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our knowledge that there are three categories. In contrast, the DTWdistance fails and
assigns time series of different categories to the same cluster at an early stage. The
second observation to be made is that RRR is able to recover the ground truth even
if a large portion of the time series is noisy. The DTW distance, however, groups
time series into the same clusters, if they have globally a similar shape. Therefore,
the noisy parts of the time series supersede or superimpose the relevant recurring
patterns.
12.9.3 Real-Life Data
This experiment aims at assessing the time series prototypes identified by the pro-
posed RRR distance measure compared to the DTW distance.
For our evaluation, we consider the VW DRIVE dataset, which consists of 124
real-life test drives recorded by one vehicle operated by seven different individuals.
Test drives are represented as multivariate time series of varying length and com-
prise vehicular sensor data of the same observed measurements. Since we aim to
identify operations profiles that characterize recurring driving behavior, we exclu-
sively consider accelerator, speed, and revolution measurements, which are more or
less directly influenced by the driver. The complete VW DRIVE dataset contains
various other measurements, such as airflow and engine temperature, and can be
obtained by mailing the first author of this paper.
To measure the (dis)similarity of the VW DRIVE time series using our proposed
RRRdistance, we first need to determine the optimal similarity threshold
and pattern
length
l
min
for each of the considered measurements, such that a considerable amount
of the recurring patterns is preserved.
Figure
12.5
shows the determinism value for the accelerator, speed, and revolu-
tion signal in regard to different parameters settings. We can observe that for all
considered signals the DET value decreases with increasing pattern length
l
min
and
decreasing similarity threshold
. Furthermore, Fig.
12.5
reveals that the speed sig-
nal is highly deterministic, meaning that the same patterns occur frequently, whereas
the acceleration and revolution signal are less predictable and show more chaotic
behavior.
Since we aim to analyze all signals jointly by means of the proposed joint cross
recurrence plot (JCRP) approach, we have to choose a pattern length or rather min-
imum diagonal line length
l
min
that is suitable for all signals. In general, we are
looking for relatively long patterns with high similarity. In other words, we aim to
find a parameter setting with preferably large
l
min
and small
which results in a DET
value that is above a certain threshold. To preserve the underlying characteristics or
rather recurring patterns contained in examined data, at least 20% of the recurrence
points should form diagonal line structures, which corresponds to DET
≥
0
.
2. Based
on this criterion, we choose
l
min
=
40 for the accelerator, speed, and
revolution signal, respectively. Note that the individual signals were not normalized,
5 and
=
14
/
2
/
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