Optimal global alignment of signals by maximization of Pearson correlation

The problem of detecting the similarity between noisy signals obtained from electronic instrument measurements arises in several different contexts and it is approached with specific strategies accordingly. In this paper we propose a simple and general method for the comparison of noisy signals of different lengths. Assuming any a-priori knowledge about two noisy signals, their degree of similarity can be detected by computing the global alignment that maximizes their Pearson correlation. The Pearson correlation coefficient is a widely used measure of linear dependence between two random variables of the same length. The optimal alignment of two signals with respect to the Pearson correlation identifies the sub-regions of the two signals that exhibit the highest pairwise degree of similarity. We show that the optimal alignment of two signals by maximization of the Pearson correlation can be computed in (quadratic) polynomial-time by a simple application of the Needleman-Wunsch algorithm. Our approach can be used for the comparison of one-dimensional signals, multi-dimensional signals and multiple-alignments of (one-dimensional or multi-dimensional) signals.