Robust Estimation of Shift–Invariant Patterns Exploiting Correntropy

We propose a novel framework for robust estimation of recurring patterns in time series. Particularly, we utilize correntropy and a shift-invariant adaptation of sparse modeling techniques as the underpinnings of a data-driven scheme where potential outliers, such as spikes, dropouts, high-amplitude impulsive noise, gaps, and overlaps are managed in a principled manner. The Maximum Correntropy Criterion (MCC) is applied to the estimation paradigms and solved via the Half-Quadratic (HQ) technique, which allows a fast and efficient computation of the optimal projection vectors without adding extra free parameters. We also posit a heuristic regarding the initial set of functions to be estimated; specifically, we restrict the search space to patterns with modulatory activity only. We then implement a robust clustering routine to provide a principled initial seed for the greedy algorithms. This heuristic is proved to alleviate the computational burden that shift-invariant unsupervised learning usually entails. The framework is tested on synthetic time series built from weighted Discrete Cosine Transform (DCT) atoms under four different variants of outliers. In addition, we present preliminary results on winding data that illustrate the clear advantages of the methods.