What is the difference between clustering and matching?

Question

What is the difference between clustering and matching?

For example: There's a pool of four elements and in the one scenario I want to generate pairs. What I do is I measure the distance of each element to each other which yields a 2x2 matrix. Then the matching algorithm finds the two pairings with the lowest or highest weighted sum.

What is a clustering algorithm doing? When I demand a cluster number of two then the result is the same, or not?

Answer 1

Specifying the number of elements in a cluster (pairs for example) doesn't make much sense. If you have been looking at k-means (k-medoids), the k actually indicates how many clusters will be created in total. So, if you have 4 elements and use k = 2, you can get one cluster with 1 element and another cluster with 3 elements, depending on the data you have. Anyway, clustering on 4 elements doesn't make sense.