# Distance between very large discrete probability distributions

I have 192 countries where each country has some value for 1 million attributes which sum up to 1 (a discrete probability distribution). For any one country most of the values for the attributes are 0.

Now I am trying to find the distance/similarity between those countries using these attributes. I know we can use Jensen Shannon Divergence between two discrete probability distributions to get a distance measure, but the caveat is that all the values have to be non-zero.

Given that there are zero valued attributes for the countries, is there any other suitable statistical distance measure that can help me to cluster these countries using these 1 million attributes?

• Use regularization so none of the probabilities are precisely zero. You should be using regularization anyway; it reduces variance. Welcome to the site.
– Emre
Jul 3 '18 at 22:55
• Could you elaborate a bit? Do you mean replacing 0 with very small non-zero value? Jul 3 '18 at 23:41
• For example, while ensuring the result still adds to unity. Read about Bayesian priors and conjugates.
– Emre
Jul 3 '18 at 23:44