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shachen / PLDS

The Penalized Linear Dynamical System Project
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d(A,B) #44

Closed jovo closed 9 years ago

jovo commented 9 years ago

you don't need the log, or the 1/n Tr() is not defined and, i don't think its correct.

in particular, i'd write something like:

argmin_P || A - P B ||

ie, the permutation matrix needs to go in the middle of A & B.

shachen commented 9 years ago

I agree with the format of the distance, yet we still need the -log{} just to make it a "distance". Without the negative log, what we get is a correlation: the bigger the correlation, the smaller the "distance". We can also use the reciprocal of the correlation. Does this sound reasonable?

shachen commented 9 years ago

I would also include the 1/n, just to make the measure invariant to dimension. Otherwise, the measure is not normalized and increase with dimension.

jovo commented 9 years ago

ok, these are all suggestions, i trust your judgement. regardless, i vote you put everything inside the \min

On Tue, Jun 2, 2015 at 4:03 PM, shachen notifications@github.com wrote:

I would also include the 1/n, just to make the measure invariant to dimension. Otherwise, the measure is not normalized and increase with dimension.

— Reply to this email directly or view it on GitHub https://github.com/shachen/PLDS/issues/44#issuecomment-108079916.

shachen commented 9 years ago

great. Will make an update.