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• W2895878604 abstract "In this paper we investigate into analogue of a Singular Value Decomposition for rectangular matrices over a complete idempotent semifields (i-SVD), many of whose instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications. We carry on further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields ($mathcal{K}$-FCA) started in prior work. We find out that for each relation with entries considered in a complete idempotent semifield, for each of the four types of Galois connections defined by the relation, there are two basis of left- and right-singular vectors to choose from for reconstructing the matrix. These are each of the join-dense or meet-dense sets object or attribute concepts of the concept lattice created by the connection. We suggest why these can never form an orthonormal basis, and refer to prior art describing the spectral lattices of such matrices for meaningful representations in the idempotent settings." @default.
• W2895878604 created "2018-10-26" @default.
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• W2895878604 date "2018-07-01" @default.
• W2895878604 modified "2023-09-25" @default.
• W2895878604 title "On the Relation between Semifield-Valued FCA and the Idempotent Singular Value Decomposition" @default.
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• W2895878604 doi "https://doi.org/10.1109/fuzz-ieee.2018.8491644" @default.
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