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Supervised learning algorithms are nowadays successfully scaling up to datasets that are very large in volume, leveraging the potential of in-memory cluster-computing Big Data frameworks. Still, massive datasets with a number of large-domain categorical features are a difficult challenge for any classifier. Most off-the-shelf solutions cannot cope with this problem. In this work we introduce DAC, a Distributed Associative Classifier. DAC exploits ensemble learning to distribute the training of an associative classifier among parallel workers and improve the final quality of the model. Furthermore, it adopts several novel techniques to reach high scalability without sacrificing quality, among which a preventive pruning of classification rules in the extraction phase based on Gini impurity. We ran experiments on Apache Spark, on a real large-scale dataset with more than 4 billion records and 800 million distinct categories. The results showed that DAC improves on a state-of-the-art solution in both prediction quality and execution time. Since the generated model is human-readable, it can not only classify new records, but also allow understanding both the logic behind the prediction and the properties of the model, becoming a useful aid for decision makers.