Contrastive Multivariate Singular Spectrum Analysis

We introduce contrastive multivariate singular spectrum analysis, a novel unsupervised method for dimensionality reduction and signal decomposition of time series data. By utilizing an appropriate background dataset, the method transforms a target time series dataset in a way that evinces the sub-signals that are enhanced in the target dataset, as opposed to only those that account for the greatest variance. This shifts the goal from finding signals that explain the most variance to signals that matter the most to the analyst. We demonstrate our method on an illustrative synthetic example, as well as show the utility of our method in the downstream clustering of real electrocardiogram and electromyogram signals. We end with a physical interpretation of what the algorithm is doing.