0
votes
1answer
27 views

Is mean pairwise distance a metric over subsets of a metric space.

Specifically, I am looking at finite subsets of a set that is a discrete metric space under Jaccard Distance. I'm having trouble proving the triangle inequality or coming up with a counterexample. ...
2
votes
1answer
58 views

Embedding finite (discrete) metric spaces to Eulidean space as isometrically as possible

Let $X = \{1, 2, 3, ..., k\}$ with the discrete metric (distance is 1 for every pair of points). How can this be embedded into $\mathbb{R}^n$ (with the usual metric) such that the embedding would be ...
2
votes
1answer
82 views

How to calculate number of lumps of a 1D discrete point distribution?

I would like to calculate the number of lumps of a given set of points. Defining "number of lumps" as "the number of groups with points at distance 1" Supose we have a discrete 1D space in this ...