"Spaghetti" PCA analysis: An extension of principal components analysis to time dependent interval data

In this paper a we present an extension of Principal Component Analysis to analyse time dependent interval data. Indeed, in our approach each observation is characterized by an oriented interval of values with a starting and an ending value for each period of observation: for example, the open and the close price of a share in a stock market for a day or a week, initial expression value and final one of a gene in an experiment involving time. From a geometrical point of view, this analysis can be viewed as an analysis on oriented segments in the multidimensional space spanned by periods. We denote these segments as “spaghetti”. We introduce the formulas for the calculation and the interpretation of the results of the factorial analysis as in classic PCA.