Yesterday, 04:18 PM
Here is another general questions about the JS distance. I have no experience with it (but I like its name for some reason), so sorry if the questions are stupid or obvious.
Suppose we are using it to compare D-dimensional data vectors which are probability distributions on D things. Since probs are non-negative and add to 1, each data vector is a point in the canonical (D-1)-dimensional simplex S with the D vertices (1,0,0,..0), (0,1,0,..0),.. (0,0,0,..1).
The JS distance Jdist is a metric on S. I suppose that it is distinct from the Euclidean metric Edist on S. How does Jdist(p,q) compare to Edist(p,q) for two points that are ε apart near the center of S? And for two points near a vertex of S?
What are the geodesics of Jdist in S? They are not straight in the Euclidean sense, are they?
Is there a mapping F of S to R^D or R^(D-1) such that Jdist(p,q) = Edist(F(p),F(q))?
All the best, --stolfi
Suppose we are using it to compare D-dimensional data vectors which are probability distributions on D things. Since probs are non-negative and add to 1, each data vector is a point in the canonical (D-1)-dimensional simplex S with the D vertices (1,0,0,..0), (0,1,0,..0),.. (0,0,0,..1).
The JS distance Jdist is a metric on S. I suppose that it is distinct from the Euclidean metric Edist on S. How does Jdist(p,q) compare to Edist(p,q) for two points that are ε apart near the center of S? And for two points near a vertex of S?
What are the geodesics of Jdist in S? They are not straight in the Euclidean sense, are they?
Is there a mapping F of S to R^D or R^(D-1) such that Jdist(p,q) = Edist(F(p),F(q))?
All the best, --stolfi