CLUSKEXT: CLUstering model for SKew-symmetric data including EXTernal information

A CLUstering model for SKew-symmetric data including EXTernal information (CLUSKEXT) is proposed, which relies on the decomposition of a skewsymmetric matrix into within and between cluster effects which are further decomposed into regression and residual effects when possible external information on the objects is available. In order to fit the imbalances between objects, the model jointly searches for a partition of objects and appropriate weights which are in turn linearly linked to the external variables. The proposal is fitted in a least-squares framework and a decomposition of the fit is derived. An appropriate Alternating Least-Squares algorithm is provided to fit the model to illustrative real and artificial data.