Fast and Accurate $k$-means++ via Rejection Sampling

• URL: http://arxiv.org/abs/2012.11891v1
• Date: Tue, 22 Dec 2020 09:14:41 GMT
• Title: Fast and Accurate $k$-means++ via Rejection Sampling
• Authors: Vincent Cohen-Addad and Silvio Lattanzi and Ashkan Norouzi-Fard and Christian Sohler and Ola Svensson
• Abstract summary: $k$-means++ sometimes suffers from being slow on large data-sets. We present a near linear time algorithm for $k$-means++ seeding.
• Score: 44.155614837392214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: $k$-means++ \cite{arthur2007k} is a widely used clustering algorithm that is easy to implement, has nice theoretical guarantees and strong empirical performance. Despite its wide adoption, $k$-means++ sometimes suffers from being slow on large data-sets so a natural question has been to obtain more efficient algorithms with similar guarantees. In this paper, we present a near linear time algorithm for $k$-means++ seeding. Interestingly our algorithm obtains the same theoretical guarantees as $k$-means++ and significantly improves earlier results on fast $k$-means++ seeding. Moreover, we show empirically that our algorithm is significantly faster than $k$-means++ and obtains solutions of equivalent quality.

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