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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.

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    What do this have to do with the Mahalonobis distance? – 2017-02-27
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    Isnt Maha. distance the difference of vectors ? – 2017-02-27
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    Well, kind of, but the Mahalonobis distance (https://en.wikipedia.org/wiki/Mahalanobis_distance) is related to statistics. So the question is if/what this has anything to do with Mahalanobis distance. – 2017-02-27
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    Numerical computation of Mahalonobis isn't part of Mahalonobis statistics ? (numerical computation is also part of mathematics...). – 2017-02-27
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    Well, that's a relation, but I thought there ought to have more with Maha than that. For one you need a covariance matrix. Anyway you're not guaranteed that DistMax**2/timeDiffMax**2 being the correct coefficient for TimeDiff**2 anyway. – 2017-02-27
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    Hence, my question..... – 2017-02-27

1 Answers 1

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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....)