Linear Detrending Subsequence Matching in Time-Series Databases

TL;DR

This paper introduces an efficient index-based method for linear detrending in time-series subsequence matching, addressing the challenge of removing linear trends to improve matching accuracy.

Contribution

It proposes the concept of LD-windows and a lower bounding theorem, enabling efficient index-based linear detrending subsequence matching.

Findings

The method outperforms existing approaches in accuracy and speed.

Extensive experiments validate the effectiveness of the proposed solution.

Abstract

Each time-series has its own linear trend, the directionality of a timeseries, and removing the linear trend is crucial to get the more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to a huge number of possible subsequences. In this paper we define this problem the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present a notion of LD-windows (LD means linear detrending), which is obtained as follows: we eliminate the linear trend from a subsequence rather than each window itself and obtain LD-windows by dividing the subsequence into windows. Using the LD-windows we then present a lower bounding theorem for the index-based matching solution and formally prove its correctness. Based on the lower bounding theorem, we next propose the index building and subsequence matching algorithms for linear detrending subsequence matching.We finally show the superiority of our index-based solution through extensive experiments.