The Accuracy Comparison

Finally, the experiments were conducted to evaluate the quality of the frequent itemsets and the indirect association patterns by comparing the results obtained by EMIA and EMIA-LM on synthetic and real datasets by different block sizes and various mediator support thresholds.

Since MIA-LM and EMIA-LM use the same pruning technology, so we only evaluate the quality on EMIA-LM.

In this experiment, we used both synthetic and real datasets with different mediator support thresholds and different error threshold  (=1/block size). The itempair support threshold (σs) was set to be the same as the mediator support threshold (σ_f) and the dependence threshold (σ_d) was set to 0.1. We analyzed the accuracy from two aspects: the accuracy rate and the recall. Here, the results generated by EMIA were used as baseline for computing the accuracy.

We adopt the following formula for calculating the accuracy:

(4) The second term in (4) denotes the average error rate of itemset frequencies.

From Figure 6-9, we can observe that all frequent itemsets discovered by EMIA-LM are exactly the same as those by EMIA. It also asserts Theorem 1 in section 5.4.1, i.e., no false negative frequent itemsets are generated by EMIA-LM.

55 (a)

(b)

(c)

56 (d)

Figure 6-9 Accuracy comparison of frequent itemsets derived by EMIA-LM (σd = 0.1) and EMIA.

From Figure 6-9 and Table 6-2, we can discover that the memory usage of EMIA-LM is less than EMIA with same mediator support on same dataset but still has very high accuracy.

This indicates that the pruning approach only pruned those infrequent itemsets. Now, we discuss that why EMIA-LM is faster than EMIA as mediator support threshold is 0.05. This is because many infrequent itemsets are pruned, so it can reduce the execution time.

Table 6-2 Execution time and memory usage comparison for dataset BMS-POS (error=0.00004 for EMIA-LM)

BMS-POS

Mediator Support Threshold

0.005 0.05

Execution Time(sec)

EMIA 783.6 21.1

EMIA-LM 740.8 40.4

Memory Usage(MB)

EMIA 164.7 145.5

EMIA-LM 123.9 104.7

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Finally, we examined how many percentages of indirect association patterns are missed.

We use the well-know recall as the measurement.

(5) The results are shown in Figure 6-10. Noticeably no indirect association is missed.

(a)

(b)

58 (c)

(d)

Figure 6-10 Comparison results of derived indirect association patterns by using EMIA-LM (σ_d = 0.1) and EMIA.

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Chapter 7

Conclusions and Future Work

7.1 Conclusions

In this thesis, we have proposed three indirect association mining algorithms, EMIA for static data, and MIA-LM and EMIA-LM for streaming data.

Inspired by the success of HI-mine*, the EMIA algorithm adopts a more compact data structure and simple but more efficient way for indirect association generation. The EMIA algorithm consists of three phases, including compact transactions table construction, MSSs and IIS construction and Indirect Association generation. In compact transactions table construction phase, the algorithm does not need to reorder items according to the itemset frequency and uses a hash table to speed up the transaction data compression time; in MSSs and IIS construction phase, the algorithm adds pointer link to reduce the number of comparisons for saving more execution time; finally, in the Indirect Association generation phase it uses the same concept with HI-mine*, thus can quickly find indirect associations from IIS and MSSs.

To the best of our knowledge, no research work has been conducted on mining indirect associations over data streams. In this thesis, we have proposed two algorithms, MIA-LM and EMIA-LM. Both algorithms adopt some data compression or projection techniques thus require only one data scanning, and use data pruning techniques to reduce memory usage, while sustain a very high accuracy. The MIA-LM algorithm has hybridized the data structures used in DSM-FI and HI-mine, resulting in an efficient and effective algorithmic design. The EMIA-LM algorithm is modified from EMIA to fit the streaming data environment. Experimental results on both synthetic and real world datasets have shown that EMIA-LM is superior to MIA-LM both

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in performance and memory usage. We also have conducted some theoretical analyses on the effectiveness of MIA-LM and EMIA-LM. We has proved that: (1) The support error of the generated frequent itemsets is smaller than the user specified error threshold ; and (2) if the mediator dependence threshold is set smaller than a specific value (= _f  ), then all possible indirect association patterns can be generated.

7.2 Future Work

The study of mining indirect associations from streaming data is in its infancy. Many research issues are worthy of further investigation. First, we will continue to improve the efficiency of the proposed algorithms, seeking more effective way for reducing the memory usage. We will also extend the proposed algorithms to different window models such as time-fading model and sliding-window model. Recently, the design of adaptive data stream mining methods that can perform adaptively under constrained resources has emerged into an important and challenging research issue to the data mining community. In the future, we will study how to apply or incorporate some adaptive technique such as load shedding into our approach, especially when the situation is that we have very limited resources, such as CPU computing power or memory size, without sacrificing too much the quality of the discovered indirect associations.

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