Co-Clustering of ordinal data via latent continuous random variables and a classification EM algorithm

This paper is about the co-clustering of ordinal data. Such data are very common on e-commerce platforms where customers rank the products/services they bought. More in details, we focus on arrays of ordinal (possibly missing) data involving two disjoint sets of individuals/objects corresponding to the rows/columns of the arrays. Typically, an observed entry (i, j) in the array is an ordinal score assigned by the individual/row i to the object/column j. A generative model for arrays of ordinal data is introduced along with an inference algorithm for parameters estimation. The model relies on latent continuous random variables and the fitting allows to simultaneously co-cluster the rows and columns of an array. The estimation of the model parameters is performed via a classification expectation maximization (C-EM) algorithm. A model selection criterion is formally obtained to select the number of row and column clusters. In order to show that our approach reaches and often outperforms the state of the art, we carry out numerical experiments on synthetic data. Finally, applications on real datasets highlight the model capacity to deal with very sparse arrays.