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- Title
GEOMETRICAL CONCEPTIONS IN THE ANALYSIS OF QUALITATIVE VARIABLES.
- Authors
Mirkin, B. G.
- Abstract
The article focuses on the geometrical conceptions in the analysis of qualitative variables. It is easy to see that matrices corresponding to nominal attributes can be reduced to block-diagonal form. Similarly, matrices of rank attributes are reducible to block-triangular form. The data set by matrices of a more general form can also be considered. The classification of objects by factor x is naturally associated with the classification of objects in terms of distances between them which is based on the following statement. The formulae suggested in the article indicate how the distance is expressed through the frequencies of the values of different variables. This permits to interpret variable d in the terms of probabilistic prediction of the values of one attribute by the values of the other. The theorem presented in this article relates the tasks of building the factor of the system of non-numerical attributes to the tasks of analyzing the structure of the matrix of indices of interrelation between objects.
- Subjects
QUALITATIVE research; MATHEMATICAL variables; GEOMETRIC modeling; MATRICES (Mathematics); MEASUREMENT of distances; INDEXES
- Publication
Quality & Quantity, 1975, Vol 9, Issue 4, p317
- ISSN
0033-5177
- Publication type
Article
- DOI
10.1007/BF00144051