Clustering non-linear interactions in factor analysis

Factor analysis is a powerful tool for dimensionality reduction in multivariate studies. This study extends the factor model with non-linear interactions. The main contribution of our work is to present two approaches to cluster the non-linear interactions and thus develop new models that are not restricted to the extreme scenarios where all non-null interactions are different or all are the same. The first strategy to handle the clusters involves a finite mixture of degenerate components. The second option is specified via the Dirichlet process. A comprehensive simulation study is developed to explore the performance of the proposals. A sensitivity analysis is carried out to evaluate advantages of estimating a smoothness parameter defined in a covariance function of the Gaussian process establishing the non-linearity of the interactions. In terms of application, the methodology is illustrated with the analysis of gene expression levels related to four breast cancer data sets. The genes belonging to disjoint genome regions, with copy number alteration, are connected to the main factors and their non-linear interactions are estimated and clustered. The mutual investigation and comparison of these four breast cancer data sets is rarely found in the literature.