Matrix Profile XVII: Indexing the Matrix Profile to Allow Arbitrary Range Queries

Since its introduction several years ago, the Matrix Profile has received significant attention for two reasons. First, it is a very general representation, allowing for the discovery of time series motifs, discords, chains, joins, shapelets, segmentations etc. Secondly, it can be computed very efficiently, allowing for fast exact computation and ultra-fast approximate computation. For analysts that use the Matrix Profile frequently, its incremental computability means that they can perform ad-hoc analytics at any time, with almost no delay time. However, they can only issue global queries. That is, queries that consider all the data from time zero to the current time. This is a significant limitation, as they may be interested in localized questions about a contiguous subset of the data. For example, "do we have any unusual motifs that correspond with that unusually cool summer two years ago". Such ad-hoc queries would require recomputing the Matrix Profile for the time period in question. This is not an untenable computation, but it could not be done in interactive time. In this work we introduce a novel indexing framework that allows queries about arbitrary ranges to be answered in quasilinear time, allowing such queries to be interactive for the first time.