  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.
