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Factorization of a single matrix or tensor has been used widely to reveal interpretable factors or predict missing data. However, in many cases side information may be available, such as social network activities and user demographic data together with Netflix data. In these situations, coupled matrix tensor factorization (CMTF) can be employed to account for additional sources of information. When...
To enable low-rank tensor completion and factorization, this paper puts forth a novel tensor rank regularization method based on the ℓ1,2-norm of the tensor's parallel factor analysis (PARAFAC) factors. Specifically, for an N-way tensor, upon collecting the magnitudes of its rank-1 components in a vector, the proposed regularizer controls the tensor's rank by inducing sparsity in the vector of magnitudes...
We give an overview of recent developments in numerical optimization-based computation of tensor decompositions that have led to the release of Tensorlab 3.0 in March 2016 (www.tensorlab.net). By careful exploitation of tensor product structure in methods such as quasi-Newton and nonlinear least squares, good convergence is combined with fast computation. A modular approach extends the computation...
Learn 2D filter banks are currently being used in high-impact applications such convolutional neural networks, convolutional sparse representations, etc. However such filter banks usually have plentiful filters, each being non-separable, accounting for a large portion of the overall computational cost. In this paper we propose a novel and computationally appealing alternating optimization based algorithm...
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