Probabilistic Metrics for Soft-Clustering and Topic Model Validation

In this paper the problem of performing external validation of the semantic coherence of topic models is considered. The Fowlkes-Mallows index, a known clustering validation metric, is generalized for the case of overlapping partitions and multi-labeled collections, thus making it suitable for validating topic modeling algorithms. In addition, we propose new probabilistic metrics inspired by the concepts of recall and precision. The proposed metrics also have clear probabilistic interpretations and can be applied to validate and compare other soft and overlapping clustering algorithms. The approach is exemplified by using the Reuters-21578 multi-labeled collection to validate LDA models, then using Monte Carlo simulations to show the convergence to the predicted results. Additional statistical evidence is provided to better understand the relation of the metrics presented.