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• W2037994918 abstract "Abstract Much recent work has been focused on non-probabilistic multidimentional scaling techniques for binary data. A paradigm to which many of these methods apply involves interpreting the data matrix as defining a binary relation R from the set A of subjects to the set M of response items. Generally assumptions are made which permit the task of determining the minimum number of dimensions mediating response with which the data are consistent to be recast into the problem of finding as small as possible a family Γ of relations of a particular type such that ⋂Γ = R (⋃ Γ = R) Typically the latter task turns out to be NP-hard. Consequently, the practicability of a given algebraic representation method depends in large part on the degree to which the relation to be represented can be collapsed prior to processing. We define for any relation R , a couple of distinguished restrictions, the ∩- core and the ∪- core of R such that 1. (i) the cardinalities of these restrictions are often substantially smaller than that of R ; 2. (ii) they may be constructed at polynomial expense; 3. (iii) for an important subclass of algebraic representation techniques the task of obtaining a minimal family Γ satisfying (∗) is polynomially reducible to the same task with respect to the ∩-core (or ∪-core) of R . The collapsing methods developed are applied to a body of data drawn from S.A. Stouffer, L. Guttman, E. A. Schuman, P. Lazarsfeld, S. A. Star, and J. A. Clausen (1950, Measurement and prediction , Princeton, NJ: Princeton Univ. Press) in the construction of a representation reflecting the underlying dimensions of combat-readiness of World War II GI's." @default.
• W2037994918 created "2016-06-24" @default.
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• W2037994918 date "1986-06-01" @default.
• W2037994918 modified "2023-09-27" @default.
• W2037994918 title "Collapsing binary data for algebraic multidimensional representation" @default.
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• W2037994918 doi "https://doi.org/10.1016/0022-2496(86)90012-x" @default.
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