K-bMOM: A robust Lloyd-type clustering algorithm based on bootstrap median-of-means

The median-of-means is an estimator of the mean a random variable that has emerged as efficient and flexible tool to design robust learning algorithms with optimal theoretical guarantees. However, its use for clustering task suggests dividing dataset into blocks, which may provoke disappearance some clusters in blocks lead bad performances. To overcome this difficulty, procedure termed “bootstrap median-of-means” proposed, where are generated replacement dataset. Considering estimation variable, bootstrap better breakdown point than if enough generated. A algorithm called K-bMOM designed, by performing Lloyd-type iterations together strategy. Good performances obtained on simulated real-world datasets color quantization emphasis put benefits our intialization procedure. On side, also proven have non-trivial probabilistic well-clusterizable situations.