Xiao Liu PhD Thesis.pdf - Faculty of Information and Communication ...

ecognition. Sliding Window ranks in the second place, but since it lacks the ability
of looking backwards, it tends to over segment when the system performance is
stable (i.e. the number of segments is small) such as the test cases of 11, 33, 48 and
53. Bottom-Up ranks the third place but since it lacks the ability of splitting, it tends
to over segment when the system performance is dynamic such as the test cases of
12, 20, 47 and 76. When the system performance is less dynamic (e.g. the number of
segments is around 4 to 5 as depicted in Figure 4.5, its performance is close to that
of Sliding Window. Top-Down behaves the worst in most cases due to its nature for
over-segmenting. Since the only action for Top-Down is splitting and it stops the
segmentation process as long as the testing criterion is met, Top-Down ignores the
probability of merging small segments into large ones. Therefore, Top-Down
usually has more segments than others.
Before we demonstrate the comparison results on the accuracy of interval
forecasting, we briefly review the 6 representative forecasting strategies and
introduce the setting of their parameters. Here, the actual value of the k th point is
denoted as Y k and the predicted value for the k th point is denoted as P k . The length
of the latest duration sequence is randomly selected from 4 to 8.
1) LAST. LAST takes the last value of the time series as the predicted value for
the next point. Therefore, Formula 4.3 for LAST is defined as follows:
P k = Y k −1 ( ≥ 1
k ) Formula 4.3
In the experiments, LAST takes the last point of the latest duration sequence as
the predicted value.
2) MEAN. MEAN takes the mean value of all its previous points as the predicted
value for the next point. Therefore, Formula 4.4 for LAST is defined as follows:
1 k −1
i=
0
P k = ∑Y i ( k ≥ 1) Formula 4.4
k
In the experiments, MEAN takes the mean value of the entire time series where
the latest duration sequence belongs to.
3) Exponential Smoothing (ES). ES makes the prediction for the next value
based on both the actual value and the predicted value of its previous point. ES does
not react directly to peaks while it reacts fast enough to significant changes of the
mean values (e.g. the changes from one segment to another segment). The parameter
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