A model selection approach for clustering a multinomial sequence with non-negative factorization
This work addresses clustering challenges for multinomial sequences, particularly in sparse settings, but it appears incremental as it builds on existing criteria like AIC and BIC.
The authors tackled the problem of clustering sequences of multinomial observations by proposing a model selection criterion with a penalty term that extends AIC and BIC to handle sparse data with varying trial counts, and they introduced a preliminary estimation step using reduced rank projection and non-negative factorization. They demonstrated consistency under assumptions and validated the approach with numerical experiments on real and simulated data.
We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC criteria but also extends the conventional criteria in a way that it can be applicable also to a sequence of sparse multinomial observations, where even within a same cluster, the number of multinomial trials may be different for different observations. In addition, as a preliminary estimation step to maximum likelihood estimation, and more generally, to maximum $L_{q}$ estimation, we propose to use reduced rank projection in combination with non-negative factorization. We motivate our approach by showing that our model selection criterion and preliminary estimation step yield consistent estimates under simplifying assumptions. We also illustrate our approach through numerical experiments using real and simulated data.