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k-means is one of the most influential and utilized machine learningalgorithms. Its computation limits the performance and scalability of manystatistical analysis and machine learning tasks. We rethink and optimizek-means in terms of modern NUMA architectures to develop a novelparallelization scheme that delays and minimizes synchronization barriers. The\textit{k-means NUMA Optimized Routine} (\textsf{knor}) library has (i)in-memory (\textsf{knori}), (ii) distributed memory (\textsf{knord}), and (iii)semi-external memory (\textsf{knors}) modules that radically improve theperformance of k-means for varying memory and hardware budgets. \textsf{knori}boosts performance for single machine datasets by an order of magnitude ormore. \textsf{knors} improves the scalability of k-means on a memory budgetusing SSDs. \textsf{knors} scales to billions of points on a single machine,using a fraction of the resources that distributed in-memory systems require.\textsf{knord} retains \textsf{knori}'s performance characteristics, whilescaling in-memory through distributed computation in the cloud. \textsf{knor}modifies Elkan's triangle inequality pruning algorithm such that we utilize iton billion-point datasets without the significant memory overhead of theoriginal algorithm. We demonstrate \textsf{knor} outperforms distributedcommercial products like H$_2$O, Turi (formerly Dato, GraphLab) and Spark'sMLlib by more than an order of magnitude for datasets of $10^7$ to $10^9$points.

knor: A NUMA-Optimized In-Memory, Distributed and Semi-External-Memory k-means Library