MS-Index: Fast Top-k Subsequence Search for Multivariate Time Series under Euclidean Distance

Modern applications frequently collect and analyze temporal data in the form of multivariate time series (MTS) -- time series that contain multiple channels. A common task in this context is subsequence search, which involves identifying all MTS that contain subsequences highly similar to a query time series. In practical scenarios, not all channels of an MTS are relevant to every query. For instance, airplane sensors may gather data on a plethora of components and subsystems, but only a few of these are relevant to a specific query, such as identifying the cause of a malfunctioning landing gear, or a specific flight maneuver. Consequently, the relevant query channels are often specified at query time. In this work, we introduce the Multivariate Subsequence Index (MS-Index), a novel algorithm for nearest neighbor MTS subsequence search under Euclidean distance that supports ad-hoc selection of query channels. The algorithm is exact and demonstrates query performance that scales sublinearly to the number of query channels. We examine the properties of name with a thorough experimental evaluation over 34 datasets, and show that it outperforms the state-of-the-art one to two orders of magnitude for both raw and normalized subsequences.