Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling.

We propose a novel and efficient method for link prediction in bipartite networks, using \textit{formal concept analysis} (FCA) and the Transformer encoder. Link prediction in bipartite networks finds practical applications in various domains such as product recommendation in online sales, and prediction of chemical-disease interaction in medical science. Since for link prediction, the topological structure of a network contains valuable information, many approaches focus on extracting structural features and then utilizing them for link prediction. Bi-cliques, as a type of structural feature of bipartite graphs, can be utilized for link prediction. Although several link prediction methods utilizing bi-cliques have been proposed and perform well in rather small datasets, all of them face challenges with scalability when dealing with large datasets since they demand substantial computational resources. This limits the practical utility of these approaches in real-world applications. To overcome the limitation, we introduce a novel approach employing iceberg concept lattices and the Transformer encoder. Our method requires fewer computational resources, making it suitable for large-scale datasets while maintaining high prediction performance. We conduct experiments on five large real-world datasets that exceed the capacity of previous bi-clique-based approaches to demonstrate the efficacy of our method. Additionally, we perform supplementary experiments on five small datasets to compare with the previous bi-clique-based methods for bipartite link prediction and demonstrate that our method is more efficient than the previous ones.

Likewise, the current trend is to produce new resources in a digital format (e.g., in the context of social networks), which entails an in-depth paradigm shift in almost all the humanistic, social, scientific and technological fields. In particular, the field of the humanities is one which is going through a significant transformation as a result of these digitalization efforts and the paradigm shift associated with the digital age. Indeed, we are witnessing the emergence of a whole host of disciplines, those of Digital Humanities (Berry 2012), which are closely dependent on the production and proper organization of digital collections. As a result of the undoubted importance of digital collections in modern society, the search for effective and efficient methods to carry out the production, preservation and enhancement of such digital collections has become a key challenge in modern society (Calhoun, 2013). In particular, the annotation of resources with metadata that enables their proper cataloging, search, retrieval and use in different application scenarios is one of the key elements to ensuring the profitability of these collections of digital objects.

Dimensionality is an important aspect for analyzing and understanding (high-dimensional) data. In their 2006 ICDM paper Tatti et al. answered the question for a (interpretable) dimension of binary data tables by introducing a normalized correlation dimension. In the present work we revisit their results and contrast them with a concept based notion of intrinsic dimension (ID) recently introduced for geometric data sets. To do this, we present a novel approximation for this ID that is based on computing concepts only up to a certain support value. We demonstrate and evaluate our approximation using all available datasets from Tatti et al., which have between 469 and 41271 extrinsic dimensions.

Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.

We propose BERT4FCA, a novel method for link prediction in bipartite networks, using formal concept analysis (FCA) and BERT. Link prediction in bipartite networks is an important task that can solve various practical problems like friend recommendation in social networks and co-authorship prediction in author-paper networks. Recent research has found that in bipartite networks, maximal bi-cliques provide important information for link prediction, and they can be extracted by FCA. Some FCA-based bipartite link prediction methods have achieved good performance. However, we figured out that their performance could be further improved because these methods did not fully capture the rich information of the extracted maximal bi-cliques. To address this limitation, we propose an approach using BERT, which can learn more information from the maximal bi-cliques extracted by FCA and use them to make link prediction. We conduct experiments on three real-world bipartite networks and demonstrate that our method outperforms previous FCA-based methods, and some classic methods such as matrix-factorization and node2vec.

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.

Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially parallelizability, is offset by the loss of explainability. Statistical methods are often used to compensate for this disadvantage. Yet, their ability for local explanations, and in particular for global explanations, is limited. In the present work we propose an algebraic method, rooted in lattice theory, for the (global) explanation of tree ensembles. In detail, we introduce two novel conceptual views on tree ensemble classifiers and demonstrate their explanatory capabilities on Random Forests that were trained with standard parameters.

Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To investigate the granules with some special needs, we propose a novel type of compound concepts in this paper, i.e., common-and-necessary concept. Based on the definitions of concept-forming operations, the logical formulas are derived for each of the following types of concepts: formal concept, object-induced three-way concept, object oriented concept and common-and-necessary concept. Furthermore, by utilizing the logical relationship among various concepts, we have derived concise and unified equivalent conditions for definable granules and approaching descriptions for indefinable granules for all four kinds of concepts.

Based on rectangle theory of formal concept and set covering theory, the concept reduction preserving binary relations is investigated in this paper. It is known that there are three types of formal concepts: core concepts, relative necessary concepts and unnecessary concepts. First, we present the new judgment results for relative necessary concepts and unnecessary concepts. Second, we derive the bounds for both the maximum number of relative necessary concepts and the maximum number of unnecessary concepts and it is a difficult problem as either in concept reduction preserving binary relations or attribute reduction of decision formal contexts, the computation of formal contexts from formal concepts is a challenging problem. Third, based on rectangle theory of formal concept, a fast algorithm for reducing attributes while preserving the extensions for a set of formal concepts is proposed using the extension bit-array technique, which allows multiple context cells to be processed by a single 32-bit or 64-bit operator. Technically, the new algorithm could store both formal context and extent of a concept as bit-arrays, and we can use bit-operations to process set operations "or" as well as "and". One more merit is that the new algorithm does not need to consider other concepts in the concept lattice, thus the algorithm is explicit to understand and fast. Experiments demonstrate that the new algorithm is effective in the computation of attribute reductions.