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In our previous work, we introduced LinCbO—an algorithm for fast computation of the Duquenne-Guigues basis based on Close-by-One and LinClosure. We also proposed additional speed-ups using pruning techniques, like those used in FCbO, In-Close, or LCM. In the present work, we describe the pruning techniques for LinCbO and experimentally evaluate their effect. Additionally, we describe and evaluate algorithms using a similar idea to LinCbO but using naïve closure or Wild's closure instead of the LinClosure. According to our extensive experimental evaluation, LinCbO with pruning techniques performs significantly faster than already known algorithms. The differences between the performance of the four pruning techniques seem negligible. [ABSTRACT FROM AUTHOR]

LCM is an algorithm for enumeration of frequent closed itemsets in transaction databases. It is well known that when we ignore the required frequency, the closed itemsets are exactly intents of formal concepts in Formal Concept Analysis (FCA). We describe LCM in terms of FCA and show that LCM is basically the Close-by-One algorithm with multiple speed-up features for processing sparse data. We analyze the speed-up features and compare them with those of similar FCA algorithms, like FCbO and algorithms from the In-Close family. [ABSTRACT FROM AUTHOR]

We propose and evaluate a novel algorithm for computation of the Duquenne-Guigues basis which combines Close-by-One and LinClosure algorithms. This combination enables us to reuse attribute counters used in LinClosure and speed up the computation. Our experimental evaluation shows that it is the most efficient algorithm for computation of the Duquenne-Guigues basis. keyword: non-redundancy; attribute implications; minimalization; closures. [ABSTRACT FROM AUTHOR]

We present a general framework which provides a unified approach to attribute reduction in decision contexts across various generalizations of Formal Concept Analysis. The framework is demonstrated on an attribute reduction method which has been studied multiple times separately for each of the generalizations. Specifically, we use the framework to elevate the discernibility matrix based method to a more general setting. [ABSTRACT FROM AUTHOR]