ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series

Elsworth, Steven and Güttel, Stefan (2019) ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series. [MIMS Preprint]

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Abstract

A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic representation. We show that the reconstruction error of this representation can be modelled as a random walk with pinned start and end points, a so-called Brownian bridge. This insight allows us to make ABBA essentially parameter-free, except for the approximation tolerance which must be chosen. Extensive comparisons with the SAX and 1d-SAX representations are included in the form of performance profiles, showing that ABBA is able to better preserve the essential shape information of time series at compression rates comparable to other algorithms. A Python implementation is provided.

Item Type: MIMS Preprint
Uncontrolled Keywords: time series, symbolic aggregation, dimension reduction, Brownian bridge
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Divisions: Manchester Institute for the Mathematical Sciences
Depositing User: Stefan Güttel
Date Deposited: 28 May 2019 16:59
Last Modified: 28 May 2019 16:59
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2712

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