Sparse regularization of tensor decompositions

Multi-linear techniques using tensor decompositions provide a unifying framework for the high-dimensional data analysis. Sparsity in tensor decompositions clearly improves the analysis and inference of multi-dimensional data. Other than non-negative tensor factorizations, the literature on tensor estimation using sparsity is limited. In this paper, we introduce sparse regularization methods for tensor decompositions which are useful for dimensionality reduction, feature selection as well as signal recovery. One major challenge in most of the tensor decomposition algorithms is their heavy dependence on good initializations. To alleviate such a critical problem we propose a reliable method based on the ridge regression to provide good starting values taking advantage of sparsity. Combined with such initializations our sparse regularization methods show highly improved performance over the conventional methods in the demonstrated simulation studies.