Formal Concept Analysis Tools Research Articles

Identifying Adversaries’ Signatures Using Knowledge Representations of Cyberattack Techniques on Cloud Infrastructure

Advanced Persistent Threats (APTs) have increased in parallel to growing cloud infrastructure and cloud Software-as-a-Service (SaaS) needs, exposing new vulnerabilities within the cloud environment. Moreover, APT groups are becoming more sophisticated and organised which needs to be addressed by the research community to enable faster response and more importantly, prevent threats within the domain. The MITRE ATT&CK Cloud framework offers one of the leading structured inventories within this context. Our research is to expose patterns and signatures of a select group of APT’s on the MITRE Cloud Framework by using Formal Concept Analysis (FCA) to construct a “lattice graph” and an ontology. The goal is to develop a better conceptualisation of the MITRE ATT&CK Cloud Matrix framework for cyber security experts to be able to proactively act upon adversary techniques. The MITRE ATT&CK framework was retrieved, cleaned, and pre-processed to construct the lattice and ontology using data cleaning methods, FCA tools such as Concept Explorer, and the Web Ontology Language (OWL), with additional symbolic reasoning and inference generation. This resulted in knowledge representations/graphs, which are highly efficient representations of this knowledge field. The underlying linkages between techniques and targets specific to those APTs are further exposed and enriched and presented visually and integrated into the ontology. The ontology gives formalisation to associations and implications between techniques, tactics, and APTs – enabling cyber security practitioners to forecast potential targets and techniques based on their scenario, but also to attribute certain technique patterns and signatures to individual APTs. Cyber security practitioners can query from this knowledge graph and formulate strategic proactive measures. From these findings, the applications and constraints of the APTs’ cyber-attack techniques and their associated patterns were determined. The findings provide a guideline for future additional research in the field of AI knowledge representation in cybersecurity, as well as highlighting certain limitations in this field of research.

Colour morphological operators based on formal concept analysis

To avoid the destruction of the colour topology of image and the loss of details caused by the existing morphological operators, new colour morphological operators are proposed based on formal concept analysis (FCA). The main idea is to define a set of structuring elements (SEs) for morphological operators, one for each pixel of the image, which can be adapted to the image content. FCA tools, which have good performance in structuring information, are used to find similar pixels that can form SEs. Then, the new operators are defined and applied to different colour spaces. Experimental results show that the proposed operators outperform other kind of operators in preserving detail information and the structures within colour images, which improve the precision of image processing.

Graph Theoretic Lattice Mining Based on Formal Concept Analysis (FCA) Theory for Text Mining

The growth of the semantic web has fueled the need to search for information based on the understanding of the intent of the searcher, coupled with the contextual meaning of the keywords supplied by the searcher. The common solution to enhance the searching process includes the deployment of formal concept analysis (FCA) theory to extract concepts from a set of text with the use of corresponding domain ontology. However, creating a domain ontology or cross-platform ontology is a tedious and time consuming process that requires validation from domain experts. Therefore, this study proposed an alternative solution called Lattice Mining (LM) that utilizes FCA theory and graph theory. This is because the process of matching a query to related documents is similar to the process of graph matching if both the query and the documents are represented using graphs. This study adopted the idea of FCA in the determination of the concepts based on texts and deployed the lattice diagrams obtained from an FCA tool for further analysis using graph theory. The LM technique employed in this study utilized the adjacency matrices obtained from the lattice outputs and performed a distance measure technique to calculate the similarity between two graphs. The process was realized successively via the implementation of three algorithms called the Relatedness Algorithm (RA), the Adjacency Matrix Algorithm (AMA) and the Concept-Based Lattice Mining (CBLM) Algorithm. A similarity measure between FCA output lattices yielded promising results based on the ranking of the trace values from the matrices. Recognizing the potential of this method, future work includes refinement in the steps of the CBLM algorithm for a more efficient implementation of the process.

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.

Partner selection for interfirm collaboration in ship design

PurposeThe purpose of this paper is to apply a mathematical method of formal concept analysis (FCA) to facilitate evaluation of potential partners, and to select the most appropriate partner for horizontal strategic alliances. Horizontal collaboration between ship design firms is important in relation to business cyclicality in the industry. The workload in ship design firms drops during the troughs of the shipbuilding cycle and increases dramatically during the peaks of the cycle.Design/methodology/approachThe proposed method of partnership selection applies FCA, which is based on mathematical lattice theory. FCA allows firms to evaluate and select the best suitable partners for horizontal interfirm cooperation from several possible candidate firms. Utilization of FCA allows a firm to visually analyze a potential partner for a horizontal strategic alliance.FindingsThe contribution of this study to the literature is twofold. First, it contributes to the literature on the application of FCA in management field. Second, this study contributes to the partner selection literature. The contribution of the study is an alternative quantitative method for partner selection based on FCA. FCA compliments qualitative approaches in the process of alternatives evaluation and decision‐making regarding partner selection for horizontal collaboration.Practical implicationsPractitioners from ship design firms can use the FCA tool to facilitate decision‐making relating to the screening of potential partners for horizontal cooperation with regard to pre‐specified selected criteria.Originality/valueFCA has been marginally applied to aid managerial decision making. The FCA tool is valuable for practitioners from ship design firms to manage the selection of partners for horizontal collaboration. The FCA tool is associated with numerous advantages, notably, relative simplicity and versatility of visual analysis when compared with other mathematical approaches such as the analytic hierarchy process, the analytic network process, optimization modeling, and fuzzy set logic.

형식개념분석을 위한 자동화 도구의 개발과 의료분야에서의 적용사례

형식개념분석기법(FCA: Formal Concept Analysis)은 대상 도메인의 데이터를 사용자의 관점과 해석을 바탕으로 개념화함으로서 필요한 정보의 추출과 접근을 제공하기 위한 기법으로서 다양한 분야에서 널리 사용되고 있다. 그러나, 기존의 형식개념분석기법 지원 도구들은 대부분 객체와 속성간의 관계를 나타낸 One-valued context에 대한 분석만을 중점적으로 지원하고 있고, 다종다양한 값을 갖는 데이터들로 구성된 Many-valued context에 대한 분석을 충분히 지원하지 못하고 있다. 따라서, 본 논문에서는 다양한 값을 갖는 입력 데이터를 사용자의 목적에 맞도록 해석하여 간결화하기 위한 스케일링(Scaling) 알고리즘과 입력 데이터들로부터 개념을 추출하여 계층구조화하기 위한 알고리즘을 제안한다. 이와 같은 연구결과를 토대로 개념분석과 계층구조화를 위한 자동화 도구(FCA Wizard)를 개발하여, 실제 의료 분야에서의 적용사례를 소개한다. For extracting and processing information explicitly from given data, Formal Concept Analysis(FCA) is provided a method which is widely used for data analysis and clustering. The data can be structured into concepts, which are formal abstractions human thought allowing meaningful comprehensible interpretation. However, most FCA tools mainly focus on analyzing one-valued contexts that represent objects, attributes and binary relations between them. There we few FCA tools available that provide scaling and analyzing many-valued contexts representing objects, attributes and relations with attributes' values. In this paper, we propose not only a scaling algorithm for interpreting and simplifying the multivalued input data, but also an algorithm to generate concepts and build concept hierarchy from given raw data as well. Based on these algorithms, we develop an automate tool, FCA Wizard, for concept analysis and concept hierarchy. We also present FCA Wizard based applications in medical domain.