Efficient matrix profile computation with Euclidean distance using Eigen transformation: Performance evaluation based on beat‐to‐beat interval (BBI) data

Abstract

The matrix profile serves as a fundamental tool to provide insights into similar patterns within time series. Existing matrix profile algorithms have been primarily developed for the normalized Euclidean distance, which may not be a proper distance measure in many settings. The methodology work of this paper was motivated by statistical analysis of beat‐to‐beat interval (BBI) data collected from smartwatches to monitor e‐cigarette users' heart rate change patterns for which the original Euclidean distance (‐norm) would be a more suitable choice. Yet, incorporating the Euclidean distance into existing matrix profile algorithms turned out to be computationally challenging, especially when the time series is long with extended query sequences. We propose a novel methodology to efficiently compute matrix profile for long time series data based on the Euclidean distance. This methodology involves four key steps including (1) projection of the time series onto eigenspace; (2) enhancing singular value decomposition (SVD) computation; (3) early abandon strategy; and (4) determining lower bounds based on the first left singular vector. Simulation studies based on BBI data from the motivating example have demonstrated remarkable reductions in computational time, ranging from one‐fourth to one‐twentieth of the time required by the conventional method. Unlike the conventional method of which the performance deteriorates sharply as the time series length or the query sequence length increases, the proposed method consistently performs well across a wide range of the time series length or the query sequence length.