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In the application of clustering models to real data there is often rich prior information that constrains the relationships among the samples, or the relationships between the samples and the parameters. For example, in biological or clinical experiments, it may be known that two samples are technical replicates and should be assigned to the same cluster, or it may be known that the mean value for control samples is in a certain range. However, standard model-based clustering methods make it difficult to enforce such hard logical constraints and may fail to provide a globally optimal clustering. We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model. Our approach can accommodate side constraints and preserves the combinatorial structure of the MAP clustering problem by its formulation as a mixed-integer nonlinear optimization problem (MINLP). We approximate the MINLP through a mixed-integer quadratic program (MIQP) transformation that improves computational aspects while guaranteeing $\epsilon$-global optimality. An important benefit of our approach is the explicit quantification of the degree of suboptimality, via the optimality gap, en route to finding the globally optimal MAP clustering. Numerical experiments comparing our method to other approaches show that our method finds better optima than standard clustering methods. Finally, we cluster a real breast cancer
gene expression data set incorporating intrinsic subtype information the induced constraints substantially improve the computational performance and produce more coherent and biologically meaningful clusters.

zoom info available https://sites.google.com/view/maddd After the talk, we will do virtual tea/coffee get-together at https://gather.town/KOoFj0aKT5GkEj40/Alder-Room