Fuzzy decision trees (FDTs) have shown to be an effective solution in the framework of fuzzy classification. The approaches proposed so far to FDT learning, however, have generally neglected time and space requirements. In this paper, we propose a distributed FDT learning scheme shaped according to the MapReduce programming model for generating both binary and multi-way FDTs from big data. The scheme relies on a novel distributed fuzzy discretizer that generates a strong fuzzy partition for each continuous attribute based on fuzzy information entropy. The fuzzy partitions are therefore used as input to the FDT learning algorithm, which employs fuzzy information gain for selecting the attributes at the decision nodes. We have implemented the FDT learning scheme on the Apache Spark framework. We have used ten real-world publicly available big datasets for evaluating the behavior of the scheme along three dimensions: i) performance in terms of classification accuracy, model complexity and execution time, ii) scalability varying the number of computing units and iii) ability to efficiently accommodate an increasing dataset size. We have demonstrated that the proposed scheme turns out to be suitable for managing big datasets even with modest commodity hardware support. Finally, we have used the distributed decision tree learning algorithm implemented in the MLLib library and the Chi-FRBCS-BigData algorithm, a MapReduce distributed fuzzy rule-based classification system, for comparative analysis.

Associative classifiers have proven to be very effective in classification problems. Unfortunately, the algorithms used for learning these classifiers are not able to adequately manage big data because of time complexity and memory constraints. To overcome such drawbacks, we propose a distributed association rule-based classification scheme shaped according to the MapReduce programming model. The scheme mines classification association rules (CARs) using a properly enhanced, distributed version of the well-known FP-Growth algorithm. Once CARs have been mined, the proposed scheme performs a distributed rule pruning. The set of survived CARs is used to classify unlabeled patterns. The memory usage and time complexity for each phase of the learning process are discussed, and the scheme is evaluated on seven real-world big datasets on the Hadoop framework, characterizing its scalability and achievable speedup on small computer clusters. The proposed solution for associative classifiers turns to be suitable to practically address big datasets even with modest hardware support. Comparisons with two state-of-the-art distributed learning algorithms are also discussed in terms of accuracy, model complexity, and computation time

Fuzzy associative classification has not been widely analyzed in the literature, although associative classifiers (ACs) have proved to be very effective in different real domain applications. The main reason is that learning fuzzy ACs is a very heavy task, especially when dealing with large datasets. To overcome this drawback, in this paper, we propose an efficient distributed fuzzy associative classification approach based on the MapReduce paradigm. The approach exploits a novel distributed discretizer based on fuzzy entropy for efficiently generating fuzzy partitions of the attributes. Then, a set of candidate fuzzy association rules is generated by employing a distributed fuzzy extension of the well-known FP-Growth algorithm. Finally, this set is pruned by using three purposely adapted types of pruning. We implemented our approach on the popular Hadoop framework. Hadoop allows distributing storage and processing of very large data sets on computer clusters built from commodity hardware. We have performed an extensive experimentation and a detailed analysis of the results using six very large datasets with up to 11 000 000 instances. We have also experimented different types of reasoning methods. Focusing on accuracy, model complexity, computation time, and scalability, we compare the results achieved by our approach with those obtained by two distributed nonfuzzy ACs recently proposed in the literature. We highlight that, although the accuracies result to be comparable, the complexity, evaluated in terms of number of rules, of the classifiers generated by the fuzzy distributed approach is lower than the one of the nonfuzzy classifiers.

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