A Regression-Based Approach For Measuring Similarity In Discrete Signals

This article proposes a novel approach for measuring similarity in discrete signals/time series. The proposed approach is based on a linear regression analysis which considers the relations of the sequences in time domain. Linear regression is an efficient measure to compare signals when translations such as amplitude-scale and amplitude-shift are involved in the signal. However, it fails to measure similarity of sequences when they are similar in shape but different in time-shifting or phase delay. These deficiencies are resolved when the sequences are analysed using the proposed optimised regression algorithm. In this approach, a re-sampling technique may be used to modify the shorter sequence to have the same length as the other sequence. Then, one sequence is circularly shifted along the time axis, sample by sample, using the proposed optimised regression algorithm to obtain the highest similarity between the two sequences. Similarity of the two modified sequences is computed using a modified block distance measure. Comparative simulation results are carried out, which indicate a better accuracy for the proposed method in classification problems.