Knowledge Reduction in Formal Contexts through CUR Matrix Decomposition

Sumangali, K.; Cherukuri, Aswani Kumar

doi:10.1080/01969722.2019.1602300

Cited by 5 publications

(6 citation statements)

References 37 publications

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“…To decrease the formal context, non-negative matrix factorization was applied [59]. Recently, Sumangali and Kumar [60] have developed a unique strategy that decomposes the original context in terms of dimensionally reduced low-rank matrices comprising real columns and rows using the CUR matrix decomposition technique. As a result, using CUR decomposition in FCA reduction techniques might help us extract the most significant data from the datasets.…”

Section: Non-essential Distinctions Eliminationmentioning

confidence: 99%

“…Regarding the exceptions, we can mention the method in [2], which has formal context as a point to start the reduction process and the method in [81], which has both formal concepts and concept lattice as a point to begin the reduction process. Under the non-essential distinctions elimination category, all of those [32], [33], [43], [59], [60], [82]- [85] reduction methods have formal context as a preliminary step for the reduction process, except for the method in [86], which has both formal context and formal concepts as a point to start the reduction process and the method in [76], which has both formal concepts and concept lattice as a preliminary step for the reduction process. In the concept filtration category, eight methods [65], [71], [79], [82], [87]- [90] use formal context as a preliminary step for the reduction process, four methods [35], [64], [91], [92] use concept lattice as a preliminary step for the reduction process, three reduction methods [61], [69], [73] use both formal concepts and concept lattice as a preliminary step for the reduction process, and two reduction methods [20], [36] use both formal context and formal concepts as a preliminary step for the reduction process.…”

mentioning

confidence: 99%

“…In the non-essential distinctions elimination category, all methods modify occurrences (incidences); as well as another two methods [32], [83] modify the set of objects, five methods [59], [60], [84]- [86] alter the set of attributes too, and one [33] alters both the set of objects and the set of attributes along with incidences. −…”

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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: Non-essential Distinctions Eliminationmentioning

confidence: 99%

mentioning

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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“…In [41,42], the binary approach is generalized to fuzzy data and relationships, such that properties and theorems from formal concepts used in BFA apply also if attributes and relations are assessed by the truth value from multimodal logic, i.e., by values from the interval [0, 1]. Recent advances regarding formal concept analysis involving dimensionality reduction may also be found, for example, in [43,44].…”

Section: Background and Related Workmentioning

confidence: 99%

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Grobelny

Michalski

Weber

2020

Neural Comput & Applic

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In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic ordinal-scale (LOS) matrix as a max–min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach are treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

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“…In particular, Guo et al introduced the six types of lifting on a relationally enriched context and the notion of power contexts [11]. Various types of research related to FCA are being actively conducted to solve the problems necessary for the practical applications of the FCA in the real world [5,[12][13][14][15][16][17][18][19][20][21]. Other studies on knowledge reduction have been actively conducted in information systems as well as in FCA [13,[22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Attribute Reduction in Soft Contexts Based on Soft Sets and Its Application to Formal Contexts

Min¹

2020

Mathematics

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We introduce the notion of the reduct of soft contexts, which is a special notion of a consistent set for soft contexts. Then, we study its properties and show that this notion is well explained by the two classes, 1 0 and 2 0 , of independent attributes. In particular, we describe in detail how to extract a reduct from a given consistent set. Then, based on this extraction process, we propose a six-step method for constructing a reduct from a given consistent set. Additionally, to apply this method to formal contexts, we examine the relationship between the reducts of a given formal context and the reducts of the associated soft context. We finally illustrate the process of obtaining reducts in a formal context using this relationship and the six-step method using an example.

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Knowledge Reduction in Formal Contexts through CUR Matrix Decomposition

Cited by 5 publications

References 37 publications

Survey on attribute and concept reduction methods in formal concept analysis

Survey on attribute and concept reduction methods in formal concept analysis

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Attribute Reduction in Soft Contexts Based on Soft Sets and Its Application to Formal Contexts

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