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I am trying to compute the normalized information distance (statistical correlation between two random variables)

Normalized information Distance formula

H(X), H(Y ), and H(X, Y ) denote the entropy of X, the entropy of Y, and the joint entropy of {X, Y }, respectively. It is a true metric and hence follows the non-negativity property.

But when I try to compute the value for this metric, I am getting my value to be below 0. I am not sure how to proceed with this

  • What does it mean to have a negative value for a matric that can only be between 0 and 1
  • I have checked my computation of NID and it seems to be correct to me
DeepLearning
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  • You should post your computation. Joint entropy has the property that $H(X,Y) \geq 0$ and $H(X,Y) \geq \max{H(X),H(Y)}$, so the formula you posted will never give a negative number. – kccu Sep 28 '19 at 00:48
  • By the definition of a metric, it is always nonnegative and positive for different points. Either the formula you have been given is not a metric or you are computing it incorrectly. – Ross Millikan Sep 28 '19 at 01:40
  • @RossMillikan Can it be possible that the data points of Variable X and Y that we are comparing could be wrong ? – DeepLearning Sep 30 '19 at 17:26
  • It is possible, but the distance between points should be positive, whether they are right or wrong. – Ross Millikan Sep 30 '19 at 18:49
  • @RossMillikan Thank you! You were right! I had made a silly error while computing the metric. So far, it seems to be a true metric. I will test further – DeepLearning Oct 09 '19 at 01:40

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