Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D

01/25/2017
by   Allan Grønlund, et al.
0

The k-Means clustering problem on n points is NP-Hard for any dimension d> 2, however, for the 1D case there exist exact polynomial time algorithms. Previous literature reported an O(kn^2) time dynamic programming algorithm that uses O(kn) space. We present a new algorithm computing the optimal clustering in only O(kn) time using linear space. For k = Ω( n), we improve this even further to n 2^O(√( n k)) time. We generalize the new algorithm(s) to work for the absolute distance instead of squared distance and to work for any Bregman Divergence as well.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset