I'm looking for a measure to analysis the uncertainty observed in a set of variables (with multivariate Gaussian distribution). So, I've tried conventional Shanon entropy (differential entropy) which results into the following equation for MVG distributions:
H(s) = ln(sqrt((2πe)^k*det(cov)))
H(s) = 0.5*[k*ln(2πe)+sum(log(eigs))]
Where, Sigma(Σ) is the covariance matrix. Thus, it's just a constant term plus sum of logarithm of eigenvalues of covariance matrix. But, when I've a small eigenvalue among eigenvalues, the small value affects the whole thing dramatically. In other words, this measure is not robust to small eigenvalues. On the other hand if I use sum of eigenvalues itself (instead of logarithmic scales), I won't face this issue. I was wondering if there is any other measures of uncertainty which may result in to sum of eigs instead of sum of log(eigs)?