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(b)
(b)
(a)
(a)
Fig. 12.6 Evaluation of RRR and DTW distance for clustering a univariate and b multivariate
time series of our DRIVE dataset. We compare the index E for the number of clusters k where
the (normalized) index I reaches its maximum. The results are based on 1
,
000 runs of k -medoids
clustering with random initialization
wherefore the
-threshold represents the accelerator pedal angle, kilometers per hour,
and rotations per minute.
To identify prototypical time series using RRR and DTW distance respectively,
we applied k -medoids clustering with random initialization. For evaluation purpose,
we computed index I and E for a varying number of k prototypes. The results of
index I were normalized in a way that the highest value, which indicates the optimal
number of clusters, equals one. Since index E is a sum of RRR values (see Eq. 12.9 )
and RRR
=
DET, the lower E , the higher the average DET value, and the more
recurring (driving behavior) patterns are comprised of the prototypes identified by
the respective distance measure.
Figure 12.6 shows the empirical results for clustering univariate and multivariate
time series of the VW DRIVE dataset using RRR and DTW distance, respectively.
Since the VW DRIVE dataset consists of 'only' 124 test drives recorded by one
and the same vehicle, the optimal number of clusters for both RRR and DTW dis-
tance is rather small. However, the proposed RRR distance is able to find cluster
configurations with lower index E values or rather prototypes with higher amount
of recurring patterns than the DTW distance. In case of univariate time series (a),
in particular speed measurements, RRR and DTW achieved an index E value of
around 0
1
65 for the optimal number of clusters, which corresponds to a
determinism value of 0
.
52 and 0
.
35, respectively. In the multivariate case (b), RRR
and DTW reached an index E value of around 0
.
48 and 0
.
.
74 and 0
.
84 for the optimal number
 
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