Principal component analysis for non-precise data

Abstract

Many real world phenomena are better represented by non-precise data rather than by single-valued data. In fact, non-precise data represent two sources of variability: the natural phenomena variability and the variability or uncertainty induced by measurement errors or determined by specific experimental conditions. The latter variability source is named imprecision. When there are information about the imprecision distribution the fuzzy data coding is used to represent the imprecision. However, in many cases imprecise data are natively defined only by the minimum and maximum values. Technical specifications, stock-market daily prices, survey data are some examples of such kind of data. In these cases, interval data represent a good data coding to take into account the imprecision. This paper aims at describing multiple imprecise data by means of a suitable Principal Component Analysis that is based on specific interval data coding taking into account both sources of variation.