Partition-Based Clustering

The overall strategy here is to partition the Dataset into a set of $k$ clusters $C_{i}$ such that the sum of squared distances to $c_{i}$ is minimized, where $c_{i}$ is the centroid or medoid of a cluster $C_{i}$ .

\min \sum_{i=1}^k (\sum_{j=1}^n d\left(o_j, c_i\right)^2

You could enumerate all possible partitions and therefore find the optimal solution or you could use heuristic methods like:

k-means Clustering
k-medoids Clustering
Clustering Large Applications
Randomized CLARA