2018/04/19 by Rosanna Verde, Verde, Rosanna, Antonio Irpino +1 · 1 citation
Agricultural and Biological Sciences · Computer Science · Mathematics · #62-07 #62-09 #FOS: Computer and information sciences #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Methodology (stat.ME) #Other Statistics (stat.OT) #Sensory Analysis and Statistical Methods #msc:62-07 #msc:62-09 #stat.ME #stat.OT
paper · pdf · doi:10.48550/arxiv.1804.07192
Accepted from STATSTICA APPLICATA: Italian Journal of Applied Statistics on 12/2017
arxiv created 2018/04/19 · openalex publication_date 2018/04/19 · arxiv updated 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of Symbolic Data Analysis (SDA), distribution-variables are a particular case of multi-valued variables: each unit is represented by a set of distributions (e.g. histograms, density functions or quantile functions), one for each variable. Factor analysis (FA) methods are primary exploratory tools for dimension reduction and visualization. In the present work, we use Multiple Factor Analysis (MFA) approach for the analysis of data described by distributional variables. Each distributional variable induces a set new numeric variable related to the quantiles of each distribution. We call these new variables as quantile variables and the set of quantile variables related to a distributional one is a block in the MFA approach. Thus, MFA is performed on juxtaposed tables of quantile variables. We show that the criterion decomposed in the analysis is an approximation of the variability based on a suitable metrics between distributions: the squared L2 Wasserstein distance. Applications on simulated and real distributional data corroborate the method. The interpretation of the results on the factorial planes is performed by new interpretative tools that are related to the several characteristics of the distributions (location, scale and shape).