What does it mean to use K-means clustering on a data set that indicates relative distances from one item to another?
K-means clustering assigns items to clusters such that the total intra-cluster distance is minimized. Hence, the only input that is needed is a distance function d(a,b). Often, the items are vectors in a normed vector space and d is chosen as d(a,b) = ||a-b|| for some norm ||x||. But in general, any distance function that fulfills d(a,a) = 0 (distance from a point to itself is zero), d(a,b) <= d(a,c) + d(c,b) (triangle inequality), and d(a,b) = d(b,a) (symmetry) can be used. It can even be a matrix where the entry M(i,j) gives the distance between items i and j, as long as the entries obey the rules above.
what does it mean to use K-means clustering on a data set that indicates relative distances from one item to another?
For example, each item is given a relative distance to every other item.