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The classification approach, which is based on formal concept analysis, is a symbolic approach allowing the extraction of correlations, reasons and rules according to the concepts discovered from data. Many learning methods based on Formal Concept Analysis are proposed, such as: JSM-method (Blinova, Dobrynin, Finn, Kuznetsov & Pankratova, 2003), CLANN (Tsopze, Mephu-Nguifo & Tindo, 2007)), CITREC (Douar, Latiri & Slimani, 2008), NAVIGALA (Visani, Bertet & Ogier, 2011), HMCS-FCA-SC (Ferrandin et al, 2013), SPFC (Ikeda & Yamamoto, 2013) and MCSD-FCA-PS (Buzmakov et al, 2016). Unfortunately, this approach encountered some problems such as exponential complexity (in the worst case), a high error rate and over-fitting (Meddouri & Maddouri, 2008,2010). Most of them handle only binary data. The construction of the all concepts can be either exhaustive or non-contextual. There is absence of the adaptive selection of concepts (Meddouri & Maddouri, 2008).
For these reasons, we focused in our research on ensemble methods used to improve the error rate of any single learner. We proposed BFC (MeddouriI & Maddouri, 2009) and BNC (Meddouri & Maddouri, 2010) methods based on sequential learning (Boosting). All the data are considered in each learning step and weights are assigned to learning instances. However, it was proved that sequential learning (Boosting) is not interesting, insufficient for a more efficient classifier as Decision Tree (Meddouri & Maddouri, 2010). Other ensemble learning methods exists, and they are based on parallel learning. The difference between these two ensemble methods, derives from how to select data for learning. They are distinguished by the data sampling techniques as Bootstrapping used to learn the classifiers from particular subsets. The particularity of learning from a Bootstrap is to combine hard learning instances to misleading instances in the training set (unlike the sequential approach) (Breiman, 96a, 96b). The best known method, which is based on this type of learning is Dagging (Disjoint samples aggregating) (Kotsiantis, Anyfantis, Karagiannopoulus & Pintelas, 2007) that creates a number of disjoint groups and stratified data from the original learning data set (Ting & Witten, 1997), each considered as a subset of learning. The classifier is built on this learning sets. The predictions are then obtained by combining the classifiers outputs by majority voting (Ting & Witten, 1997). This method has shown its importance in recent work (Meddouri, Khoufi & Maddouri, 2014). Then, we propose to use this technique in this work to study the classifier ensembles based on formal concepts, since, no study has focused on the formal concepts in the context of parallel learning.
In section 2, we present a state of the art on Formal Concept Analysis. In section 3, we propose classifiers using closure operators based on Formal Concept Analysis. In the section 4, an experimental study is presented to evaluate the performance of nominal classifiers based on different closure operators. An experimental study is also presented showing the importance of parallel learning compared to single learning for classifiers based on Formal Concept Analysis.