As mentioned earlier, the objective of principal components analysis is to
represent the rows and columns of a data matrix in a subspace of reduced
dimensionality and to highlight the relations unseen by computations. Therefore
the points of *N *(* i *) and *N *(* j* *)* in a *p*-dimensional
subspace, generated by the first factorial axes, are plotted in a series of
two-dimensional plots.

*Variable points*

Since the a -coordinates of the
variable points, *j* of *N( j ),* are similar to correlation coefficient
(or Cosine squared), these points can be projected on to a circle (called a
correlation circle), whose axes are pairs of factorial axes. The variables are
represented in a correlation circle.

*Individual points*

The points *i* of *N *(*
I *) are projected on to a 2-dimensional factor space.

*Joint Graphics*

The points of clouds *N* ( *I *) and *N *( *J* ) can be
projected on to the same graphic, though the meaning of both sets is not the
same. The proximity between one point *i* of *N* ( *I* ) and
point j of *N* ( *J* ) cannot be interpreted, because the points of*
N* ( *I* ) are centered at G, the center of gravity of *N* ( *I*
), whereas the points of *N* ( *J* ) are centered at O (the origin of
the row variables).

*Graphics for Supplementary Elements*:

The supplementary points can be plotted in the factor space generated by explicative factor axes. To avoid confusion, it is suggested that the symbols for supplementary and principal points should not be the same.

*Interpretation of Graphics *

Distances between individual points are interpreted in terms of similar
patterns of response to the variables Distances between variables are
interpreted (when using normalized principal components analysis) in terms of
correlation. However, a great deal of caution is needed in interpreting the
distance between a variable point and an individual point, because these two
points do not belong to the same space. *However, we can legitimately compare
relative positions of two individuals with respect to the entire set of variables
or two variables with respect to the entire set of individuals*