Proceedings of the twenty-second annual symposium on Computational geometry
How slow is the k-means method?
Proceedings of the twenty-second annual symposium on Computational geometry
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Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
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On the performance of the ICP algorithm
Computational Geometry: Theory and Applications
Improved smoothed analysis of the k-means method
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
k-means requires exponentially many iterations even in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
Frequency-based views to pattern collections
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
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Pattern Recognition Letters
Geometric algorithms for the constrained 1-D K-means clustering problems and IMRT applications
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
ACO-based Projection Pursuit clustering algorithm
CAR'10 Proceedings of the 2nd international Asia conference on Informatics in control, automation and robotics - Volume 1
Algorithms and theory of computation handbook
Smoothed Analysis of the k-Means Method
Journal of the ACM (JACM)
The effectiveness of lloyd-type methods for the k-means problem
Journal of the ACM (JACM)
Hartigan's K-means versus Lloyd's K-means: is it time for a change?
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Proceedings of the VLDB Endowment
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We present polynomial upper and lower bounds on the number of iterations performed by the k-means method (a.k.a. Lloyd’s method) for k-means clustering. Our upper bounds are polynomial in the number of points, number of clusters, and the spread of the point set. We also present a lower bound, showing that in the worst case the k-means heuristic needs to perform Ω(n) iterations, for n points on the real line and two centers. Surprisingly, the spread of the point set in this construction is polynomial. This is the first construction showing that the k-means heuristic requires more than a polylogarithmic number of iterations. Furthermore, we present two alternative algorithms, with guaranteed performance, which are simple variants of the k-means method. Results of our experimental studies on these algorithms are also presented.