We formalize the problem of clustering mathematically; that is, we want to group data together that are similar to each other while keeping dissimilar data as far away from the group as possible. We discuss the complexity of solving this sort of problem, for which the use of heuristics is required. Then we discuss four families of clustering methodologies based on 1) centroid, 2) density, 3) distribution, and 4) connectivity. Note that these families of methods are not extensive in the sense that they don’t cover all the clustering methods existing in the literature.   

After studying this subsection, you should be able to:

• Formulate a clustering problem using centroids.
• Explain the technique of centroid-based clustering and density-based clustering.
• Explain the technique of distribution-based clustering and connectivity-based clustering.