Discovery of Driving Behavior Patterns - Smart Information Systems: Computational Intelligence for Real-Life Applications - page 315

ber of possible candidates of motifs, Chiu et al. [ 2 ] propose to omit consecutive
subsequences that resemble each other. Furthermore, the set of subsequences in each
motif should be mutually exclusive, because otherwise the motifs would be essen-
tially the same. Although normalization techniques are commonly applied to com-
pare time series with different offset and amplitude, Chiu et al. [ 2 ] state that these are
important characteristics that might prove to be useful to distinguish motifs, because
after normalization most subsequences correspond to almost the same upward or
downward trend and become indistinguishable.
Time Series Shapelets . Most existing methods for time series clustering rely
on distances calculated on the shape of the signals. However, time series usually
contain a great amount of measurements that do not contribute to the differentiation
task or even decrease cluster accuracy. Hence, to cluster time series, we are generally
better off ignoring large sections of extraneous data and keeping intervals with high
discriminative power. Recent work [ 28 , 40 ] proposes to use local patterns, so called
shapelets, to cluster time series databases. According to the definition [ 40 ], a shapelet
is a time series snippet that can separate and remove a subset of the data from the
rest of the database, while maximizing the separation gap or rather information gain.
Although the experiments demonstrate that shapelet-based clustering gives better
results than statistical-based clustering of the entire time series, finding optimal
shapelets is a nontrivial task, and almost certainly harder than the clustering itself
[ 40 ]. However, the results underline the importance of ignoring some data to cluster
time series in real-world applications under realistic settings.
Time Series Discords . Different from motifs or shapelets, time series discords
are subsequences of longer time series that are most unusual or rather maximally
different to all the rest of the time series subsequences. Keogh et al. [ 7 ]haveshown
that time series discords are particularly attractive as anomaly detectors because
they only require one intuitive parameter, namely the length of the subsequences.
Furthermore, discords have implications for the time series clustering, cleaning, and
summarization.
Time Series Prototypes . To sum up, the concepts that may possibly be adapted to
identify time series prototypes (as described in our problem statement in Sect. 12.2 )
include motifs [ 2 , 16 ] and shapelets [ 28 , 40 ]. However, in both cases this would
require major modifications of the existing algorithm. A straightforward approach
to solve the stated problem is presented in the following sections.
12.4 Recurrence Plots
Recurrence plots (RPs) are used to visualize and investigate recurrent states of
dynamical systems or rather time series [ 23 , 31 ]. Even though RPs give very vivid
and impressive images of dynamical system trajectories, their implicit mathematical
foundation is deceptively simple [ 18 ]: