对每个聚类大小都有上限要求的聚类算法

Question

I need to do a partition of approximately 50000 points into distinct clusters. There is one requirement: the size of every cluster cannot exceed K. Is there any clustering algorithm that can do this job?

Please note that upper bound, K, of every cluster is the same, say 100.

Answer 1

Most clustering algorithms can be used to create a tree in which the lowest level is just a single element - either because they naturally work "bottom up" by joining pairs of elements and then groups of joined elements, or because - like K-Means, they can be used to repeatedly split groups into smaller groups.

Once you have a tree, you can decide where to split off subtrees to form your clusters of size <= 100. Pruning an existing tree is often quite easy. Suppose that you want to divide an existing tree to minimise the sum of some cost of the clusters you create. You might have:

f(tree-node, list_of_clusters)
{
  cost = infinity;
  if (size of tree below tree-node <= 100)
  {
    cost = cost_function(stuff below tree-node);
  }
  temp_list = new List();
  cost_children = 0;
  for (children of tree_node)
  {
    cost_children += f(child, temp_list);
  }
  if (cost_children < cost)
  {
    list_of_clusters.add_all(temp_list);
    return cost_children;
  }
  list_of_clusters.add(tree_node);
  return cost;
}

Answer 2

One way is to use hierarchical K-means , but you keep splitting each cluster which is larger than K, until all of them are smaller.

Another (in some sense opposite approach) would be to use hierarchical agglomerative clustering , ie a bottom up approach and again make sure you don't merge cluster if they'll form a new one of size > K.

Answer 3

The issue with naive clustering is that you do indeed have to calculate a distance matrix that holds the distance of A from every other member in the set. It depends whether you've pre-processed the population or your amalgamating the clusters into typical individuals then recalculating the distance matrix again.