Joint Time Series Chain: Detecting Unusual Evolving Trend across Time Series

TL;DR

This work introduces a new definition called \textit{Joint Time Series Chain}, which is specially designed for the task of finding unexpected evolving trend across interrupted time series or two related time series, and proposes an effective ranking criterion to identify the best chain.

Abstract

Time series chain (TSC) is a recently introduced concept that captures the evolving patterns in large scale time series. Informally, a time series chain is a temporally ordered set of subsequences, in which consecutive subsequences in the chain are similar to one another, but the last and the first subsequences maybe be dissimilar. Time series chain has the great potential to reveal latent unusual evolving trend in the time series, or identify precursor of important events in a complex system. Unfortunately, existing definitions of time series chains only consider finding chains in a single time series. As a result, they are likely to miss unexpected evolving patterns in interrupted time series, or across two related time series. To address this limitation, in this work, we introduce a new definition called \textit{Joint Time Series Chain}, which is specially designed for the task of finding unexpected evolving trend across interrupted time series or two related time series. Our definition focuses on mitigating the robustness issues caused by the gap or interruption in the time series. We further propose an effective ranking criterion to identify the best chain. We demonstrate that our proposed approach outperforms existing TSC work in locating unusual evolving patterns through extensive empirical evaluations. We further demonstrate the utility of our work with a real-life manufacturing application from Intel. Our source code is publicly available at the supporting page https://github.com/lizhang-ts/JointTSC .

Figures (5)

• Figure 1: An illustration of our problem definition of Joint Time Series Chain (JTSC). (a) Two time series, $T_A$ and $T_B$ are shown. (b) JTSC captures evolving patterns across two time series.
• Figure 2: An example of a detected backward time series chain on the concatenated reference and target time series.
• Figure 3: Samples of generated $T_A$ and $T_B$ from UCR data instances. The blue shaded portion is the target time series $T_B$.
• Figure 4: Two snippets from the reference and target time series from Intel Production Data.
• Figure 5: (a) Z-normalized reference sub-chain and (b) target sub-chain for Intel Production Data. (c) Zoom in view of the most deviance node in detected target sub-chain against its nearest neighbor in reference time series $T_A$.

Theorems & Definitions (13)

• definition 1
• definition 2
• definition 3
• definition 4
• definition 5
• definition 6
• definition 7
• definition 8
• definition 9
• definition 10