A greedy algorithm for model selection of tensor decompositions

Various tensor decompositions use different arrangements of factors to explain multi-way data. Components from different decompositions can vary in the number of parameters. Allowing a model to contain components from different decompositions results in a combinatoric number of possible models. Model selection balances approximation error and the number of parameters, but due to the number of possible models, post-hoc model selection is infeasible. Instead, we incrementally build a model. This approach is analogous to sparse coding with a union of dictionaries. The proposed greedy approach can estimate a model consisting of a combination of tensor decompositions.