The generalized approach to multidimensional scaling

• Author: Malyaretz L., Dorokhov O., Ponomarenko V.
• Pages: 479-486

Bulletin of the Transilvania University of Braşov

Series V: Economic Sciences • Vol. 8 (57) No. 2 - 2015

The generalized approach to multidimensional scaling

Ludmila МАLYARETZ1, Oleksandr DOROKHOV1,

Vladimir PONOMARENKO1

Abstract: Often in practice of solving economic problems there is a need to analyse objects

with properties that are measured in different non-metric scales. Most popular mathematical

approach of processing that properties is multidimensional scaling method. There are metric

and non-metric scaling. The most reasonable of them is the Torgerson metric method, but it

is supposed to have metric scale input variables. The paper proposes a modified method of

factor analysis, which allows non-metric data as input. The paper presents arguments that

the proposed modification is the improvement of the method of multidimensional scaling. The

proposed method is less time-consuming than the Torgerson method, but is mathematically

justified as well. So the mathematical explanation of the generalized multidimensiona l

scaling method has been described. This approach broadens the range of possible ways to

describe objects in economics by means of factors measured on different scales.

Key-words: methodology of multidimensional scaling, generalization, universality, metric

factors, non-metric factors.

1. Introduction

In conditions of indeterminacy, objects in economics are described by means of non-

metric scales. The further research of these objects requires the use of mathematical

methods. It leads to certain problems caused by the limited choice of methods that

allow ordinal numbers or nominations as the original data (Маlyaretz 2010,

Ponomarenko 2007). The multidimensional scaling is the method that makes it

possible to perform the analysis of non-metric factors. The multidimensional scaling

can be metric and non-metric (Egorshin 2007).

Torgerson’s scaling is the most valid of them. The elements of this method

are also used in other methods of multidimensional scaling (Ponomarenko 2009).

The existing algorithms of the multidimensional scaling method have a lot of

drawbacks: the heuristic validity, laboriousness, the limit of two stimuli, the visual

presentation on a plane only etc (Маlyaretz 2007, Manly 2004).

1 Department of Informations Systems Kharkiv National University of Economics (KhNUE), Kharkiv,

Ukraine; aleks.dorokhov@meta.ua