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為頻繁單變量不確定樣式產生摘要
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first group, because the second and third FU2Ps are similar to the first FU2P in
appearance
,
i.e., the intervals of attributes in the FU2Ps. In addition, we provide the maximal range of
each attribute's interval that appears in the group to users. For the first group, the maximal
ranges of each attribute's intervals are [15, 33] (
A
1
), [104, 178] (
A
2
), and [51, 68] (
A
3
),
respectively. This indicates the FU2Ps in the group are composed of attributes with intervals
smaller than or equal to the maximal range of the corresponding attribute. For the second
group, the fourth FU2P is selected as the representative FU2P and the maximal ranges of
each attribute's intervals are [18, 35] (
A
1
), [201, 251] (
A
2
), and [44, 51] (
A
3
), respectively. We
also consider the
expected supports
of the FU2Ps. The expected support of a FU2P is the
expected number of transactions that contain the FU2P (we define the expected support in
Definition 5 on page 8). Then, we include the minimum and maximum expected supports of
the FU2Ps in each group in the summary. Therefore, the users can know the range of the
expected supports of the FU2Ps in each group. In most cases, it is sufficient to know the
approximate expected supports instead of precise ones. Finally, the maximal number of
attributes in a FU2P in each cluster is recorded in the summary to indicate the possible
number of attributes in a FU2P in each cluster. In a large set of FU2Ps, the summary greatly
compresses the information that the users need to go over. For example, if we summarize a
set FU2Ps concerning weather conditions or air quality, the users would quickly know the
most representative weather conditions or air quality by examining tens of representative
FU2Ps, instead of examining thousands, or even tens or hundreds of thousands of FU2Ps.
Table 2 Two Sets of FU2Ps
The first set of FU2Ps
The second set of FU2Ps
[
A
1
:[15, 30],
A
2
:[104, 178],
A
3
:[55, 66]]
[
A
1
:[15, 30],
A
2
:[104, 178],
A
3
:[55, 66]]
[
A
1
:[15, 30],
A
2
:[104, 178]]
[
A
1
:[17, 33],
A
2
:[104, 178]]
[
A
1
:[15, 30],
A
3
:[55, 66]]
[
A
1
:[15, 30],
A
3
:[51, 68]]
[
A
1
:[20, 35],
A
2
:[203, 251],
A
3
:[44, 51]]
[
A
1
:[18, 35],
A
2
:[201, 251],
A
3
:[44, 51]]
[
A
2
:[203, 251],
A
3
:[44, 51]]
[
A
2
:[201, 244],
A
3
: [44, 51]]
[
A
1
:[20, 35],
A
2
:[203, 251]]
[
A
1
:[20, 32],
A
2
:[203, 251]]
We review the important existing studies concerning concise representations in the next
section. All of these existing studies handle precise data. None of them can be directly
applied to univariate uncertain data. Furthermore, to the best of our knowledge, construction
of a concise representation of frequent patterns in univariate uncertain data has not been
addressed in the literature. Therefore, our proposed method can fill the gap in the research of