Distribution Agnostic Symbolic Representations for Time Series Dimensionality Reduction and Online Anomaly Detection

TL;DR

This paper introduces two new data-driven symbolic representations for time series that improve upon traditional SAX by reducing information loss and enhancing anomaly detection, verified through theoretical analysis and experiments.

Contribution

It proposes two novel SAX-based symbolic representations using kernel density estimation with Lloyd-Max quantization and Mean-Shift clustering, addressing limitations of Gaussian assumptions.

Findings

Outperforms traditional SAX in real-world datasets

Enhances anomaly detection capabilities

Reduces information loss compared to existing methods

Abstract

Due to the importance of the lower bounding distances and the attractiveness of symbolic representations, the family of symbolic aggregate approximations (SAX) has been used extensively for encoding time series data. However, typical SAX-based methods rely on two restrictive assumptions; the Gaussian distribution and equiprobable symbols. This paper proposes two novel data-driven SAX-based symbolic representations, distinguished by their discretization steps. The first representation, oriented for general data compaction and indexing scenarios, is based on the combination of kernel density estimation and Lloyd-Max quantization to minimize the information loss and mean squared error in the discretization step. The second method, oriented for high-level mining tasks, employs the Mean-Shift clustering method and is shown to enhance anomaly detection in the lower-dimensional space. Besides, we verify on a theoretical basis a previously observed phenomenon of the intrinsic process that results in a lower than the expected variance of the intermediate piecewise aggregate approximation. This phenomenon causes an additional information loss but can be avoided with a simple modification. The proposed representations possess all the attractive properties of the conventional SAX method. Furthermore, experimental evaluation on real-world datasets demonstrates their superiority compared to the traditional SAX and an alternative data-driven SAX variant.