This paper studies the k-means++ algorithm for clustering as well as the class of D sampling algorithms to which k-means++ belongs. It is shown that for any constant factor β > 1, selecting βk cluster centers by D sampling yields a constant-factor approximation to the optimal clustering with k centers, in expectation and without conditions on the dataset. This result extends the previously known O(log k) guarantee for the case β = 1 to the constant-factor bi-criteria regime. It also improves upon an existing constant-factor bi-criteria result that holds only with constant probability.
Wei REF improved the K-means++ algorithm by selecting the cluster centers using the sampling method in the K-means++ algorithm and then producing k centers with the expectation of having an approximately constant factor for the best clustering result.
A Constant-Factor Bi-Criteria Approximation Guarantee for $k$-means++
ArXiv
ArXiv
Computer Science Mathematics