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為頻繁單變量不確定樣式產生摘要
40
(3)
The partial distance
D
j
is calculated by comparing
P
A
's and
P
B
's intervals of attribute
j
.
There are thirteen relations for the comparison. We list these relations and the corresponding
equations for computing partial distance in Table 5 In Table 5 the column “Relation on
attribute
j
” presents the relations between
P
A
's and
P
B
's intervals of attribute
j
. The column
“Illustration” illustrates the relations between the two intervals. The column “Equation”
describes how to derive the partial distance, where “
L
A
” and “
U
A
” represent the lower bound
and upper bound of
P
A
's interval, respectively, and “
L
B
” and “
U
B
” represents the lower bound
and upper bound of
P
B
's interval, respectively.
Each of the first six relations is reversible. For example, “
P
A
takes place before
P
B
” is
similar to “
P
B
takes place before
P
A
”. Therefore, their equations are similar. Thus, there are
thirteen relations in total. We omit the equations for reverse relation for ease of presentation.
In addition, if
P
A
(or
P
B
) has an interval on an attribute but
P
B
(or
P
A
) does not, the partial
distance of this attribute is 1; if both
P
A
and
P
B
do not have intervals on an attribute, the
partial distance of this attribute is 0.
D
App
is zero for the last four relations because the across-
attribute extensions and within-attribute extensions of a U2 pattern
Pat
should be in the same
cluster which contains
Pat
to the greatest degree possible, since they have very similar
appearances. The range of
D
App
is between 0 and 1.
Table 5 The Conditions of DApp
Relation on attribute
j
Illustration
Equation
P
A
takes place before
P
B
P
A
P
B
P
A
meets
P
B
P
A
P
B
D
j
= 0.5
P
A
overlaps with
P
B
P
A
P
B
P
A
starts
P
B
P
A
P
B
D
j
= 0
P
A
during
P
B
P
A
P
B
D
j
= 0
P
A
finishes
P
B
P
A
P
B
D
j
= 0
P
A
is equal to
P
B
P
A
P
B
D
j
= 0