Gram mates, sign changes in singular values, and isomorphism

Kim, Sooyeong; Kirkland, Steve

doi:10.1016/j.laa.2022.03.001

Cited by 4 publications

(3 citation statements)

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“…Binary matrices A and B satisfying AA ⊺ ≙ BB ⊺ are known as Gram mates (Kirkland, 2018;Kim and Kirkland, 2022). Kirkland (2018, Corol.…”

Section: Preserving the Bipartite Joint Degree Matrixmentioning

confidence: 99%

“…the set of all binary matrices, which decreases as the number of transactions in D and/or the number of items in I grow. While Kirkland (2018) and Kim and Kirkland (2022) construct infinite families of Gram mates, they observe that these families "possess a tremendous amount of structure" (Kirkland, 2018, Sect. 4), and it seems unlikely that such a structure would ever occur on matrices corresponding to real datasets, to the point that it is still an open question to determine whether a matrix A even admits any Gram mate,…”

Section: Preserving the Bipartite Joint Degree Matrixmentioning

confidence: 99%

“…4.2). • We include a discussion of Gram mates (Kirkland, 2018;Kim and Kirkland, 2022), to explain why a model preserving the supports of itemsets of length two may not be very interesting. • We add examples and figures to help the understanding of important concepts.…”

Section: Introductionmentioning

confidence: 99%

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Alice and the Caterpillar: A more descriptive null model for assessing data mining results

Preti,

De Francisci Morales,

Riondato

2023

Knowl Inf Syst

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We introduce novel null models for assessing the results obtained from observed binary transactional or sequence datasets, using statistical hypothesis testing. Our null models maintain more properties of the observed dataset than existing ones. Specifically, they preserve the Bipartite Joint Degree Matrix of the bipartite (multi-)graph corresponding to the dataset, which ensures that the number of caterpillars, i.e., paths of length three, is preserved, in addition to other properties considered by other models. We describe Alice, a suite of Markov-Chain Monte-Carlo algorithms for sampling datasets from our null models, based on a carefully defined set of states and efficient operations to move between them. The results of our experimental evaluation show that Alice mixes fast and scales well, and that our null model finds different significant results than ones previously considered in the literature.

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“…Binary matrices A and B satisfying AA ⊺ ≙ BB ⊺ are known as Gram mates (Kirkland, 2018;Kim and Kirkland, 2022). Kirkland (2018, Corol.…”

Section: Preserving the Bipartite Joint Degree Matrixmentioning

confidence: 99%

Section: Preserving the Bipartite Joint Degree Matrixmentioning

confidence: 99%