Covariance Features Improve Low-Resource Reservoir Computing Performance in Multivariate Time Series Classification

Biological systems exhibit tremendous performance and flexibility in learning for a broad diversity of inputs, which are in general time series. Inspired by their biological counterpart, artificial neural networks used in machine learning for classification aim to extract activity patterns within input signals to transform them into stereotypical output patterns that represent categories. For the vast majority, they rely on fixed target values in output to represent probabilities or implement winner-take-all decisions, which correspond in the case of time series to first-order statistics. In other words, the basis for such classification of time series is the transformation of input high-order statistics into output first-order statistics. However, the transformation of input statistics to second- or higher-order statistics has not been much explored yet. Here, we consider a computational scheme based on a reservoir that maps information engrained in input multivariate time series statistics to second-order statistics of its own activity, before being fed to a usual classifier (logistic regression). We compare this covariance decoding with the "classical" mean decoding applied to the reservoir for classification with both synthetic and real datasets of multivariate time series. We show that covariance decoding can extract a broader diversity of second-order statistics from the input signals, yielding higher performance with smaller resources (i.e., reservoir size). Our results pave the way for the characterization of elaborate input-output mappings between statistical orders to efficiently represent and process input signals with complex spatio-temporal structures.