THEME: THEmatic model exploration through multiple co‐structure maximization

After showing that plain covariance or correlation‐based criteria are generally not suitable to deal with multiple‐block component models in an exploratory framework, we propose an extended criterion: multiple co‐structure (MCS). MCS combines the goodness‐of‐fit indicator of the component model to a flexible measure of structural relevance of the components. Thus, it allows to track various kinds of interpretable structures within the data, on top of variance–maximizing components: variable‐bundles, components close to satisfying relevant structural constraints, and so on. MCS is to be maximised under unit‐norm constraints on coefficient‐vectors. We provide a dedicated ascent algorithm for it. This algorithm is nested into a more general one, named THEME (thematic equation model explorator), which calculates several components per data‐array and extracts nested structural component models. The method is tested on simulated data and applied to physicochemical data.