Pruning in Map-Reduce Style CbO Algorithms.

Enumeration of formal concepts is crucial in formal concept analysis. Particularly efficient for this task are algorithms from the Close-by-One family (shortly, CbO-based algorithms). State-of-the-art CbO-based algorithms, e.g. FCbO, In-Close4, and In-Close5, employ several techniques, which we call pruning, to avoid some unnecessary computations. However, the number of the formal concepts can be exponential w.r.t. dimension of the input data. Therefore, the algorithms do not scale well and large datasets become intractable. To resolve this weakness, several parallel and distributed algorithms were proposed. We propose new CbO-based algorithms intended for Apache Spark or a similar programming model and show how the pruning can be incorporated into them. We experimentally evaluate the impact of the pruning and demonstrate the scalability of the new algorithm.