A Beyond-Worst-Case Analysis of Greedy k-means++

Greedy $k$-means++ is a generalization of $k$-means++ where, in each iteration, a new seed is greedily chosen among multiple $\ell \geq 2$ points sampled, as opposed to a single seed being sampled in $k$-means++. While empirical studies consistently show the superior performance of greedy $k$-means++, making it a preferred method in practice, a discrepancy exists between theory and practice. No theoretical justification currently explains this improved performance.