Research On Heterogeneous Value Difference Metric And Its Applications In MDS

Multidimensional Scaling is a traditional multivariate statistical method, andwith the deepening of the study, the range of its application has been becoming moreand more extensive since being proposed several decades before. At present, theacademic applied research on MDS is still very active. MDS has been widely used inmany different areas, such as economics, management science, psychology, sociology,archeology, biology, medicine, chemistry, network analysis, and good economic andsocial benefits have been achieved. In this regard, foreign researchers are in theforefront.MDS is run on (dis)similarity matrix, which is obtained by the calculation of thedistance between different objects on the nondimensionalized data. The method forcalculating the distance has a great impact on the output of MDS, especially when theobjects are described by mixed attributes. In general, MDS uses Euclidean distance tomeasure the (dis)similarity of objects. But due to some characteristics of Euclideandistance, such as its relationship with the dimension of attributes, and ignorance thecorrelation of different attributes, the output of MDS will be affected to some extent.In particular, if objects have nominal attributes, such as sex or color, common practiceis digitizing first and then applying Euclidean distance. Obviously, this approach isnot reasonable, for it basically negates the inherent characteristics of the nominalattributes, resulting in loss of information.On the other hand, the MDS has two types, metric MDS for quantitativeprocessing and non-metric MDS for qualitative. Metric MDS creates a configurationof points whose inter-point distances approximate the given dissimilarities. Instead oftrying to approximate the dissimilarities themselves, non-metric MDS approximates anonlinear, but monotonic, transformation of them. So the non-metric MDS worksbetter on ordinal data, but doesn’t necessarily on nominal data. Taking the fact intoconsideration that metric MDS is quantitative, which can reveal the internal structureof data more accurately than non-metric MDS, we prefer to adopt metric MDS on a complete data set that contains nominal data, on the hypothesis that the nominal datacan be preprocessed appropriately.Therefore, considering the limitations of the Euclidean distance and thecharacteristics of the MDS itself, we apply Heterogeneous Value Difference Metric(HVDM), a distance metric computing distance for nominal attributes differently fromEuclidean distance, to MDS to improve its reasonableness on nominal attributes.Experimental results on UCI Abalone dataset shows that the proposed method givespromising results on both reconstruction ability and accuracy.In the real world, the characteristics of the object needs to be described fromdifferent aspects, so the distance calculation of the mixed attributes object containingnominal data is more common. Therefore, our work will provide some support forthis.