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

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 often able to better preserve the essential shape information of time series compared to other approaches, in particular when time warping measures are used. Advantages and applications of ABBA are discussed, including its in-built differencing property and use for anomaly detection, and Python implementations provided.

Symbolic deep learning based prognostics for dynamic operating proton exchange membrane fuel cells

“…The fuel cell health indicator conversion method used in this paper, called adaptive Brownian bridge-based aggregation (ABBA), allows the representation and reconstruction of a health indicator. ABBA uses increments in time and value coordinates to capture data trends in health indicator without preprocessing [25]. The implementation of the representation consists of two stages: compression and digitization.…”

“…From the inequation, the compression rate which is represented by 𝑙𝑒 can be regulated by setting the tolerance parameter 𝑜𝑙. Usually, this value ranges from 0.05 to 0.5 and a large 𝑜𝑙 indicates a coarser compression process [25].…”

“…On the other hand, in contrast to the representation, the reconstruction means that ABBA converts symbolic string back to a health indicator. Reconstruction can be considered as the inverse process of representation and applies a similar mathematical approach [25].…”

“…Nevertheless, it is recommended to do the initial polarization curve test to correctly identify the constant parameters and the reasonable parameter intervals in Table 2. Moreover, by bringing the above identified parameters into equation (25), the identified stack voltage can be obtained. Then the degradation behavior model is quantitatively evaluated using equation (26).…”

An efficient aggregation method for the symbolic representation of temporal data

“…In this paper, we focus on a recent symbolic representation called adaptive Brownian bridge-based symbolic aggregation (ABBA) [15] and propose an accelerated version called fABBA. The new method serves the same purpose as ABBA, i.e., it is dimension and noise reducing whilst preserving the essential shape of the time series.…”