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Mining top-K frequent itemsets from data streams

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Abstract

Frequent pattern mining on data streams is of interest recently. However, it is not easy for users to determine a proper frequency threshold. It is more reasonable to ask users to set a bound on the result size. We study the problem of mining top K frequent itemsets in data streams. We introduce a method based on the Chernoff bound with a guarantee of the output quality and also a bound on the memory usage. We also propose an algorithm based on the Lossy Counting Algorithm. In most of the experiments of the two proposed algorithms, we obtain perfect solutions and the memory space occupied by our algorithms is very small. Besides, we also propose the adapted approach of these two algorithms in order to handle the case when we are interested in mining the data in a sliding window. The experiments show that the results are accurate.

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Notes

  1. To obtain the K-th frequent itemset, we assume all itemsets are sorted in descending order by their frequencies. For itemsets with the same frequencies, the order is arbitrary. The K-th itemset in such a sorted list is a K-th frequent itemset.

  2. Note that there may be more than K itemsets in the output when there are more than one itemset with frequency f l .

  3. In our implementation, we store the frequency/count of all itemsets, instead of the support (in fraction). So, in this step, we just need to increment the count of e in F l by c. Similar arguments can be made for other updates on the frequency of the itemsets.

  4. Note that in Yu et al. (2004) where Problem A is tackled, there is a bound on the memory space for the single item mining but not for the case of itemsets with multiple items.

  5. Note that in Line 12 of the algorithm, we could use f + Δ instead of f since Δ bounds the error in f and the greatest possible frequency is f + Δ. This will ensure no false dismissal but will generate more false positives. We therefore use f instead.

  6. As Metwally et al. (2005) only considers mining frequent items, we adapt the algorithm in Metwally et al. (2005) for mining frequent itemsets. The modification is just a straightforward approach which is similar to Manku and Motwani (2002).

  7. Note: The meaning of \(\overline{\epsilon}\) in the algorithm is different from the error parameter ∊ in Lossy Counting Algorithm.

  8. Yu et al. (2004) adopted the default setting of δ − 0.1, which means the probability that the real frequent itemsets are missed is at most 0.1. In this paper, we have to make a smaller default value δ − 0.05 because Theorem 2 suggests that the probability that the top K frequent itemsets are missed is at most 2 * 0.05−0.052 = 0.0975 ≈ 0.1.

  9. In Manku and Motwani (2002), ∊ is set to be 0.1 × s, where s is the user support threshold in Problem A. In this paper, as the problem of mining top K frequent itemsets has no information of the support threshold, we adopt ∊ = 0.001 which was also used in Manku and Motwani (2002) when the support threshold was set to be 0.01.

  10. We randomly re-order data in a unit of segment (1,000 items).

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Acknowledgments

We thank Y.L. Cheung for providing us the coding of BOMO. This research was supported by the RGC Earmarked Research Grant of HKSAR CUHK 4179/01E, and the Innovation and Technology Fund (ITF) in the HKSAR [ITS/069/03].

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  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Ho Sin-Hang Engineering Building, Shatin N.T., Hong Kong, P. R. China

    Raymond Chi-Wing Wong & Ada Wai-Chee Fu

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  1. Raymond Chi-Wing Wong
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  2. Ada Wai-Chee Fu
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Correspondence to Raymond Chi-Wing Wong.

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Wong, R.CW., Fu, A.WC. Mining top-K frequent itemsets from data streams. Data Min Knowl Disc 13, 193–217 (2006). https://doi.org/10.1007/s10618-006-0042-x

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