Marek Walesiak

On The General Distance Measure

In [1993], pp. 44–45 the distance measure was proposed, which can be used for the ordinal data. In the paper the proposal of the general distance measure is given. This measure can be used for data measured in ratio, interval and ordinal scale. The proposal is based on the idea of the generalised correlation coefficient.

Standardisation of Data Set under Different Measurement Scales

Standardisation of multivariate observations is the important stage that precedes the determination of distances (dissimilarities) in clustering and multidimensional scaling. Different studies (e.g. Milligan, Cooper (1988)) show the effect of standardisation on the cluster structure in various data configurations. In the paper a survey of standardisation formulas is given. Then we consider the problem of different scales of measurement and their impact on: n n n— the selection of the standardisation formula; n n n— the selections of the appropriate dissimilarity (or similarity) measure.

Finding Groups in Ordinal Data: An Examination of Some Clustering Procedures

The article evaluates, based on ordinal data simulated with cluster.Gen function of clusterSim package working in R environment, some cluster analysis procedures containing GDM distance for ordinal data (see Jajuga et al. 2003; Walesiak 1993, 2006), nine clustering methods and eight internal cluster quality indices for determining the number of clusters. Seventy two clustering procedures are evaluated based on simulated data originating from a variety of models. Models contain the known structure of clusters and differ in the number of true dimensions, the number of categories for each variable, the density and shape of clusters, the number of true clusters, the number of noisy variables. Each clustering result was compared with the known cluster structure from models applying (Hubert and Arabie 1985) corrected Rand index.

Ordinal Variables in the Segmentation of Advertisement Receivers

The paper presents segmentation study, which employs methods of classification to single out the segments. The variables measured on the ordinal scale were used as the criteria of market segmentation. Variables used reflected students’ attitude towards 20 statements about advertising. Ordinal character of the data required application of specific measure (1) of object’s distance. This measure was used in order to evaluate the similarities of objects, which were based on numbers of relations “equal to”, “greater than” and “smaller than”.

Functional structure of Polish regions in the period 2004-2013 – measurement via HHI Index, Florence’s coefficient of localization and cluster analysis

The article addresses the measurement and identification problems covering particular social and economic areas (referred to as functions) in the regions of the country, based on the employment structure analysis and assessment by the sectors of the economy. The Herfindahl-Hirschman index was applied to measure sectoral concentration and Florence’s coefficient of localization to determine regional functional specialization. Finally, cluster analysis was conducted to produce the functional typology of regions.

Identification of noisy variables for nonmetric and symbolic data in cluster analysis

A proposal of an extended version of the HINoV method for the identification of the noisy variables (Carmone et al. (1999)) for nonmetric, mixed, and symbolic interval data is presented in this paper. Proposed modifications are evaluated on simulated data from a variety of models. The models contain the known structure of clusters. In addition, the models contain a different number of noisy (irrelevant) variables added to obscure the underlying structure to be recovered.