ABSTRACT
Up to now, small data sets (Exhibits 2.1 and 3.1) were used specifically because they were low-dimensional and hence easy to visualize exactly. These tables with three columns involve three-dimensional profiles, which are actually twodimensional, as we saw in Chapter 2, and can thus be laid flat for inspection in a triangular coordinate system. In most applications, however, the table of interest has many more rows and columns and the profiles lie in a space of much higher dimensionality. Since we cannot easily observe or even imagine points in a space with more than three dimensions, it becomes necessary to reduce the dimensionality of the points. This dimension-reducing step is the crucial analytical aspect of CA and can be performed only with a certain loss of information, but the objective is to restrict this loss to a minimum so that a maximum amount of information is retained.
