A comprehensive overview on the foundations of formal concept analysis

Sumangali, K.; Cherukuri, Aswani Kumar

doi:10.34105/j.kmel.2017.09.032

Cited by 3 publications

(3 citation statements)

References 59 publications

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“…A large formal context results in a concept lattice that is difficult to work with in practice. As a result, problems with FCA applications, such as dealing with a large formal context and reducing the size of the concept lattice, are highlighted as critical issues in FCA applications [38].…”

Section: Categorization Of Fca Reduction Methodsmentioning

confidence: 99%

“…Not every concept in a context is an object or an attribute concept. Any concept can be an object concept, an attribute concept, a combination of the two, or none [38]. From the concept lattice, the extent part (concept objects) for a formal concept can be reached by a downward path from the node to capture all concept objects.…”

Section: Fca: Key Terminology and Notionsmentioning

confidence: 99%

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Survey on attribute and concept reduction methods in formal concept analysis

Alwersh

Kovács

2023

IJEECS

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Formal concept analysis (FCA) is now widely recognized as a useful approach for extracting, representing, and analyzing knowledge in various domains. The high computational cost of knowledge processing and the difficulty of visualizing the lattice are two key challenges in practical FCA implementations. Moreover, assessing the finalized built-up lattice may be problematic due to the enormous number of formal concepts and the complexity of their connections. The challenge of constructing concept lattices of adequate size and structure to convey high-importance context features remains a significant FCA aim. In the literature, various strategies for concept lattice reduction have been presented. In this work, we suggest a categorization of reduction methods for concept lattice based on three main categories: context pre-processing, non-essential distinctions elimination, and concept filtration, whereby using FCA-based analysis, the most important methods in the literature are analyzed and compared based on six pillars: the preliminary step of the reduction process, domain expert, changing the original data structure, final concept lattice, quality of reduction, and category of reduction method.

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Section: Categorization Of Fca Reduction Methodsmentioning

confidence: 99%

Section: Fca: Key Terminology and Notionsmentioning

confidence: 99%

Survey on attribute and concept reduction methods in formal concept analysis

Alwersh

Kovács

2023

IJEECS

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“…It's worth highlighting that not every concept within a particular context is necessarily an object or an attribute concept. Any concept has the potential to be an object concept, an attribute concept, a blend of the two, or neither [12,13].…”

Section: Expanding On Tablementioning

confidence: 99%

K-Means Extensions for Clustering Categorical Data on Concept Lattice

Alwersh,

Kovács

2023

IJACSA

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Formal Concept Analysis (FCA) is a key tool in knowledge discovery, representing data relationships through concept lattices. However, the complexity of these lattices often hinders interpretation, prompting the need for innovative solutions. In this context, the study proposes clustering formal concepts within a concept lattice, ultimately aiming to minimize lattice size. To address this, The study introduces introduce two novel extensions of the k-means algorithm to handle categorical data efficiently, a crucial aspect of the FCA framework. These extensions, namely K-means Dijkstra on Lattice (KDL) and Kmeans Vector on Lattice (KVL), are designed to minimize the concept lattice size. However, the current study focuses on introducing and refining these new methods, laying the groundwork for our future goal of lattice size reduction. The KDL utilizes FCA to build a graph of formal concepts and their relationships, applying a modified Dijkstra algorithm for distance measurement, thus replacing the Euclidean distance in traditional k-means. The defined centroids are formal concepts with minimal intra-cluster distances, enabling effective categorical data clustering. In contrast, the KVL extension transforms formal concepts into numerical vectors to leverage the scalability offered by traditional k-means, potentially at the cost of clustering quality due to oversight of the data's inherent hierarchy. After rigorous testing, KDL and KVL proved robust in managing categorical data. The introduction and demonstration of these novel techniques lay the groundwork for future research, marking a significant stride toward addressing current challenges in categorical data clustering within the FCA framework.

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Distributed three-way formal concept analysis for large formal contexts

Chunduri

Cherukuri

2023

Journal of Parallel and Distributed Computing

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A comprehensive overview on the foundations of formal concept analysis

Cited by 3 publications

References 59 publications

Survey on attribute and concept reduction methods in formal concept analysis

Survey on attribute and concept reduction methods in formal concept analysis

K-Means Extensions for Clustering Categorical Data on Concept Lattice

Distributed three-way formal concept analysis for large formal contexts

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