Clustering multivariate count data via Dirichlet-multinomial network fusion

Clustering of multivariate count data has widespread applications in areas such as text analysis and microbiome studies. The need to account for overdispersion generally results in a nonconvex loss function, which does not fit into the existing convex clustering framework. Moreover, prior knowledge of a network over the samples, often available from citation or similarity relationships, is not taken into account. We introduce Dirichlet-multinomial network fusion (DMNet) for clustering multivariate count data, which models the samples via Dirichlet-multinomial distributions with individual parameters and employs a weighted group L1 fusion penalty to pursue homogeneity over a prespecified network. To circumvent the nonconvexity issue, we present two exponential family approximations to the Dirichlet-multinomial distribution, which are amenable to efficient optimization and theoretical analysis. We derive an ADMM algorithm and establish nonasymptotic error bounds for the proposed methods. Our bounds involve a trade-off between the connectivity of the network and its fidelity to the true parameter. The usefulness of our methods is illustrated through simulation studies and two text clustering applications.