A Proximal Approach for Nonnegative Tensor Decomposition

Abstract : This communication deals with N-th order tensor decompo-sitions. More precisely, we are interested in the (Canonical) Polyadic Decomposition. In our case, this problem is formulated under a variational approach where the considered criterion to be minimized is composed of several terms: one accounting for the fidelity to data and others that can represent not only regularization (such as sparsity prior) but also hard constraints (such as nonnegativity). The resulting optimization problem is solved by using the Block-Coordinate Variable Metric Forward-Backward (BC-VMFB) algorithm. The robustness and efficiency of the suggested approach is illustrated on realistic synthetic data such as those encountered in the context of environmental data analysis and fluores-cence spectroscopy. Our simulations are performed on 4-th order tensors.
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Xuan Vu, Caroline Chaux, Nadège Thirion-Moreau, Sylvain Maire. A Proximal Approach for Nonnegative Tensor Decomposition. 13th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2017), Feb 2017, Grenoble, France. ⟨hal-01485331⟩

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