Concepts In Formal Concept Analysis Research Articles

Concepts of neighbors and their application to instance-based learning on relational data

Knowledge graphs and other forms of relational data have become a widespread kind of data, and powerful methods to analyze and learn from them are needed. Formal Concept Analysis (FCA) is a mathematical framework for the analysis of symbolic datasets, which has been extended to graphs and relational data, like Graph-FCA. It encompasses various tasks such as pattern mining or machine learning, but its application generally relies on the computation of a concept lattice whose size can be exponential with the number of instances. We propose to follow an instance-based approach where the learning effort is delayed until a new instance comes in, and an inference task is set. This is the approach adopted in k-Nearest Neighbors, and this relies on a distance between instances. We define a conceptual distance based on FCA concepts, and from there the notion of concepts of neighbors, which can be used as a basis for instance-based reasoning. Those definitions are given for both classical FCA and Graph-FCA. We provide efficient algorithms for computing concepts of neighbors, and we demonstrate their inference capabilities by presenting three different applications: query relaxation, knowledge graph completion, and relation extraction.

Semantic similarity measures for formal concept analysis using linked data and WordNet

Formal Concept Analysis (FCA) is a field of applied mathematics with its roots in order theory, in particular the theory of complete lattices. It is not only a method for data analysis and knowledge representation, but also a formal formulation for concept formation and learning. Over the past 20 years, FCA has been widely studied. In this paper, the current research progresses and the existing problems of similarity measures in FCA are analyzed. To address the drawbacks of the existing methods, we propose a kind of novel semantic similarity measure for FCA by using Linked Data and WordNet. We aim to develop a method that is fully automatic without requiring predefined domain ontologies and can be used independently of the domain in applications requiring semantic similarity measures in FCA. To realize the semantic similarity estimation for FCA, we firstly extend the similarity assessment methods for resources (or entities) in Linked Data into semantic cases by using WordNet. Furthermore, we propose two kinds of semantic similarity measures (i.e., context-free method and context-aware method) for FCA concepts and concept lattices, respectively. Compared with the existing similarity measure methods in FCA, the proposed approach uses concept of possibility theory to determine lower and upper bounds of similarity intervals. Finally, we evaluate the proposed similarity assessment approaches by applying them to real-worlds datasets.

The Connection between Concepts in Formal Concept Analysis and Concepts in a Dual Description Logic

Formal concept analysis (FCA) and description logics (DLs) are two major formalisms around concepts. However, concepts in FCA and concepts in DLs are of different nature. The former are tuples/properties pairs in a given relation, the later are just subsets of domains in terminological interpretations. To represent the logical difference of tuples and attribute values in relations, a dual description logic (DDL) is introduced, in which constants are classified into two classes: tuple constants and value constants, and they are interpreted into two disjoint parts in domain, respectively. Given a model M for DDL, we can obtain a normal relation RM. This paper demonstrates how to connect FCA-concepts in RM and concepts in DDL. To do so, we introduce logical operations negation, disjunction and conjunction on values and on attribute-value pairs, and then build Φ-statements from attribute-value pairs inductively with these operations, and further define a kind of extended FCA-concepts, called Γ-concepts. Each Γ-concept consists of two parts: the extent (tuples the concept covers) and the intent (Φ-statements describing the concept), and there are the following results: the union of any number of extents is always an extent; the complement of an extent is always an extent. Consequently, we obtain two isomorphic lattices: one is LM=(Θ, ∪,∩,–), which is the lattice of subsets of Θ, and the other is concept lattice L(↑RM), where Θ consists of the interpretations of DDL-concepts, and ↑RM is an extend relation from the normal relation RM.

The correspondence between the concepts in description logics for contexts and formal concept analysis

Formal concept analysis (FCA) and description logic (DL) are meant to be formalizations of concepts. A formal concept in the former consists of its intent and extent, where the intent is the set of all the attributes shared by each object in the extent of the concept, and the extent is the set of all the objects sharing each property in the intent of the concept. A concept in the latter formalization is simply a concept name, the interpretation of which is a subset of a universe. To consider the correspondence between concepts in both formalizations, a multi-valued formal context must be represented both as a knowledge base and as a model of the DL for contexts, where concepts are decomposed into tuple concepts C, interpreted as a set of tuples and value concepts V, interpreted as a set of attribute-value pairs. We show that there is a difference between the interpretation of concepts ∀R.V/∀R−.C and the Galois connection between the extent/intent of formal concepts in FCA. According to the Galois connection, there should be concepts of the form +∀R.V and +∀R−.C interpreted in FCA, and hence the logical language L for DL is extended to be L+ together with +∀ as a constructor so that +∀R.V and +∀R−.C are well-defined concepts. Conversely, according to the interpretation in DL there should be pseudo concepts in FCA so that the interpretation of concepts ∀R.V/∀R−.C is the extent/intent of pseudo concepts. The correspondence between formal concepts and concepts in L+, and between pseudo concepts and concepts in L are presented in this paper.

Concept similarity in Formal Concept Analysis: An information content approach

Formal Concept Analysis (FCA) is revealing interesting in supporting difficult activities that are becoming fundamental in the development of the Semantic Web. Assessing concept similarity is one of such activities since it allows the identification of different concepts that are semantically close. In this paper, a method for measuring the similarity of FCA concepts is presented, which is a refinement of a previous proposal of the author. The refinement consists in determining the similarity of concept descriptors (attributes) by using the information content approach, rather than relying on human domain expertise. The information content approach which has been adopted allows a higher correlation with human judgement than other proposals for evaluating concept similarity in a taxonomy defined in the literature.

Ontology-based concept similarity in Formal Concept Analysis

Both domain ontologies and Formal Concept Analysis (FCA) aim at modeling concepts, although with different purposes. In the literature, a promising research area concerns the role of FCA in ontology engineering, in particular, in supporting the critical task of reusing independently developed domain ontologies. With this regard, the possibility of evaluating concept similarity is acquiring an increasing relevance, since it allows the identification of different concepts that are semantically close. In this paper, an ontology-based method for assessing similarity between FCA concepts is proposed. Such a method is intended to support the ontology engineer in difficult activities that are becoming fundamental in the development of the Semantic Web, such us ontology merging and ontology mapping and, in particular, it can be used in parallel to existing semi-automatic tools relying on FCA.

Chu Spaces, Concept Lattices, and Domains

This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross-disciplinary connections. Among other results, we show that the notion of states in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”.