I need to cluster units into $k$ clusters to minimize within-group sum of squares (WSS), but I need to ensure that the clusters each contain at least $m$ units. Any idea if any of R's clustering functions allow for clustering into $k$ clusters subject to a minimum cluster size constraint? kmeans() does not seem to offer a size constraint option.
Use EM Clustering
In EM clustering, the algorithm iteratively refines an initial cluster model to fit the data and determines the probability that a data point exists in a cluster. The algorithm ends the process when the probabilistic model fits the data. The function used to determine the fit is the log-likelihood of the data given the model.
If empty clusters are generated during the process, or if the membership of one or more of the clusters falls below a given threshold, the clusters with low populations are reseeded at new points and the EM algorithm is rerun.
This problem is addressed in this paper:
Bradley, P. S., K. P. Bennett, and Ayhan Demiriz. "Constrained k-means clustering." Microsoft Research, Redmond (2000): 1-8.
I have an implementation of the algorithm in python.
I think it would just be a matter of running the k means as part of an if loop with a test for cluster sizes, I.e. Count n in cluster k - also remember that k means will give different results for each run on the same data so you should probably be running it as part of a loop anyway to extract the "best" result
How large is your data set? Maybe you could try to run a hierarchical clustering and then decide which clusters retain based on your dendrogram.
If your data set is huge, you could also combine both clustering methods: an initial non-hierarchical clustering and then a hierarchical clustering using the groups from the non-hierarchical analysis. You can find an example of this approach in Martínez-Pastor et al (2005)
This can be achieved by modifying the cluster assignment step (E in EM) by formulating it as a Minimum Cost Flow (MCF) linear network optimisation problem.
I have written a python package which uses Google's Operations Research tools's SimpleMinCostFlow which is a fast C++ implementation. Its has a standard scikit-lean API.