Comparison of QSARs and Characterization of Structural Basis of Bioactivity Using Partial Order Theory and Formal Concept Analysis: A Case Study with Mutagenicity

2011 ◽  
Vol 7 (2) ◽  
pp. 109-121 ◽  
Author(s):  
Guillermo Restrepo ◽  
Subhash C. Basak ◽  
Denise Mills
Keyword(s):  
Partial Order ◽  
Formal Concept Analysis ◽  
Order Theory ◽  
Concept Analysis ◽  
Structural Basis ◽  
Formal Concept

scholarly journals Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 173
Author(s):  
Francisco José Valverde-Albacete ◽  
Carmen Peláez-Moreno
Keyword(s):  
Data Mining ◽  
Formal Concept Analysis ◽  
Order Theory ◽  
Concept Analysis ◽  
Galois Connection ◽  
Formal Concept ◽  
Data Mining Technique ◽  
Full Spectrum ◽  
Mining Technique ◽  
Ordered Pairs

Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is K¯-four-fold Formal Concept Analysis (K¯-4FCA) where K¯ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in dually-ordered pairs—e.g., the complete max-plus and min-plus semirings—the basic construction shows dual-order-, row–column- and Galois-connection-induced dualities that appear simultaneously a number of times to provide the full spectrum of variability. Our results lead to a fundamental theorem of K¯-four-fold Formal Concept Analysis that properly defines quadrilattices as 4-tuples of (order-dually) isomorphic lattices of vectors and discuss its relevance vis-à-vis previous formal conceptual analyses and some affordances of their results.

Two Characterizations of Antimatroids

2013 ◽  
Vol 59 (2) ◽  
pp. 453-466
Author(s):  
Hua Mao
Keyword(s):  
Time Delay ◽  
Polynomial Time ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Concept

Abstract NextClosure algorithm is a fast and good algorithm in formal concept analysis. With the assistance of NextClosure algorithm, this article provides a characterization of antimatroids. Additionally, this article introduces a characterization of k- truncated antimatroids. The characterization can be realized by an algorithm which works with polynomial time delay.

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