Principal Axes Analyses of Distributional Data

• Activity Number: 80
• Type: Contributed
• Date/Time: Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Sun Makosso-Kallyth* and Brahim Brahim
• Companies: McMaster University and Big Data Visualizations Inc.
• Keywords: principal component analyis ; distributional data ; quantiles ; clustering ; symbolic data

Abstract

We present the application of two extensions of principal component analysis to histogram data. Data where each observations and variable are histogram or empirical distribution are called histogram or distributional data. In the period of "Big Data" this type of data are more and more common. Several Histogram Principal Component Analysis (Histogram PCA) have been proposed in that regard. We present two approaches respectively based on the first order moments and the quantiles. The first one involved three steps: the coding of histogram bins, the application of ordinary PCA of means of variables and the projection of input data onto factorial axes. The second approach by contrast determine a new correlation measures based on Fisher's z scores between corresponding bins of histogram variables. We compare and we show the benefits of these methods using two real data examples on movie ratings and diamond prices.