In certain situations the original variables can be
heterogeneous w.r.t. their variances. This is particularly true when
the variables are measured on heterogeneous scales (such as years, kilograms,
dollars, ...). In this case a description of the information contained
in the data needs to be provided which
is robust w.r.t. the choice of scale. This can be achieved
through a standardization of the variables, namely
(9.19) |
(9.20) |
The NPCs, , provide a representation of
each individual, and is given by
(9.22) | |||
(9.23) |
1mm
The NPCs provide a perspective similar to that of the
PCs, but in terms of the relative position of individuals,
NPC gives each variable the same weight
(with the PCs the variable with the largest variance received the largest
weight).
Computing the covariance and correlation between
and is straightforward: