amplitude scaling, as a little adjustment of scale can actually double the error rates. Unfortunately, sensor data and most real-world time series data usually contain noise, missing values, outlier, and variability or scaling in both axes, which is not suitable for the widely used Z-normalization. We introduce the Local Feature Normalization (LFN) and its Local Scaling Feature (LSF), which can be used to robustly normalize noisy/warped/missing-valued time series. In addition, we utilize LSF to match time series containing multiple subsequences with a variety of scales; this algorithm is called Longest Common Local Scaling Feature (LCSF). Comparing to the usage of Z-normalized data, our classification results show that our proposed LFN is impressively robust, especially on high-error and noisy datasets. On both synthetic and real application data for wrist strengthening rehabilitation exercise using a mobile phone sensor, our LCSF similarity measure also significantly outperforms other existing methods by a large margin.