Choosing the covariance constraints

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 $ \rho _n$ may be obtained by observing the data on 2-dimensional projections. You should select $ \rho _n$ consistent with the width of the smallest visible cluster of data. For example, by looking at the top of Figure 13.3, $ \rho_1$ and $ \rho_2$ would be estimated by taking cross-sections of the visible data clusters along the X and Y axes, respectively. In the bottom of Figure, we see the result of choosing $ \rho _n$ 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.

Baggenstoss 2017-05-19