Experiments were made to show the performance of the proposed approach. All the
experiments were performed on an Intel Core 2 Duo E6550 (2.33GHz) PC with 2 GB
main memory, running the Windows XP Professional operating system. The proposed
algorithm was implemented in Visual C# 9.0.
A real data set from a major grocery chain store in America was used for the
experiments. There were 21,556 transactions and 1,559 distinct items in the database.
Each transaction consisted of the products sold and their quantities. The average
transaction length was 4.03. The total utility from all the transactions in the dataset was
104,450,739. Figure 1 shows the number of candidate itemsets generated by our
proposed approach (TPAU) and Liu’s two-phased approach (TP), respectively. The
minimum utility threshold varied from 0.008% to 0.012%. From the figure, it could be
observed that TPAU generated much fewer candidate itemsets than TP did. The
number of candidate itemsets generated by TPAU decreased substantially. The
computation time could thus be greatly reduced.
0 50000 100000 150000 200000 250000
0.008% 0.009% 0.010% 0.011% 0.012%
Number of Candidate Itemsets
Minimum Utility Threshold
TPAU TP
Figure 1. Numbers of candidate itemsets along with different minimum utility thresholds for the two approaches
Table 16 presents the summary of the numbers of candidate itemsets (CI), high
average-utility itemsets (HAUI) generated by our approach and high utility itemsets
(HUI) generated by Liu’s two-phased approach. In Phase I, TPAU generated much
fewer candidate itemsets than TP did. In Phase II, the number of high average-utility
itemsets (HAUI) was much less than that of high utility itemsets (HUI). TPAU could
discover high average-utility itemsets whose utility values were much closer to the
minimum utility threshold when compared to high utility itemsets.
Table 16: Comparison of the numbers of candidate itemsets (CI), high average-utility itemsets (HAUI) and high utility itemsets (HUI) of the two approaches.
Phase I Phase II
Threshold TPAU TP TPAU TP
CI CI HAUI HUI
0.012% 1583 37707 1556 3497
0.011% 1614 53324 1557 4557
0.010% 1677 80735 1565 6486
0.009% 1896 125920 1579 9997
0.008% 2288 197251 1605 18005
Figure 2 shows the execution time of the two approaches. The execution time of
TPAU is much less than TP especially when the minimum utility threshold is small.
0
two-phase mining algorithm to discover high average-utility itemsets. The proposed
mining algorithm is divided into two phases. In phase I, this algorithm overestimates
the utility of itemsets for maintaining the “downward closure” property. The property
is then used to efficiently prune impossible utility itemsets level by level. In phase II,
one database scan is needed to determine the actual high average-utility itemsets from
the candidate itemsets generated in phase I. Since the number of candidate itemsets has
been greatly reduced when compared to that by the traditional approaches, a lot of
computational time may be saved. Considering that the length of itemsets is a major
factor to influence the utility values of itemsets in traditional approaches, the measure
“average-utility” is good to avoid the influence of the length. It can thus get a trade-off
between high utility and time complexity. The experimental results also show the
above points.
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