The nearest points in a set

I have $N$ points and I have a distance between every pair of points stored in a 2D matrix. The goal is to find the nearest $K$ points among these $N$ points. "Nearest" means the sum of all distances between the $K$ points is smallest. A brute-force way is to search all combinations of $K$ points from the $N$ points. However, $K \ll N$. For example, $K$ is 5 and $N$ is 100. It is infeasible to search all ${100 \choose 5}$ combinations.

Actually, the distance between points is a metric to measure the difference between elements in the set, so it is better to describe the problem using graph rather than computational geometry.

I have read Clique problem on wiki, but I think the setting is different from my context here.

More info: The elements are probability discrete distributions. The metric here is Hellinger distance en.wikipedia.org/wiki/Hellinger_distance, which is to measure the difference between two probability distributions. I like to find the most similar probability distribution subset from a set.

This problem does generalize the clique problem.

One example of a metric is the shortest path distance in a connected, unweighted graph $G$, where the distance between vertices $u$ and $v$, $d(u,v)$, is the length of the shortest path between them. There exists a clique of size $K$ in this graph if and only if we can find $K$ points whose distances sum to ${K \choose 2}$.

For finding cliques of size $5$ you can do slightly better than brute force: see this answer. However without more structure on the metric you are interested in it is an open problem to do significantly better.

StackExchange Computer Science Q#60342, answer score: 3