Quantifying Coincidence in Non-Uniform Time Series with Mutual Graph Approximation: Speech and ECG Examples

Abstract

Compressive sensing and arbitrary sampling are techniques of data volume reduction challenging the Shannon sampling theorem and expected to provide efficient storage while preserving original information. Irregularity of sampling is either a result of intentional optimization of a sampling grid or stems from sporadic occurrence or intermittent observability of a phenomenon. Quantitative comparison of irregular patterns similarity is usually preceded by a projection to a regular sampling space. In this paper, we study methods for direct comparison of time series in their original non-uniform grids. We also propose a linear graph to be a representation of the non-uniform signal and apply the Mutual Graph Approximation (MGA) method as a metric to infer the degree of similarity of the considered patterns. The MGA was implemented together with four state-of-the-art methods and tested with example speech signals and electrocardiograms projected to bandwidth-related and random sampling grids. Our results show that the performance of the proposed MGA method is comparable to most accurate (correlation of 0.964 vs. Frechet: 0.962 and Kleinberg: 0.934 for speech signals) and to less computationally expensive state-of-the-art distance metrics (both MGA and Hausdorf: O(L1+L2)). Moreover, direct comparison of non-uniform signals can be equivalent to cross-correlation of resampled signals (correlation of 0.964 vs. resampled: 0.960 for speech signals, and 0.956 vs. 0.966 for electrocardiograms) in applications as signal classification in both accuracy and computational complexity. Finally, the bandwidth-based resampling model plays a substantial role; usage of random grid is the primary cause of inaccuracy (correlation of 0.960 vs. for random sampling grid: 0.900 for speech signals, and 0.966 vs. 0.878, respectively, for electrocardiograms). These figures indicate that the proposed MGA method can be used as a simple yet effective tool for scoring similarity of signals directly in non-uniform sampling grids.

Keywords

• arbitrary sampling
• compressed sensing
• pattern classification
• distance metric
• correlation