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This paper extends recent advances in Support Vector Machines and kernel machines in estimating additive models for classification from observed multivariate input/output data. Specifically, we address the question how to obtain predictive models which gives insight into the structure of the dataset. This contribution extends the framework of structure detection as introduced in recent publications by the authors towards estimation of componentwise Support Vector Machines (cSVMs). The result is applied to a benchmark classification task where the input variables all take binary values.