Time Series Mining at Petascale Performance

The mining of time series data plays an important role in modern information retrieval and analysis systems. In particular, the identification of similarities within and across time series has garnered significant attention and effort over the last few years. For this task, the class of matrix profile algorithms, which create a generic structure that encodes correlations among records and dimensions—the matrix profile—is a promising approach, as it allows simplified post-processing and analysis steps by examining the resulting matrix profile structure. However, it is expensive to create a matrix profile: it requires significant computational power to evaluate the distance among all subsequence pairs in a time series, especially for very long and multi-dimensional time series with a large dimensionality. Existing approaches are limited in their scalability, as they do not target High Performance Computing systems, and—for most realistic problems—are suited only for datasets with a small dimensionality. In this paper, we introduce a novel MPI-based approach for the calculation of a matrix profile for multi-dimensional time series that pushes these limits. We evaluate the efficiency of our approach using an analytical performance model combined with experimental data. Finally, we demonstrate our solution on a 128-dimensional time series dataset of 1 million records, solving 274 trillion sorts at a sustained 1.3 Petaflop/s performance on the SuperMUC-NG system.