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

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MaxSDev is violated. Since our K-MaxSDev segmentation algorithm actually<br />

ensures that the violations <strong>of</strong> MaxSDev only occur on the edge <strong>of</strong> two adjacent<br />

segments, as shown in Table 4.4, turning points are either specified by the mean <strong>of</strong><br />

the next invalid pattern or the first value <strong>of</strong> the next valid pattern. Evidently, this<br />

specification <strong>of</strong> turning points captures the locations where large prediction errors<br />

mostly tend to happen.<br />

Table 4.4 Algorithm 3: Pattern Validation <strong>and</strong> Turning Points Discovery<br />

3) Pattern matching <strong>and</strong> interval forecasting<br />

The most important issue for pattern matching <strong>and</strong> interval forecasting is to<br />

identify the type <strong>of</strong> the given latest duration sequence. Specifically, three types <strong>of</strong><br />

duration sequences are defined in this chapter including the type where the sequence<br />

contains internal turning points, the type where the next value <strong>of</strong> the sequence is<br />

probably a turning point <strong>and</strong> the type for the remainder <strong>of</strong> the sequences. As<br />

presented in Table 4.5 (Algorithm 4), the types <strong>of</strong> sequences are identified based on<br />

st<strong>and</strong>ard deviations.<br />

56

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