Discovery of the $D$-basis in binary tables based on hypergraph dualization

J.B.Nation; Kira Adaricheva

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Discovery of the $D$-basis in binary tables based on hypergraph dualization

Kira Adaricheva, J.B.Nation

Databases · Submitted 11 Apr 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We introduce a novel approach for the discovery of a specific set of implications, called the $D$-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice.

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What the abstract itself states, as probabilities: claims first 0.21 · states limitation 0.29 · human participants 0.42 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.03.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a specific set of implications, called the $D$-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice. At the core of the method are the $D$-relation defined in the lattice theory framework, and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given Sperner hypergraph. The latter algorithm, first developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, artificial intelligence and game theory. One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the University of Hawaii Cancer Center.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web.	background 1.00	0.04	0.03	asserted 1.00
s1	We introduce a novel approach for the discovery of a specific set of implications, called the $D$-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice.	contribution 1.00	0.92	0.52	asserted 1.00
s2	At the core of the method are the $D$-relation defined in the lattice theory framework, and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given Sperner hypergraph.	method 0.99	0.65	0.13	asserted 1.00
s3	The latter algorithm, first developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, artificial intelligence and game theory.	background 0.90	0.04	0.03	asserted 1.00
s4	One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the University of Hawaii Cancer Center.	contribution 0.61	0.88	0.07	asserted 0.95

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from analysis of existing data 0.57.

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arXiv listing abstract v2

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a specific set of implications, called the $D$-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice. At the core of the method are the $D$-relation defined in the lattice theory framework, and the hypergraph dualization algorithm that allows us to effectively produce the set of transversals for a given Sperner hypergraph. The latter algorithm, first developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, artificial intelligence and game theory. One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the University of Hawaii Cancer Center.

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