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Award ID contains: 1916071

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  1. ; (, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
    null (Ed.)
    Full Text Available 
  2. ; ; ; (, Electronic Journal of Statistics)
    null (Ed.)
    Full Text Available 
  3. ; (, Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021)
    Banerjee, A.; Fukumizu, K. (Ed.)
    We establish the consistency of K-medoids in the context of metric spaces. We start by proving that K-medoids is asymptotically equivalent to K-means restricted to the support of the underlying distribution under general conditions, including a wide selection of loss functions. This asymptotic equivalence, in turn, enables us to apply the work of Pärna (1986) on the consistency of K-means. This general approach applies also to non-metric settings where only an ordering of the dissimilarities is available. We consider two types of ordinal information: one where all quadruple comparisons are available; and one where only triple comparisons are available. We provide some numerical experiments to illustrate our theory. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Journal of machine learning research)
    Accepted Manuscript Full Text Available