In this paper, we introduce a new method for querying triadic concepts through partial or complete matching of triples using an inverted index, to retrieve already computed triadic concepts that contain a set of terms in their extent, intent, and/or modus. As opposed to the approximation approach described in Ananias, this method (i) does not need to keep the initial triadic context or its three dyadic counterparts, (ii) avoids the application of derivation operators on the triple components through context exploration, and (iii) eliminates the requirement for a factorization phase to get triadic concepts as the answer to one-dimensional queries. Additionally, our solution introduces a novel metric for ranking the retrieved triadic concepts based on their similarity to a given query. Lastly, an empirical study is primarily done to illustrate the effectiveness and scalability of our approach against the approximation one. Our solution not only showcases superior efficiency, but also highlights a better scalability, making it suitable for big data scenarios.

In knowledge discovery applications, the pattern set generated from data can be tremendously large and hard to explore by analysts. In the Formal Concept Analysis (FCA) framework, there have been studies to identify important formal concepts through the stability index and other quality measures. In this paper, we introduce the Base-Equivalent Conceptual Relevance (BECR) score, a novel conceptual relevance interestingness measure for improving the identification of actionable concepts. From a conceptual perspective, the base and equivalent attributes are considered meaningful information and are highly essential to maintain the conceptual structure of concepts. Thus, the basic idea of BECR is that the more base and equivalent attributes and minimal generators a concept intent has, the more relevant it is. As such, BECR quantifies these attributes and minimal generators per concept intent. Our preliminary experiments on synthetic and real-world datasets show the efficiency of BECR compared to the well-known stability index.

Discovering meaningful conceptual structures is a substantial task in data mining and knowledge discovery applications. While off-the-shelf interestingness indices defined in Formal Concept Analysis may provide an effective relevance evaluation in several situations, they frequently give inadequate results when faced with massive formal contexts (and concept lattices), and in the presence of irrelevant concepts. In this paper, we introduce the Conceptual Relevance (CR) score, a new scalable interestingness measurement for the identification of actionable concepts. From a conceptual perspective, the minimal generators provide key information about their associated concept intent. Furthermore, the relevant attributes of a concept are those that maintain the satisfaction of its closure condition. Thus, the guiding idea of CR exploits the fact that minimal generators and relevant attributes can be efficiently used to assess concept relevance. As such, the CR index quantifies both the amount of conceptually relevant attributes and the number of the minimal generators per concept intent. Our experiments on synthetic and real-world datasets show the efficiency of this measure over the well-known stability index.

Identifying important actors (or nodes) in a two-mode network often remains a crucial challenge in mining, analyzing, and interpreting real-world networks. While traditional bipartite centrality indices are often used to recognize key nodes that influence the network information flow, they frequently produce poor results in intricate situations such as massive networks with complex local structures or a lack of complete knowledge about the network topology and certain properties. In this paper, we introduce Bi-face (BF), a new bipartite centrality measurement for identifying important nodes in two-mode networks. Using the powerful mathematical formalism of Formal Concept Analysis, the BF measure exploits the faces of concept intents to identify nodes that have influential bicliques connectivity and are not located in irrelevant bridges. Unlike off-the shelf centrality indices, it quantifies how a node has a cohesive-substructure influence on its neighbour nodes via bicliques while not being in network core-peripheral ones through its absence from non-influential bridges. Our experiments on several real-world and synthetic networks show the efficiency of BF over existing prominent bipartite centrality measures such as betweenness, closeness, eigenvector, and vote-rank among others.

Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software engineering, and knowledge engineering, and in many domains like medicine, psychology, linguistics and ecology. For instance, it has been exploited for the design, mapping and refinement of ontologies. In this paper, we show how FCA can benefit from a given domain ontology by analyzing the impact of a taxonomy (on objects and/or attributes) on the resulting concept lattice. We willmainly concentrate on the usage of a taxonomy to extract generalized patterns (i.e., knowledge generated from data when elements of a given domain ontology are used) in the form of concepts and rules, and improve navigation through these patterns. To that end, we analyze three generalization cases and show their impact on the size of the generalized pattern set. Different scenarios of simultaneous generalizations on both objects and attributes are also discussed