Question

Multivariate Classification

Another possibility is using Gaussian densities is to have them all diagonal but allow them to be different. Look at Fig. 5.7. of the book. How would the new version change the appearance of the ellipsoids?

Population likelihoods and posteriors 3 > 2 1 2 4 X Shared covar. Arbitrary covar 4 4 3 3 > 2 > 2 1 10 2 4 2 4 X X Diag. covar Equal var 4 4 3 3 > 2 > 2 1 1 0 10 2 2 4 4 X X Figure 5.7 Different cases of the covariance matrices fitted to the same data lead to different boundaries

Answer 1

In multivariate normal distribution using Gaussian densities, a single dimension is used to reach and acquire higher dimensions. It is used to illustrate any set of co-related random variables along a mean value. Below is the representation of k dimensional random vector that will help you to understand the multivariate normal distribution:

X ~ N_k( )

и,

The following figures are
Global optimum -Funetion isóline Superiór solution Inferior solution Probability deasity ellips oid FIGURE 1. The change of probability density ellipsoid in basic GEDA.

3 3 2 2, 1 1 0 1 1 2. 3 3 5 10 10 5 10 10 -5 -10 -15 -15 -5 -10 Pitch Yaw Pitch Yaw (a) (b) LC LO N
new versions for the appearance of the ellipsoids: