Application Of Formal Concept Analysis Research Articles

A combination of SEMMA & CRISP-DM models for effectively handling big data using formal concept analysis based knowledge discovery: A data mining approach

Data analytics has emerged as one of the most advanced technologies in recent times. However, the successful implementation of analytics is still a great challenge since they suffer from technical barriers and have a lack of structured approaches for performing analytics. Data mining models are considered as a potential tool for solving problems related to data analytics. Data mining is a process used for extracting the relevant attributes from raw data, which is further processed using the mechanism of knowledge discovery for support decision making. Formal concept analysis (FCA) provides a robust platform for knowledge discovery and helps in the successful adoption of data mining for handling big data. Several mining techniques powered by FCA are discussed by the researchers. However, the analysis of FCA suggests that the effectiveness of FCA for big data needs, a deeper investigation in order to expand its application horizon. In this context, this research emphasizes the application of FCA for developing an effective strategy through a combination of SEMMA and CRISP models for handling big data by integrating knowledge discovery with data mining.

Refining Constructivist Assessment. How to Measure the Main Traditional Indexes in Binary Grids through Formal Concept Analysis

This paper aims to expand knowledge on the application of formal concept analysis, a mathematical theory, to the elaboration of a repertory grid, which is a method designed for exploring the structure and content of a respondent’s system of constructs. After a critical reexamination of the ways in which the commonly used statistical procedures for the analysis of repertory grids can affect data analysis, we revisit an alternative methodology that is more consistent with both personal construct theory and measurement properties of the variables collected by means of repertory grids. We use a classic example of repertory grid technique and describe it according to both traditional analysis and the alternative methodology. This comparison is aimed at displaying how formal concept analysis applied to repertory grids can provide all the main measures and cognitive indexes that are included in traditional repertory grid analysis. We then provide further evidence to highlight how this proposal can be used to collect more consistent and detailed information from repertory grids, thus preserving the nature of the respondents’ data.

Exploring Different Paradigms to Extract Proper Implications From High Dimensional Formal Contexts

Formal Concept Analysis (FCA) is an applied mathematical technique for data analysis, in which the relations between objects and attributes are identified. It introduces the notion of concepts and their hierarchical structure, from which we can obtain a set of implications between attributes that characterize a knowledge domain. The volume of information to be processed makes the use of FCA difficult in domains with a high number of dimensions, creating a demand for new solutions and algorithms for FCA applications. This article explores different approaches to extract proper implications from high dimensional contexts based on constraints to obtain the set of implications rules. We propose algorithms that use a data structure called Binary Decision Diagram (BDD) to represent the formal context, which reduces its size and, due to this, operates more efficiently. We also propose a heuristic to obtain proper implications by reducing the unnecessary generation of premises. In addition, we implemented a parallel computing model for generating and obtaining different implications. To analyze the proposed algorithms, we used different synthetic contexts with a varying number of objects, attributes, and density. The results obtained presented speed gains of up to 22 times when compared to the solutions proposed in the literature such as Impec and PropIm.

Semantic Data Management in IT Service Performance Assurance

In today's dynamic and highly composed environments, IT service performance and dependability assurance require efficient reasoning about the performance and dependability effects of faults and the countermeasures to choose, using limited knowledge. Model- and observation-based qualitative error propagation analysis methods can be applied to this end; however, providing support for the human, as well as conceptually structured machine interpretation of sets of competing error propagation hypotheses is an open problem. This paper proposes the application of Formal Concept Analysis (FCA) for these tasks. A natural way to represent error propagation hypothesis sets as formal contexts is proposed, and the visual diagnostic exploration of formal context lattices is introduced. On this basis, potential applications of FCA in performance and dependability assurance activities are characterized.

FCA-based knowledge representation and local generalized linear models to address relevance and diversity in diverse social images

Abstract In social image retrieval, the main goal is to offer a relevant but also diverse result set of images to the user. To address relevance and diversity at the same time, we propose a multi-modal procedure. This approach deals with the diversification problem using a two-step procedure based on the application of Formal Concept Analysis (FCA) to organize the text content of the images, followed by a Hierarchical Agglomerative Clustering (HAC) step to find the topics addressed by the images. FCA detects the latent concepts covered by the images in the result set, organizing them according to these concepts. In the second step, clustering is carried out to group together the ones with a similar concept. To assess the relevance, we use an adaptive multi-model relevance feedback algorithm which uses the low-level visual features to estimate a relevance measurement for all the images in the dataset. Several local logistic regression models are automatically adjusted to select the best performance for each topic. Finally, the images are ranked by selecting the highest probability image at each text cluster, generating a relevant but diverse ranked list. Diverse social images 2013, 2014, 2015, 2016 and 2017 datasets from the MediaEval benchmark are used to test the performance of our approach in a real scenario. Experimental results show that the proposed joint multimedia procedure works well on multi-concept and complex collections without adjusting parameters among collections, achieving the best results with a user-based relevance feedback algorithm. Our challenge is to achieve similar results with our automatic version.

Research on Two Main Construction Methods of Concept Lattices

Because of the completeness of concept lattices, the time complexity of constructing concept lattices has become the main factor affecting the application of formal concept analysis (FCA). The key problems in the research of concept lattices are how to improve the generation efficiency and how to reduce the space and time complexity of constructing concept lattices. So far, reviews on lattice construction algorithms have not been comprehensive. In view of this situation, we give a detailed review on two categories of construction algorithms: batch methods and incremental methods. The first category is a formal context that cannot be updated once the concept lattice has been constructed; the second category is a formal context that can be updated after a new object being added to the formal context. We briefly introduce classical and improved construction methods, illustrate the deficiencies of some algorithms and point out the improvements of the follow-up algorithms. Furthermore, we compare and discuss several key algorithms, and also pay attention to the application of concept lattices. Finally, two further research directions of concept lattices are proposed, including parallel construction methods of concept lattices and research of heterogeneous data concept lattices.

ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram †

Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities.

A comprehensive overview on the foundations of formal concept analysis

The immersion of voluminous collection of data is inevitable almost everywhere. The invention of mathematical models to analyse the patterns and trends of the data is an emerging necessity to extract and predict useful information in any Knowledge Discovery from Data (KDD) process. The Formal Concept Analysis (FCA) is an efficient mathematical model used in the process of KDD which is specially designed to portray the structure of the data in a context and depict the underlying patterns and hierarchies in it. Due to the huge increase in the application of FCA in various fields, the number of research and review articles on FCA has raised to a large extent. This review differs from the existing ones in presenting the comprehensive survey on the fundamentals of FCA in a compact and crisp manner to benefit the beginners and its focuses on the scalability issues in FCA. Further, we present the generic anatomy of FCA apart from its origin and growth at a primary level.

Formal concept analysis for topic detection: A clustering quality experimental analysis

The Topic Detection task is focused on discovering the main topics addressed by a series of documents (e.g., news reports, e-mails, tweets). Topics, defined in this way, are expected to be thematically similar, cohesive and self-contained. This task has been broadly studied from the point of view of clustering and probabilistic techniques. In this work, we propose for this task the application of Formal Concept Analysis (FCA), an exploratory technique for data analysis and organization. In particular, we propose an extension of FCA-based methods for topic detection applied in the literature by applying the stability concept for the topic selection. The hypothesis is that FCA will enable the better organization of the data and stability the better selection of topics based on this data organization, thus better fulfilling the task requirements by improving the quality and accuracy of the topic detection process. In addition, the proposed FCA-based methodology is able to cope with some well-known drawbacks that clustering and probabilistic methodologies present, such as: the need to set a predefined number of clusters or the difficulty in dealing with topics with complex generalization-specialization relationships. In order to prove this hypothesis, the FCA operation is compared to other established techniques — Hierarchical Agglomerative Clustering (HAC) and Latent Dirichlet Allocation (LDA). To allow this comparison, these approaches have been implemented by the authors in a novel experimental framework. The quality of the topics detected by the different approaches in terms of their suitability for the topic detection task is evaluated by means of internal clustering validity metrics. This evaluation demonstrates that FCA generates cohesive clusters, which are less subject to changes in cluster granularity. Driven by the quality of the detected topics, FCA achieves the best general outcome, improving the experimental results for Topic Detection Task at the 2013 Replab Campaign.

Kōan-like ambiguities in John Cage's Electronic Music for Piano: a novel application of formal concept analysis

In this article I present a novel application of Formal Concept Analysis (FCA) to the problem of interpreting and analysing the non-standard graphical music score Electronic Music for Piano (1965) by American composer John Cage. The avant-garde nature of Cage's score, presented on a single page as a series of anecdotal texts written in natural language, resists traditional approaches of music theory analysis. I utilise FCA for its suitability for delving into the work's taxonomy as well as its ability to visualise and analyse semiotic patterns and relationships within the natural language text fragments of the work. In this regard, FCA is also used as a means in which to frame what many writers have previously identified as kōan-like qualities in many of Cage's works. A kōan is generally understood as a type of unsolvable Zen Buddhist riddle filled with contradictions and ambiguities. I subsequently theorise Electronic Music for Piano as a type of musical kōan, and by applying FCA, demonstrate how various derived formal concepts, object extensions, and subset groupings of the work support this theory.

Formal concept analysis for knowledge discovery from biological data

Due to rapid advancement in high-throughput techniques, such as microarrays and next generation sequencing technologies, biological data are increasing exponentially. The current challenge in computational biology and bioinformatics research is how to analyze these huge raw biological data to extract biologically meaningful knowledge. This review paper presents the applications of formal concept analysis for the analysis and knowledge discovery from biological data, including gene expression discretization, gene co-expression mining, gene expression clustering, finding genes in gene regulatory networks, enzyme/protein classifications, binding site classifications, and so on. It also presents a list of FCA-based software tools applied in biological domain and covers the challenges faced so far.

Application of Formal Concept Analysis in Ontology Engineering

Application of Formal Concept Analysis in Ontology Engineering

Formal concept analysis for knowledge discovery from biological data

Owing to the rapid advancement in high-throughput technologies, such as microarrays and next generation sequencing, the volume of biological data is increasing exponentially. The current challenge in computational biology and bioinformatics research is how to analyse these huge raw biological datasets to extract meaningful biological knowledge. Formal concept analysis is a method based on lattice theory and widely used for data analysis, knowledge representation, knowledge discovery and knowledge management across several domains. This paper reviews the applications of formal concept analysis for knowledge discovery from biological data, including gene expression discretisation, gene co-expression mining, gene expression clustering, finding genes in gene regulatory networks, enzyme/protein classifications, binding site classifications, and domain-domain interaction. It also presents a list of FCA-based software tools applied to the biological domain, and covers the challenges and future directions in this field.

Creating corroborated crisis reports from social media data through formal concept analysis

During a crisis citizens reach for their smart phones to report, comment and explore information surrounding the crisis. These actions often involve social media and this data forms a large repository of real-time, crisis related information. Law enforcement agencies and other first responders see this information as having untapped potential. That is, it has the capacity extend their situational awareness beyond the scope of a usual command and control centre. Despite this potential, the sheer volume, the speed at which it arrives, and unstructured nature of social media means that making sense of this data is not a trivial task and one that is not yet satisfactorily solved; both in crisis management and beyond. Therefore we propose a multi-stage process to extract meaning from this data that will provide relevant and near real-time information to command and control to assist in decision support. This process begins with the capture of real-time social media data, the development of specific LEA and crisis focused taxonomies for categorisation and entity extraction, the application of formal concept analysis for aggregation and corroboration and the presentation of this data via map-based and other visualisations. We demonstrate that this novel use of formal concept analysis in combination with context-based entity extraction has the potential to inform law enforcement and/or humanitarian responders about on-going crisis events using social media data in the context of the 2015 Nepal earthquake.

Performance-friendly rule extraction in large water data-sets with AOC posets and relational concept analysis

In this paper, we consider data analysis methods for knowledge extraction from large water data-sets. More specifically, we try to connect physico-chemical parameters and the characteristics of taxons living in sample sites. Among these data analysis methods, we consider formal concept analysis (FCA), which is a recognized tool for classification and rule discovery on object–attribute data. Relational concept analysis (RCA) relies on FCA and deals with sets of object–attribute data provided with relations. RCA produces more informative results but at the expense of an increase in complexity. Besides, in numerous applications of FCA, the partially ordered set of concepts introducing attributes or objects (AOC poset, for Attribute–Object–Concept poset) is used rather than the concept lattice in order to reduce combinatorial problems. AOC posets are much smaller and easier to compute than concept lattices and still contain the information needed to rebuild the initial data. This paper introduces a variant of the RCA process based on AOC posets rather than concept lattices. This approach is compared with RCA based on iceberg lattices. Experiments are performed with various scaling operators, and a specific operator is introduced to deal with noisy data. We show that using AOC poset on water data-sets provides a reasonable concept number and allows us to extract meaningful implication rules (association rules whose confidence is 1), whose semantics depends on the chosen scaling operator.

A fast incremental algorithm for deleting objects from a concept lattice

The formal context may not be fixed in a real-life application of formal concept analysis, which means that we have to update the present lattice or compute a new lattice from scratch. In this paper, we propose an efficient incremental algorithm, referred to as FastDeletion, to delete objects from a concept lattice. The algorithm improves two fundamental procedures shared by other algorithms. These two procedures include determining which concepts need to be deleted and fixing the covering relation. We describe the algorithm thoroughly, prove correctness of our improvements, discuss time complexity issues, and present an experimental evaluation of its performance and comparison with another algorithm. Empirical analyses demonstrate that our algorithm is superior when applied to various types of formal contexts.

Fuzzy concept lattice reduction using Shannon entropy and Huffman coding

In the last decade, formal concept analysis (FCA) in a fuzzy setting has received more attention for knowledge processing tasks in various fields. The hierarchical order visualisation of generated formal concepts is a major concern for the practical application of FCA. In this process, a major issue is the huge number of formal concepts generated from ‘a large context’, and another problem is their ‘storage’ complexity. To deal with these issues a method is proposed in this paper based on Shannon entropy and Huffman coding. The proposed method is illustrated using crisply generated concepts such that the changes between obtained concepts can be measured using Levenshtein distance. The analysis derived from the proposed method is illustrated with an example for FCA in a fuzzy setting.

Preface to the special issue on concept lattices and their applications—CLA 2012

The Ninth International Conference “Concept Lattices and Applications (CLA 2012)” was held in Fuengirola (Malaga), Spain from October 11th until October 14th 2012. CLA is a conference series which was started in 2002 and which focuses on Concept Lattices, Formal Concept Analysis (FCA) and Galois Lattices. FCA was invented by Rudolf Wille in the 1980s as a mathematical modeling of hierarchies, data analysis and conceptual descriptions using mathematical lattice theory. A binary relation (for example between some objects and their attributes) is modeled as a formal context which is transformed into a concept lattice. Because binary relations can be extracted from any relational database or other data repository, FCA has applications in many disciplines, such as data and knowledge processing, information retrieval, data mining, reasoning and software engineering. Since the 1980s, FCA has grown into a reasonably large international research community with two annual international conference series (CLA and ICFCA). Concept lattices can be graphically represented which encourages the development of graphical interfaces for end users and poses interesting research questions relating to graph theory. In the context of “big data”, research questions focus on improving the efficiency of FCA algorithms and on decomposing formal contexts into meaningful smaller units. More recently there has been an increasing interest in Fuzzy FCA, which supports the application of FCA to non-discrete datasets and the factorization of binary matrices as a generalization of formal contexts. This special issue contains the 9 best papers from CLA 2012. In total 44 papers were submitted to CLA 2012 out of which 28 papers were accepted as full papers and published as Volume 972 in the CEUR series (ceur-ws.org). For the special issue, the authors

Inferring Domain-Domain Interactions from Protein-Protein Interactions with Formal Concept Analysis

Identifying reliable domain-domain interactions will increase our ability to predict novel protein-protein interactions, to unravel interactions in protein complexes, and thus gain more information about the function and behavior of genes. One of the challenges of identifying reliable domain-domain interactions is domain promiscuity. Promiscuous domains are domains that can occur in many domain architectures and are therefore found in many proteins. This becomes a problem for a method where the score of a domain-pair is the ratio between observed and expected frequencies because the protein-protein interaction network is sparse. As such, many protein-pairs will be non-interacting and domain-pairs with promiscuous domains will be penalized. This domain promiscuity challenge to the problem of inferring reliable domain-domain interactions from protein-protein interactions has been recognized, and a number of work-arounds have been proposed. This paper reports on an application of Formal Concept Analysis to this problem. It is found that the relationship between formal concepts provides a natural way for rare domains to elevate the rank of promiscuous domain-pairs and enrich highly ranked domain-pairs with reliable domain-domain interactions. This piggybacking of promiscuous domain-pairs onto less promiscuous domain-pairs is possible only with concept lattices whose attribute-labels are not reduced and is enhanced by the presence of proteins that comprise both promiscuous and rare domains.

Formal concept analysis: current trends and directions

Formalization of human thinking helps in fostering the process of learning by giving an explicit representation to human thoughts. Formal Concept Analysis (FCA) finds it's core here. It considers a "concept" as a formal unit of human thought. A concept is represented as a set of inter related objects called the extent and the set of the properties of these objects, called the intent. Making use of the mathematical principles of Lattice Theory and Map Theory of Abstract Algebra, a set of tools and algorithms have been developed in FCA. These helps us to analyze and represent any context as a relation between it's extent and intent. Concepts drawn from the subsets of the extent and intent can be organized in the form of a lattice giving a subsumption hierarchy. Such concept lattices could be maintained by different operations on the lattice like scaling, pruning, navigating etc. A host of applications and software have been developed over the years which serves the usage of FCA tools and processes for specific purposes in various fields. This paper reviews the theoretical foundation, research and applications of FCA in different areas. The paper projects current trends in FCA and concludes with a discussion on open issues and limitations of FCA.