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Motivation . Microbiome sequencing allows defining clusters of samples with shared composition. However, this paradigm poorly accounts for samples whose composition is a mixture of cluster-characterizing ones and which therefore lie in between them in the cluster space. This paper addresses unsupervised learning of 2-way clusters. It defines a mixture model that allows 2-way cluster assignment and describes a variant of generalized  k -means for learning such a model. We demonstrate applicability to microbial 16S rDNA sequencing data from the Human Vaginal Microbiome Project.

2-Way k-Means as a Model for Microbiome Samples