A new similarity measure based on shape information for invariant with multiple distortions

Due to the characteristics of noise and volatility, two similar time series always appear in diverse kinds of distortions, which usually are considered as the combinations of the following basic transformations: noise, amplitude shift, amplitude scaling, temporal scaling, and linear drift. In this paper, a novel similarity measure (SIMshape) invariant to these basic distortions and any combinations of them is proposed. It is parameter-free and easy to implement. Specifically, a multi-scale shape approximation for time series based on Discrete Haar Wavelet Transform, key point extraction and symbolization is presented first; then, based on this proposed representation and a scale-weight factor, a robust similarity measure is proposed. The novelty of SIMshape lies in two aspects as follows: (a) symbolizing key points sequence extracted from approximate wavelet coefficients; (b) adding the scale-weight factor and shape similarity in the similarity criterion. To show the effectiveness and efficiency, SIMshape is compared with other popular methods Euclidean Distance (ED), LB_keogh, Complexity Invariant Distance (CID), and ASEAL (Approximate Shape Exchange ALgorithm) using two indices: the number of kinds of distortions and the degree of distortion. Obtained results show that compared with ED, CID, LB_keogh, and ASEAL, SIMshape has better robustness in synthetic data, and shows better performance in real time series classification.