I have used the following based on "regularized discriminant analysis"
(and I can't remember the author.)

If your matrix is V, then let w=Trace(V) and modify V by a fudge factor
g (I use g in the range .02 to .05) with:

X = g*w*I + (1-g)*W

The idea is to move the matrix closer to the unit matrix but keep the
trace the same.

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