Adaptation of interval PCA to symbolic histogram variables

Abstract

This paper is an adaptation of symbolic interval Principal Component Analysis (PCA) to histogram data. We proposed two methodologies. The first one involved three steps: the coding of bins of histogram, the ordinary PCA of means of variables and the representation of dispersion of symbolic observations we call concepts. For the representation of dispersion of these concepts we proposed the transformation of histograms into intervals. Then, we suggest the projection of the hypercubes or the interval lengths associated to each concept on the principal axes of the ordinary PCA of means. In the second methodology, we proposed the use of the three previous steps with the angular transformation.