Fast and Improved SLEX Analysis of High-dimensional Time Series

We address the problem of segmenting a multi-dimensional time series into stationary blocks by improving AutoSLEX[1], which has been successfully used for this purpose. AutoSLEX finds the best basis in a library of smoothed localized exponentials (SLEX) basis functions that are orthogonal and localized in both time and frequency. We introduce DynamicSLEX, a variant of AutoSLEX that relaxes the dyadic intervals constraint of AutoSLEX, allowing for more flexible segmentation while maintaining tractability. Then, we introduce RandSLEX, which uses random projections to scale-up SLEX-based segmentation to high dimensional inputs and to establish a notion of strength of splitting points in the segmentation. We demonstrate the utility of the proposed improvements on synthetic and real data.