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Implementation of certificate for k-means optimality based on algorithm from paper: Probably certifiably correct k-means clustering. https://arxiv.org/pdf/1509.07983v2.pdf
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Probably certifiably correct kmeans clustering ***** Authors: Takayuki Iguchi, Dustin G. Mixon, Jesse Peterson, and Soledad Villar. contact: email@example.com ***** This code contains the algorithms described in . In particular the function certify_clusters receives a set of clusters as input and constructs the dual certification described in . If the certification succeeds it means that it constructed a proof of the clustering’s optimality, and the algorithm returns 1. See certify_clusters.m description for more information. ***** Example >> Phi= horzcat(rand(2,10), rand(2,11)+2*ones(2,11), rand(2,8)-2*ones(2,8)); >> certify_clusters(Phi, [10,11,8]) ans=1 >> Phi2= horzcat(randn(2,10), randn(2,11)+2*ones(2,11), randn(2,8)-2*ones(2,8)); >> certify_clusters(Phi, [10,11,8]) ans=0 ***** References:  Iguchi, Mixon, Peterson, Villar. Probably certifiably correct kmeans clustering.