The Principle of Making Patterns Emerge from Data

''Making patterns emerge from data'' is the title of a groundbreaking paper by Benzecri (1969a), introducing correspondence analysis to the field of taxonomy. Benzecri's treatment (see also Benzecri, 1969b) marks a departure from a statistical, model-oriented analysis in the direction of a purely descriptive analysis of multidimensional data. This new approach toward data analysis opened up the exploration of multivariate data for which no statistical models or at best sketchy models exist, for example in anthropology and laboratory medicine. Correspondence analysis is a technique closely related to principle component analysis (PCA), and both methods will be described in detail below.

Data displayed as patterns appeal to the eye; they are easily captured "at a glance.'' Whenever data can be represented in visual form, their inter-relationship can be more easily assessed than from numerical tables (see the fascinating book on this subject by Tufte, 1983). In a way, Benzecri's phrase ''patterns emerging from data'' anticipated the new age of supercomputers and fast workstations that allow complex numerical relationships and vast numerical fields to be presented in 3D form on the computer screen. In recent years, the power of this human interaction with the computer has been recognized, and it has become acceptable to study the behavior of complex systems from visual displays of numerical simulations. In fact, looking at such visual displays may be the only way for an observer to grasp the properties of a solution of a nonlinear system of equations. (A good example was provided by the July 1994 issue of Institute of Electrical and Electronics Engineers Transactions on Visualization and Computer Graphics, which specialized in visualization and featured on its cover a parametric solution to the fourth-degree Fermat equation.)

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