  The ability to quantify distinctness of a cluster structure is fundamental
for certain simulation studies, in particular for those comparing performance
of different classification algorithms. The intrinsic integral measure based on
the overlap of corresponding mixture components is often analytically
intractable. This is also the case for Gaussian mixture models with unequal
covariance matrices when space dimension $d > 1$. In this work we focus on
Gaussian mixture models and at the sample level we assume the class assignments
to be known. We derive a measure of component overlap based on eigenvalues of a
generalized eigenproblem that represents Fisher's discriminant task. We explain
rationale behind it and present simulation results that show how well it can
reflect the behavior of the integral measure in its linear approximation. The
analyzed coefficient possesses the advantage of being analytically tractable
and numerically computable even in complex setups.
