## 4 Evaluation Results  
We evaluated our proposed data analytic algorithm MrCloud in mining user-specified constraints from uncertain big data. We used various benchmark datasets, which include real-life datasets (e.g., accidents, connect4, and mushroom) from the UCI Machine Learning Repository ([[http://archive.ics.uci.edu/ml/](http://archive.ics.uci.edu/ml/)]([http://archive.ics.uci.edu/ml/](http://archive.ics.uci.edu/ml/))) and the FIMI Repository ([[http://fimi.ua.ac.be/](http://fimi.ua.ac.be/)]([http://fimi.ua.ac.be/](http://fimi.ua.ac.be/))). We also used IBM synthetic datasets, which were generated using the IBM Quest Dataset Generator [22]. For our experiments, the generated data ranges from 2 M to 10 M transactions with an average transaction length of 10 items from a domain of 1 K items. As the above real-life and synthetic datasets originally contained only precise data, we assigned to each item contained in every transaction an existential probability from the range (0, 1.0]. All experiments were run using either (i) a single machine with an Intel Core i7 4-core processor (1.73 GHz) and 8 GB of main memory running a 64-bit Windows 7 operating system; or (ii) the Amazon Elastic Compute Cloud (EC2) cluster--specifically, 11 High-Memory Extra Large (m2.xlarge) computing nodes ([[http://aws.amazon.com/ec2/](http://aws.amazon.com/ec2/)]([http://aws.amazon.com/ec2/](http://aws.amazon.com/ec2/))). We implemented existing mining framework [35; 39; 40], UF-growth [32], tube-growth [33], BLIMP-growth [34], and our data analytic algorithm MrCloud all in the Java programming language. The stock version of Apache Hadoop 0.20.0 was used. First, we demonstrated the functionality and capability of MrCloud by using (i) a database consisting of items all with existential probability value of 1.0 (indicating that all items are definitely present in the database); and (ii) a user-specified AM constraint. Experimental results show that, in terms of accuracy, our data analytic algorithm returned the same collection of valid frequent patterns as those returned by the existing mining framework [35; 39; 40] for finding valid frequent patterns from precise data. Note that, in terms of flexibility, MrCloud is not confined to finding valid frequent patterns from a database in which existential probability values of all items are 1.0. MrCloud is capable of finding valid frequent patterns from any database, in which existential probability values of all items are ranging from 0 to 1.0. Moreover, we also experimented with (i) an uncertain database; and (ii) a user-specified AM constraint with 100% selectivity (so that every item is selected). Experimental results show that, in terms of accuracy, MrCloud returned the same collection of frequent patterns as those returned by UF-growth [32], tube-growth [33] and BLIMP-growth [34]. Note that, in terms of flexibility, MrCloud is not confined to handling AM constraints with 100% selectivity. MrCloud is capable of handling AM constraints with any selectivity. Afterwards, we demonstrated the efficiency of MrCloud. Figure 1 shows that MrCloud took much shorter runtimes than the runtimes required by the existing UF-growth algorithm [32] when handling AM constraints with 100% selectivity because UF-growth was not designed to handle different selectivity of constraints. Hence, for a fair comparison, we used 100% selectivity for this experiment. We will show in Figure 2 how the runtimes for MrCloud decreased when the selectivity increased (_i.e._, fewer patterns were selected). For the current experiment, MrCloud was run in the aforementioned EC2 cluster. As a MapReduce-based algorithm, MrCloud takes advantage of all 11 nodes in the EC2 cluster. In contrast, as a non-MapReduce-based algorithm, UF-growth was run on a single machine (_i.e._, does not take advantage of multiple nodes.) This explains why MrCloud is faster than UF-growth. Moreover, the figure shows the scalability of MrCloud.