An application of the floating reference hypothesis is
normalization of data prior to evaluation of the SPA for
a fixed reference hypothesis.
Suppose we would like to evaluate
for arbitrary vectors .
Let be an estimate of the scale of .
In practice, is a sample variance, sample mean,
or standard deviation estimate.
Important is that as is scaled, all the elements of
will vary in proportion to .
Let be a reference hypothesis that depends on this scaling.
As long as the feature contains , or can be computed
from , then remains in the ROS of . Thus,
equation (2.13) is theoretically independent of ,
If the elements of are linearly related to ,
we may write
where is the dimension of .
which provides a convenient way to normalize
prior to calculating the SPA.