Abstract:
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Traditional tensor decompositions have been widely used for dimension reduction of tensorial data. However, in the high dimensional setting, they have the same low interpretability as the traditional principal component analysis. In this talk, we propose an iterative thresholding algorithm for sparse tensor decomposition, which generalizes the higher order orthogonal iteration algorithm for traditional tensor decomposition. The minimax optimality of the proposed algorithm is studied under the spike model. We also demonstrate the numerical performance of the approach through simulations.
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