This paper shows that one can be competitive with the kmeans objective while operating online. In this model, the algorithm receives vectors v1, . . . , vn one by one in an arbitrary order. For each vector vt the algorithm outputs a cluster identifier before receiving vt+1. Our online algorithm generates Õ(k) clusters whose k-means cost is Õ(W ∗) where W ∗ is the optimal k-means cost using k cl...

Let us define some notation which will help us analyze the algorithm. L := A solution (k-subset) returned by Local Search. Copt := An optimal solution for the k-median problem. We will eventually show that Cost(L) ≤ 5 · Cost(Copt). For any p ∈ P,C ⊆ P, NN(p, C) := c̄ ∈ C that minimizes d(p, ·). So d(p,NN(p, C)) = d(p, C) by definition. Also, for any C ⊆ P, c̄ ∈ C, Cluster(C, c̄) := {q ∈ P | NN(q, ...

We run experiments showing that algorithm clarans (Ng et al., 2005) finds better Kmedoids solutions than the standard algorithm. This finding, along with the similarity between the standard K-medoids and K-means algorithms, suggests that clarans may be an effective K-means initializer. We show that this is the case, with clarans outperforming other popular seeding algorithms on 23/23 datasets w...