Machine Learning

, Volume 75, Issue 2, pp 245-248

First online:

NP-hardness of Euclidean sum-of-squares clustering

  • Daniel AloiseAffiliated withÉcole Polytechnique de Montréal Email author 
  • , Amit DeshpandeAffiliated withMicrosoft Research India
  • , Pierre HansenAffiliated withGERAD and HEC Montréal
  • , Preyas PopatAffiliated withChennai Mathematical Institute


A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al. (Mach. Learn. 56:9–33, 2004), is not valid. An alternate short proof is provided.


Clustering Sum-of-squares Complexity