If the quantization or additive
measurement error variance is known for
each feature, this
can be used as a guide for choosing the covariance constraints.
But, it can somewhat
subjective if nothing is known about the data.
A good idea of what
to use for may be obtained by
observing the data on 2-dimensional projections.
You should select consistent with the
width of the smallest visible cluster of data. For example,
by looking at the top of Figure 13.3,
and would be estimated by
taking cross-sections of the visible data clusters along
the X and Y axes, respectively. In the bottom
we see the result of choosing too large
(note the width of the small Gaussian mode is larger than the width
of the corresponsing data cluster). It may be necessary
to view the data in all possible 2-D projections
before a decision can be made.
Choosing the covariance constraints