Rokia Missaoui (editor) - Complex Data Analytics with Formal Concept Analysis

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It was in 1970s that Galois connections and respective lattices of closed sets (studied before in Mathematics by Garrett Birkhoff and Oystein Ore) were found useful for modeling information structures and processes [3,26]. After several decades of research in formal concept analysis (FCA) no one can say now that FCA proposes hardly scalable techniques for the analysis of binary data. Highly efficient FCA algorithms with various options for approximation strategies are now widely used for the analysis of complex voluminous heterogeneous data.

In spite of intrinsic complexity of computational problems related to unrestricted generation of both formal concepts and implication bases [15,16], several efficient FCA algorithms were found already around year 2000 [10,19] and new efficient implementations show excellent scalability [1]. Numerous approaches to partial generation of concepts and implications were proposed, based on interestingness constraints [17] and probabilistic considerations [2,5].

Models for treating complex data with FCA-based approaches are manifold. Several approaches were proposed and developed for relational data, first considered through the prism of conceptual scaling, which reduces complex data to binary (or unary, in terms of Rudolf Wille). Most popular approaches to treating complex data in FCA directly, i.e., without binarizing (scaling, in FCA terms) them, are logical concept analysis [7], pattern structures [9], fuzzy concept analysis [4], relational concept analysis [11], triadic concept analysis [13,20,22,23], polyadic CA [25], and probabilistic FCA [14]. Recent interest in natural language processing, knowledge graphs, and social network analysis inspired development of new FCA-based approaches [6,8,12,21].

The recent wave of interest in deep neural networks is tempered by the problems of explainability and robustness of proposed solutions. For some applied domains, like medicine, law, and finance, these issues are crucial: experts would not accept efficient accurate solutions that do not provide acceptable explanations. FCA can propose a broad scope of tools for finding interpretable solutions, since explainability is in the core of FCA. Several attempts were made already to combine neural network efficiency with explainability provided by FCA-based approaches [18,24].

This volume presents an important step in all the above-mentioned directions: meeting the challenge of big and complex data, combining FCA-based approaches with methods based on neural networks to guarantee explainability of results.