A CP-low-rank convolutional sparse coding model for tensors is equivalent to Kruskal regression and is solved by an alternating algorithm that reconstructs signals with fewer nonzero activations than unconstrained ADMM.
Estimation of Simultaneously Sparse and Low Rank Matrices
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abstract
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously. We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix. We bound generalization error in the link prediction problem. We also develop proximal descent strategies to solve the optimization problem efficiently and evaluate performance on synthetic and real data sets.
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stat.ML 1years
2019 1verdicts
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Multivariate Convolutional Sparse Coding with Low Rank Tensor
A CP-low-rank convolutional sparse coding model for tensors is equivalent to Kruskal regression and is solved by an alternating algorithm that reconstructs signals with fewer nonzero activations than unconstrained ADMM.