Data-driven pattern identification and outlier detection in time series

TL;DR

This paper presents a data-driven approach using singular value decomposition to identify patterns and detect outliers in time series data without requiring user-defined parameters, supported by systematic analysis and real-world examples.

Contribution

It introduces a systematic analysis of how SVD spectrum is affected by signal and noise characteristics in time series, enhancing pattern detection methods.

Findings

SVD effectively highlights underlying patterns in time series.

The approach is robust to noise and does not need parameter tuning.

Real-world data demonstrates practical applicability.

Abstract

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary matrix. By recasting the time series as a matrix it becomes possible to use SVD to highlight the underlying patterns and periodicities. This is done without the need for specifying user-defined parameters. From a data mining perspective, this opens up new ways of analyzing time series in a data-driven, bottom-up fashion. However, in order to get correct results, it is important to understand how the SVD-spectrum of a time series is influenced by various characteristics of the underlying signal and noise. In this paper, we have extended the work in earlier papers by initiating a more systematic analysis of these effects. We then illustrate our findings on some real-life data.