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We present a meta-method for initializing (seeding) the $k$-means clusteringalgorithm called PNN-smoothing. It consists in splitting a given dataset into$J$ random subsets, clustering each of them individually, and merging theresulting clusterings with the pairwise-nearest-neighbor (PNN) method. It is ameta-method in the sense that when clustering the individual subsets anyseeding algorithm can be used. If the computational complexity of that seedingalgorithm is linear in the size of the data $N$ and the number of clusters $k$,PNN-smoothing is also almost linear with an appropriate choice of $J$, andquite competitive in practice. We show empirically, using several existingseeding methods and testing on several synthetic and real datasets, that thisprocedure results in systematically better costs. In particular, our method ofenhancing $k$-means++ seeding proves superior in both effectiveness and speedcompared to the popular "greedy" $k$-means++ variant. Our implementation ispublicly available at https://github.com/carlobaldassi/KMeansPNNSmoothing.jl.

Systematically and efficiently improving $k$-means initialization by pairwise-nearest-neighbor smoothing