  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 compared to other approaches.
Advantages and applications of ABBA are discussed, including its in-built
differencing property and use for anomaly detection, and Python implementations
provided.
