Matrix Profile XXVII: A Novel Distance Measure for Comparing Long Time Series

TL;DR

This paper introduces PRCIS, a new distance measure for long time series that leverages dictionary-based summarization to improve similarity comparisons, especially for cyclical and shape-dependent patterns.

Contribution

The paper proposes PRCIS, a novel distance measure that enhances comparison of long time series by utilizing dictionary-based summaries to capture shape-based similarities.

Findings

PRCIS outperforms existing measures on diverse datasets

It effectively captures shape-based similarities in cyclical time series

Demonstrates improved performance in classification and clustering tasks

Abstract

The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance and Dynamic Time Warping distance are known to be extremely effective. However, for time series containing cyclical behaviors, the semantic meaningfulness of such comparisons is less clear. For example, on two separate days the telemetry from an athlete workout routine might be very similar. The second day may change the order in of performing push-ups and squats, adding repetitions of pull-ups, or completely omitting dumbbell curls. Any of these minor changes would defeat existing time series distance measures. Some bag-of-features methods have been proposed to address this problem, but we argue that in many cases, similarity is intimately tied to the shapes of subsequences within these longer time series. In such cases, summative features will lack discrimination ability. In this work we introduce PRCIS, which stands for Pattern Representation Comparison in Series. PRCIS is a distance measure for long time series, which exploits recent progress in our ability to summarize time series with dictionaries. We will demonstrate the utility of our ideas on diverse tasks and datasets.