Use Of Formal Concept Analysis Research Articles

Data depth functions for non-standard data by use of formal concept analysis

In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This covers a wide range of different data types, which we refer to as non-standard data. Depth functions have been studied intensively for normed vector spaces. However, a discussion of depth functions for non-standard data is lacking. In this article, we address this gap by using formal concept analysis to obtain a unified data representation. Building on this representation, we then define depth functions for non-standard data. Furthermore, we provide a systematic basis by introducing structural properties using the data representation provided by formal concept analysis. Finally, we embed the generalised Tukey depth into our concept of data depth and analyse it using the introduced structural properties. Thus, this article presents the mathematical formalisation of centrality and outlyingness for non-standard data and increases the number of spaces in which centrality can be discussed. In particular, we provide a basis for defining further depth functions and statistical inference methods for non-standard data.

Subgroup Discovery in Machine Learning Problems with Formal Concepts Analysis and Test Theory Algorithms

A number of real-world problems of automatic grouping of objects or clustering require a reasonable solution and the possibility of interpreting the result. More specific is the problem of identifying homogeneous subgroups of objects. The number of groups in such a dataset is not specified, and it is required to justify and describe the proposed grouping model. As a tool for interpretable machine learning, we consider formal concept analysis (FCA). To reduce the problem with real attributes to a problem that allows the use of FCA, we use the search for the optimal number and location of cut points and the optimization of the support set of attributes. The approach to identifying homogeneous subgroups was tested on tasks for which interpretability is important: the problem of clustering industrial products according to primary tests (for example, transistors, diodes, and microcircuits) as well as gene expression data (collected to solve the problem of predicting cancerous tumors). For the data under consideration, logical concepts are identified, formed in the form of a lattice of formal concepts. Revealed concepts are evaluated according to indicators of informativeness and can be considered as homogeneous subgroups of elements and their indicative descriptions. The proposed approach makes it possible to single out homogeneous subgroups of elements and provides a description of their characteristics, which can be considered as tougher norms that the elements of the subgroup satisfy. A comparison is made with the COBWEB algorithm designed for conceptual clustering of objects. This algorithm is aimed at discovering probabilistic concepts. The resulting lattices of logical concepts and probabilistic concepts for the considered datasets are simple and easy to interpret.

Formal Concept Analysis Applications in Bioinformatics

The bioinformatics discipline seeks to solve problems in biology with computational theories and methods. Formal concept analysis (FCA) is one such theoretical model, based on partial orders. FCA allows the user to examine the structural properties of data based on which subsets of the dataset depend on each other. This article surveys the current literature related to the use of FCA for bioinformatics. The survey begins with a discussion of FCA, its hierarchical advantages, several advanced models of FCA, and lattice management strategies. It then examines how FCA has been used in bioinformatics applications, followed by future prospects of FCA in those areas. The applications addressed include gene data analysis (with next-generation sequencing), biomarkers discovery, protein-protein interaction, disease analysis (including COVID-19, cancer, and others), drug design and development, healthcare informatics, biomedical ontologies, and phylogeny. Some of the most promising prospects of FCA are identifying influential nodes in a network representing protein-protein interactions, determining critical concepts to discover biomarkers, integrating machine learning and deep learning for cancer classification, and pattern matching for next-generation sequencing.

Efficient bilingual lexicon extraction from comparable corpora based on formal concepts analysis

AbstractBilingual corpora are an essential resource used to cross the language barrier in multilingual natural language processing tasks. Among bilingual corpora, comparable corpora have been the subject of many studies as they are both frequent and easily available. In this paper, we propose to make use of formal concept analysis to first construct concept vectors which can be used to enhance comparable corpora through clustering techniques. We then show how one can extract bilingual lexicons of improved quality from these enhanced corpora. We finally show that the bilingual lexicons obtained can complement existing bilingual dictionaries and improve cross-language information retrieval systems.

Virtual Machines Scheduling in Mobile Edge Computing: A Formal Concept Analysis Approach

Mobile Edge Computing (MEC) is providing cloud computing capabilities within the radio access networks and offering a new paradigm to liberate the mobile devices from heavy computational workloads. Importantly, MEC can effectively reduce latency, avoid congestion, and prolong the battery lifetime of mobile devices by offloading the computation tasks from the mobile devices to a physically proximal MEC servers. Particularly, Virtual Machines (VMs) scheduling is a critical issue for tasks offloading and computation in MEC. Regarding to the VMs scheduling problem in MEC environmnet, this paper pioneers the use of Formal Concept Analysis (FCA) methodology for identifying the mapping from tasks to VMs. Specifically, the VMs profile and tasks descriptions are initially characterized as the formal contexts, respectively. With the constructed formal contexts, the corresponding formal concepts which refer to the rules set, are then generated. To better infuse the rules set of VMs and tasks, this paper defines a similarity measurement between formal concepts of VMs and tasks. Consequently, the matching problem from a given task to a virtual machine is to return the expected virtual machine according to the principle of maximum similarity degree between formal concepts of virtual machine and task. Extensive simulations are conducted with a real dataset for the validation of feasibility and effectiveness of the proposed approach. Specifically, the proposed approach can significantly reduce the energy consumption around 28 percent comparing to the approach without consideration of energy consumption. Overall, It is demonstrated that FCA-based VMs scheduling is a novel solution for a sustainable VMs scheduling in MEC environment.

Knowledge Reduction in Formal Contexts through CUR Matrix Decomposition

The use of formal concept analysis (FCA) derives knowledge from any underlying information system in the form of concept lattices and a set of association rules. However, huge contexts increase the complexities of deriving concept lattices and their association rules. Consequently, the task of discovering knowledge and mining association rules becomes a challenging problem. Researchers have handled this problem with matrix decomposition techniques to approximate the original context which is perhaps not best suitable, because the linear combination of vectors do not yield meaningful interpretations in real-life contexts. To overcome this problem, in this article we propose a novel approach using the CUR matrix decomposition technique which decomposes the original context in terms of dimensionally reduced low-rank matrices of actual columns and rows. The main distinction of the CUR decomposition method from others is that it maintains better structural properties of the original matrix. So the use of CUR decomposition in FCA reduction techniques could assist us in retrieving the highly important information from the datasets. The proposed method is illustrated with the use of real-time medical diagnosis reports. Furthermore, the performance of the proposed method is tested on the large synthetic contexts.

Formalizing and enriching phenotype signatures using Boolean networks

In order to predict the behavior of a biological system, one common approach is to perform a simulation on a dynamic model. Boolean networks allow to analyze the qualitative aspects of the model by identifying its steady states and attractors. Each of them, when possible, is associated with a phenotype which conveys a biological interpretation. Phenotypes are characterized by their signatures, provided by domain experts. The number of steady states tends to increase with the network size and the number of simulation conditions, which makes the biological interpretation difficult. As a first step, we explore the use of Formal Concept Analysis as a symbolic bi-clustering technics to classify and sort the steady states of a Boolean network according to biological signatures based on the hierarchy of the roles the network components play in the phenotypes. FCA generates a lattice structure describing the dependencies between proteins in the signature and steady-states of the Boolean network. We use this lattice (i) to enrich the biological signatures according to the dependencies carried by the network dynamics, (ii) to identify variants to the phenotypes and (iii) to characterize hybrid phenotypes. We applied our approach on a T helper lymphocyte (Th) differentiation network with a set of signatures corresponding to the sub-types of Th. Our method generated the same classification as a manual analysis performed by experts in the field, and was also able to work under extended simulation conditions. This led to the identification and prediction of a new hybrid sub-type later confirmed by the literature.

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.

Reliable relay‐based broadcasting through formal concept analysis for WSNs

AbstractBroadcasting is a fundamental operation in wireless sensor networks and is used for querying, key distribution, time synchronization, routing, and node localization. Nevertheless, sensors are prone to failures such as software or hardware malfunctioning, exhaustion of energy, and environmental hazards. In this paper, a review of realistic dominated connected set with multipoint relay (RDS‐MPR) is performed. Then, an enhancement of this method, called reliable relay‐based broadcasting (RRB), is proposed. RRB improves RDS‐MPR by considering a trusted index for each node, which is updated during the data gathering process at the sink node. In addition, the use of formal concept analysis in RRB provides the best sorting of nodes according to their weights, which helps to refine selection of relay nodes compared with RDS‐MPR. The effectiveness of the proposed scheme is measured through a simulation study using NS‐2. Copyright © 2016 John Wiley & Sons, Ltd.

Data mining algorithms to compute mixed concepts with negative attributes: an application to breast cancer data analysis

In the design of mathematical methods for a medical problem, one of the kernel issues is the identification of symptoms and measures that could help in the diagnosis. Discovering connections among them constitute a big challenge because it allows to reduce the number of parameters to be considered in the mathematical model. In this work, we focus on formal concept analysis as a very promising technique to address this problem. In previous works, we have studied the use of formal concept analysis to manage attribute implications. In this work, we propose to extend the knowledge that we can extract from every context using positive and negative information, which constitutes an open problem.Based on the main classical algorithms, we propose new methods to generate the lattice concept with positive and negative information to be used as a kind of map of attribute connections. We also compare them in an experiment built with datasets from the UCI repository for machine learning. We finally apply the mining techniques to extract the knowledge contained in a real data set containing information about patients suffering breast cancer. The result obtained have been contrasted with medical scientists to illustrate the benefits of our proposal. Copyright © 2016 John Wiley & Sons, Ltd.

Exploring Utility of Formal Concept Analysis Approach to Coral Reef Assessment

This study explored the use of formal concept analysis (FCA), a data mining technique, to analyze coral reef transect data (in terms of life forms) and comparing its results to the standard assessment analysis. Utilizing the quadrat-life form as the object-attribute pair, the results derived from the context was analyzed to assess the coral reefs in the study site which consisted of three stations. Data from Station 1 and Station 2 showed the dominance of Acropora digitate and Acropora branching life forms, respectively. Some life forms were absent from both Stations 1 and 2 but all life forms were present in Station 3 with eight life forms having the highest occurrence. Station 3 had the highest diversity of life forms while Station 2 had the highest live coral cover. This study showed how FCA can be used to generate new knowledge from transect data that can be verified by traditional coral reef assessment results, a possible complement to standard coral reef assessment analytical tools. FCA approach shines when it deals with large data sets from many different sources, which may pave the way for data-driven ecological assessment analysis studies such as those already being done for agriculture.

On the Cognitive Process of Abstraction

Concepts are the basic elements of propositions. Concepts can be best understood as constituted by its subset of objects (Extent) and subset of attributes (Intent). Psychological capacities of human mind for example, learning, thinking, memorizing can be performed by concepts and their association. In this paper, we will explain how human will be able to generalize concrete concepts of Formal Concept Analysis into abstract concepts. In particular, we model the functionalities of concept algebra by making use of Formal Concept Analysis; we illustrate the proposed model with experiments on sample context. This model simulates the thinking process of human mind.

A Spatial Domain Watermarking Approach for Digital Images based on Image Features built on Formal Concepts Analysis

proof of ownership based on digital forensics evidence is the way forward in solving ownership disputes in the ever growing cyberspace that confronts us today. A strong proof beyond all reasonable doubts with the good standing of the law provides victory for a case before a competent court of law. The Society we live in is governed by laws and laws need evidence to pass judgments and not any kind of evidence but evidence compelling enough to attract the passing of judgment. Lessons learnt from the past of the failures of the court to provide and use strong verified evidence due to limitations of scientific evidence such as DNA, surveillance videos, authenticable images etc. have cost human life's freedom and having access to a fair trial. We cannot wait till certain loopholes are exploited in our digital cyber evolution before we get it fixed. Hence stronger and a more compelling techniques are needed for image authentication and identification. In our work, we proposed a spatial domain watermarking approach for digital images based on image features built on formal concepts analysis. We adopt the use of formal concept analysis due to the fact that a change in a pixel value can result in a change in the lattice generated from the image. We presented our results and they showed to be very effective.

Formal concept analysis approach to cognitive functionalities of bidirectional associative memory

Abstract Pattern association is one among the ways through which human brain stores and recalls information. From the literature, it is evident that cognitive abilities of human brain such as learning, memorizing, recalling and updating of information are performed via concepts and their connections. In this work we have made use of Formal Concept Analysis (FCA), a mathematical framework for data and knowledge processing, to represent memories and to perform some of the cognitive functions of human brain. In particular, we model the functionalities of bidirectional associative memories. The proposed model can learn, memorize the learnt information, bi-directionally recall the information that is associated with the presented cue with the help of object-attribute relations that exists in the scenario and update the knowledge when there is a change in the considered scenario. Also when a noisy cue is given, the model is capable of recalling the most closely associated pattern by exploiting the concept hierarchy principle of FCA. Similarly, when a new information is presented on a learnt scenario, the proposed model can update its knowledge by avoiding the need to re-learn scenario. We illustrate the proposed model with a case study and validate with experiments on few real world datasets.

A new FCA algorithm enabling analyzing of complex and dynamic data sets

Analyzing data with the use of Formal Concept Analysis (FCA) enables complex insights into hidden relationships between objects and features in a studied system. Several improvements in this research area, such as Fuzzy FCA or L-Fuzzy Concepts, bring the possibility to analyze data with a certain rate of indeterminacy. However, the usage of FCA on larger complex data brings several problems relating to the time-complexities of FCA algorithms and the size of generated concept lattices. The fuzzyfication of FCA emphasizes the mentioned problems. This article describes significant improvements of a selected FCA algorithm. The primary focus was given on the system of an effective data storage. The binary data was stored with the use of finite automata that leads to the lower memory consumption. Moreover, the better querying performance was achieved. Next, we focused on the inner process of the computation of all formal concepts. All improvements were integrated into a new FCA algorithm that can be used to analyze more complex data sets.

Exploring the Determinants of Regional Unemployment Disparities in Small Data Sets

While standard economic theory suggests that unemployment should be evenly distributed across space, casual observation of unemployment rates shows that this is not the case. This has led to the development of a substantial literature on the topic. Due to the complexity of the problem, it is not always clear what the root cause is. This is particularly true when considering a small geographic area with limited data. This article will explore what insights can be gained through the use of formal concept analysis and association rules. It is hoped that these techniques will be of use to both theoreticians and policy makers.

Curbing domestic violence: instantiating C–K theory with formal concept analysis and emergent self‐organizing maps

AbstractWe propose a human‐centred process for knowledge discovery from unstructured text that makes use of formal concept analysis and emergent self‐organizing maps. The knowledge discovery process is conceptualized and interpreted as successive iterations through the concept–knowledge (C–K) theory design square. To illustrate its effectiveness, we report on a real‐life case study of using the process at the Amsterdam–Amstelland police in the Netherlands aimed at distilling concepts to identify domestic violence from the unstructured text in actual police reports. The case study allows us to show how the process was not only able to uncover the nature of a phenomenon such as domestic violence, but also enabled analysts to identify many types of anomaly in the practice of policing. We will illustrate how the insights obtained from this exercise resulted in major improvements in the management of domestic violence cases. Copyright © 2010 John Wiley & Sons, Ltd.

Acquiring and Applying Contextualised Tacit Knowledge

The acquisition and application of knowledge, in particular tacit knowledge (TK), are seen as decisive competitive factors in the knowledge society of the twenty-first century. Despite much talk about the importance of knowledge transfer, little research shows how to identify and measure TK, less research addresses how to transfer TK between individuals and even fewer of these approaches offer any technology that can assist with transfer. This paper does not address the issues of identification and measurement of TK. The purpose of this paper is two-fold: describe a knowledge acquisition and representation technique, known as Ripple Down Rules (RDR), which can be used to capture knowledge, explicit and tacit, in context from those already identified as experts and to describe a set-theoretical technique, known as formal concept analysis (FCA) to assist transfer of the RDR knowledge to another human. Unlike most knowledge acquisition approaches, the RDR knowledge acquisition technique does not rely on the expert to specify what they know. Instead, knowledge becomes codified by the RDR system while the domain expert exercises his or her expertise. The approach does not capture all organisational knowledge, but the knowledge that is captured will be a mixture of different types of knowledge, including formal and codified knowledge that can be learnt from a book and practice-based knowledge that is passed on while on the job. The knowledge captured using RDR may be transferred to another individual through the use of FCA to retrospectively and automatically develop knowledge models that the user can explore. This work offers a possible solution to three knowledge management challenges: capture, utilisation and preservation of knowledge within an organisation.

Multi-level knowledge discovery from rule bases

The discovery of multi-level knowledge is important to allow queries at and across different levels of abstraction. While there are some similarities between our research and that of others in this area, the work reported in this paper does not directly involve databases and is differently motivated. Our research is interested in taking data in the form of rule-bases and finding multi-level knowledge. This paper describes our motivation, our preferred technique for acquiring the initial knowledge known as Ripple-Down Rules, the use of Formal Concept Analysis to develop an abstraction hierarchy, and our application of these ideas to knowledge bases from the domain of chemical pathology. We also provide an example of how the approach can be applied to other prepositional knowledge bases and suggest that it can be used as an additional phase to many existing data mining approaches.

Analysis of Computer-Mediated Communication: Using Formal Concept Analysis as a Visualizing Methodology

Computer-Mediated Communication (CMC) is used in different contexts such as business, non-profit organizations, and education and uses different tools such as computer conferencing, e-mail, and groupware. However, it is apparent that the field of CMC lacks established methodologies to analyze the phenomena. This article introduces the use of Formal Concept Analysis (FCA) as a methodology to visualize the data in CMC. FCA is based on a mathematical lattice theory and offers visual maps (graphs) with conceptual hierarchies. Combined with content analysis, FCA is proposed to be a potential method for the analysis of CMC. In this study, three categories (social, cognitive, and metacognitive) from Henri's (1992) model for CMC content analysis were applied to FCA after a previous study used a content-analysis method based on Henri's model to convert the data from a computer conference. The purpose of this article is to provide an example of the application of FCA to CMC and to argue for its potential use for analyzing on-line discourse. Although this article specifically addresses issues related to analyzing data in CMC for education, the methodology is applicable to the analysis of CMC for different purposes.