Accurate and Efficient Time Series Matching by Season- and Trend-aware Symbolic Approximation -- Extended Version Including Additional Evaluation and Proofs

TL;DR

This paper introduces a season- and trend-aware symbolic approximation method for time series data, significantly improving matching accuracy and speed over the state-of-the-art SAX technique by accounting for cyclical and trend components.

Contribution

The paper proposes a novel symbolic approximation that incorporates seasonality and trends, enhancing representation accuracy and matching efficiency without additional memory costs.

Findings

Matching speed improved up to three orders of magnitude over SAX.

Enhanced symbolic distribution accuracy by considering seasonality and trends.

Maintains low memory footprint while improving representation quality.

Abstract

Processing and analyzing time series data\-sets have become a central issue in many domains requiring data management systems to support time series as a native data type. A crucial prerequisite of these systems is time series matching, which still is a challenging problem. A time series is a high-dimensional data type, its representation is storage-, and its comparison is time-consuming. Among the representation techniques that tackle these challenges, the symbolic aggregate approximation (SAX) is the current state of the art. This technique reduces a time series to a low-dimensional space by segmenting it and discretizing each segment into a small symbolic alphabet. However, SAX ignores the deterministic behavior of time series such as cyclical repeating patterns or trend component affecting all segments and leading to a distortion of the symbolic distribution. In this paper, we present a season- and a trend-aware symbolic approximation. We show that this improves the symbolic distribution and increase the representation accuracy without increasing its memory footprint. Most importantly, this enables a more efficient time series matching by providing a match up to three orders of magnitude faster than SAX.