The theory of abstract partials: An introduction

It is customary in multivariate analysis to search out relational structure by partitioning measures of total variation or overall relatedness into components variously attributable to different sources. Although the multivariate systems most familiar today—notably, linear correlational analysis, analysis of variance, and Information theory—base their decompositions upon very different substantive quantities, they all embody the very same abstract mathematical structure which, moreover, is capable of generating potentially fruitful patterns of data analysis in many other substantive applications as well.