Total Information Analysis: Comprehensive Dual Scaling

Abstract

The traditional quantification procedure (e.g., dual scaling, correspondence analysis) is extended in order to tap into information which is typically ignored. Noting that the traditional symmetric scaling yields a visual image of distorted data structure and re- calling that the widely used practice of looking at data in reduced space may also miss capturing rare but key-information in total space, a method, called total information analysis (TIA), is proposed to subject not only within-set but also between-set relations in total space. Numerical examples are used to explain why TIA offers partial solu- tions to some theoretical problems inherent in the current practice of multidimensional quantification analysis. 1.