Robust and sparse estimation of tensor decompositions

We propose novel tensor decomposition methods that advocate both properties of sparsity and robustness to outliers. The sparsity enables us to extract some essential features from a big data that are easily interpretable. The robustness ensures the resistance to outliers that appear commonly in high-dimensional data. We first propose a method that generalizes the ridge regression in M-estimation framework for tensor decompositions. The other approach we propose combines the least absolute deviation (LAD) regression and the least absolute shrinkage operator (LASSO) for the CANDECOMP/PARAFAC (CP) tensor decompositions. We also formulate various robust tensor decomposition methods using different loss functions. The simulation study shows that our robust-sparse methods outperform other general tensor decomposition methods in the presence of outliers.