Preliminary communication

HERAKLIT - an algorithm and program for metric multidimenional scaling of objects described above a set of nominal variables

Konstantin Momirović ; Fakultet za fizičku kulturu Sveučilišta u Zagrebu
Ksenija Bosnar ; Fakultet za fizičku kulturu Sveučilišta u Zagrebu
Janez Štalec ; Fakultet za fizičku kulturu Sveučilišta u Zagrebu
Franjo Prot ; Fakultet za fizičku kulturu Sveučilišta u Zagrebu

Abstract

The algorithm and its associated program perform metric multidimensional scaling of a set of objects described above a set of nominal variables transformed into the binary form. Measures of similarity are defined by the algorithm as normalized scalar products of objects vectors. The algorithm defines dimensions by projects onto eigenvectors of the similarity measures matrix. The projections are normalized to eigenvalues. The number of dimensions is determined by the algorithm in such a way that 90% of the trace if the similarity measures matrix can be reproduces. These dimensions are then transformed by the algorithm into an oblique parsimonial system by means of orthonormal transformations. The algorithm determines relations between variables and latent dimensions for both solutions; these relations are defined as normalized scalar products of vectors of of the variables and vectors of latent dimensions. For the oblique solution the algorithm also determines vector coordinates of variables in the system defined by latent dimensions.

Keywords

multidimensional scaling; nominal variables

Hrčak ID:

253174

URI

https://hrcak.srce.hr/253174

Publication date:

4.1.1983.

Article data in other languages: croatian russian

Visits: 593 *