Am working to cluster in Space-Time, and thinking of Space Time metrics as follow:
Distance(X,Y) = DistanceDiff**2 + coeff * TimeDiff**2
Am not sure if this is a right definition for numerical usage (not the formal definition of metrics...), and especially if coeff should be proportionnal to
DistMax**2/timeDiffMax**2
ie Normalized the Space Time.
I dig into this and propose a tentative answer (although not perfect, outline the major idea).
if the space_time points represent some objects, space_time are constraints by the velocity v of the objects, if one can take v_avg (average of all velocity for all pt, at all time), one can normalize the space_time accordingly.
It supposes that objects have similar velocity (same magnitude....)