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 best when the time series pair has similar amplitude scaling. 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. This research introduces 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, LSF is utilized to help matching time series containing multiple subsequences with a variety of scales; this algorithm is called Longest Common Local Scaling Feature (LCSF). Compared to the use 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. However, LCSF has the serious drawback on speed and number of parameters. Finally, this thesis proposes local scaling Dynamic Time warping (LSDTW), which has faster speed and fewer parameters than LCSF, but LSDTW can impressively outperform LCSF and other state-of-the-art approaches.