Data placement in massively distributed environments for fast parallel mining of frequent itemsets

Abstract

Frequent itemset mining presents one of the fundamental building blocks in data mining. However, despite the crucial recent advances that have been made in data mining literature, few of both standard and improved solutions scale. This is particularly the case when (1) the quantity of data tends to be very large and/or (2) the minimum support is very low. In this paper, we address the problem of parallel frequent itemset mining (PFIM) in very large databases and study the impact and effectiveness of using specific data placement strategies in a massively distributed environment. By offering a clever data placement and an optimal organization of the extraction algorithms, we show that the arrangement of both the data and the different processes can make the global job either completely inoperative or very effective. In this setting, we propose two different highly scalable, PFIM algorithms, namely P2S (parallel-2-steps) and PATD (parallel absolute top-down). P2S algorithm allows discovering itemsets from large databases in two simple, yet efficient parallel jobs, while PATD renders the mining process of very large databases more simple and compact. Its mining process is made up of only one parallel job, which dramatically reduces the running time, the communication cost and the energy power consumption overhead in a distributed computational platform. Our different proposed approaches have been extensively evaluated on massive real-world data sets. The experimental results confirm the effectiveness and scalability of our proposals by the important scale-up obtained with very low minimum supports compared to other alternatives.

Appendix: Two rounds of closed itemset mining

Table 2 Database $\mathcal{D}$

Closed itemsets present a compact representation of the whole set of frequent itemsets. Very efficient solutions have proposed for their extraction, with orders of magnitude in performance improvements. Therefore, one would be tempted to apply frequent closed itemset mining algorithms as a local solution for pattern extraction in the first step of a 2-job schema mining algorithm such as P2S or PATD. However, frequent closed itemset has very constraining characteristics that may prevent from using them as a 2-job approach. Let us consider the illustration given by Example 5 to show that a global frequent closed itemset might never be a local frequent closed itemset (in no partition).

Example 5

Table 2 presents a database $\mathcal{D}$ with 12 transactions. Suppose we divide $\mathcal{D}$ into four data partitions $P_{1}=\{T_{1}, T_{2}, T_{3}\}$, $P_{2}=\{T_{4}, T_{5}, T_{6}\}$, $P_{3}=\{T_{7}, T_{8}, T_{9}\}$ and $P_{4}=\{T_{10}, T_{11}, T_{12}\}$, where $\mathcal{D}=P_{1} \cup P_{2} \cup P_{3} \cup P_{4}$.

The set of global frequent closed itemsets on $\mathcal{D}$, along with their support is: $\{(C:12) (A,C:8) (C,D:8) (C,E:8)\}$. In this set, the only itemset that is also a local frequent closed itemset is (C, D), because it is supported by 3 transactions in $P_3$ and it has no superset with the same support. All the remaining global frequent closed itemsets are either unfrequent or not closed in the partitions. Let us consider, for instance, the itemset (C). In partition $P_1$, it has the same support as (A, C, E). In partition $P_2$, it has the same support as (C, F). In partition $P_3$, it has the same support as (C, D). In partition $P_4$, it has the same support as (B, C).

This simple counterexample shows that, even though closed frequent itemsets are an appealing research track for distributed environments, their usage calls for particular care. It would be interesting to investigate their properties in a distributed scheme like PATD, but it calls for proofs, or counterexamples, of their compatibility with such a scheme.