ABSTRACT
The concept of a set of relative frequencies, or a profile, is fundamental to correspondence analysis (referred to from now on by its abbreviation CA). Such sets, or vectors, of relative frequencies have special geometric features because the elements of each set add up to 1 (or 100%). In analysing a frequency table, relative frequencies can be computed for rows or for columns — these are called row or column profiles respectively. In this chapter we shall show how profiles can be depicted as points in a profile space, illustrating the concept in the special case when each profile consists of only three elements.
Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Average profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Row profiles and column profiles . . . . . . . . . . . . . . . . . . . . . . 10
Symmetric treatment of rows and columns . . . . . . . . . . . . . . . . . 11
Asymmetric consideration of the data table . . . . . . . . . . . . . . . . 11
Plotting the profiles in the profile space . . . . . . . . . . . . . . . . . . 11
Vertex points define the extremes of the profile space . . . . . . . . . . . 12
Triangular (or ternary) coordinate system . . . . . . . . . . . . . . . . . 12
Positioning a point in a triangular coordinate system . . . . . . . . . . . 14
Geometry of profiles with more than three elements . . . . . . . . . . . 14
Data on a ratio scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Data on a common scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
SUMMARY: Profiles and the Profile Space . . . . . . . . . . . . . . . . 16
