Exact Acceleration of K-Means++ and K-Means||

K-Means++ and its distributed variant K-Means|| have become de facto tools for selecting the initial seeds of K-means. While alternatives have been developed, the effectiveness, ease of implementation,and theoretical grounding of the K-means++ and || methods have made them difficult to "best" from a holistic perspective. We focus on using triangle inequality based pruning methods to accelerate both of these algorithms to yield comparable or better run-time without sacrificing any of the benefits of these approaches. For both algorithms we are able to reduce distance computations by over 500×. For K-means++ this results in up to a 17×speedup in run-time and a551×speedup for K-means||. We achieve this with simple, but carefully chosen, modifications to known techniques which makes it easy to integrate our approach into existing implementations of these algorithms.