Visualizing Profiles of Large Datasets of Weighted and Mixed Data

• Published in: Mathematics (Basel) Vol. 9; no. 8; p. 891
• Main Authors: Grané, Aurea, Sow-Barry, Alpha A.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2021
• Subjects: Algorithms; Clustering; Datasets; Euclidean space; Food science; Gower’s interpolation formula; Gower’s metric; Interpolation; mixed data; multidimensional scaling; Prototypes; Retirement; Sample size; Variables
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9080891

This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k-prototypes clustering algorithm. The well-known drawback of classical MDS in large datasets is circumvented by selecting a small random sample of the dataset, whose individuals are clustered by means of an adapted version of the k-prototypes algorithm and mapped via classical MDS. Gower’s interpolation formula is used to project remaining individuals onto the previous configuration. In all the process, Gower’s distance is used to measure the proximity between individuals. The methodology is illustrated on a real dataset, obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), which was carried out in 19 countries and represents over 124 million aged individuals in Europe. The performance of the method was evaluated through a simulation study, whose results point out that the new proposal solves the high computational cost of the classical MDS with low error.