Learning the Sparse and Low Rank PARAFAC Decomposition via the Elastic Net
This work addresses tensor decomposition challenges in data analysis, offering a robust method for handling missing values and noise, but it appears incremental as it builds on existing elastic net and PARAFAC techniques.
The authors tackled the problem of learning sparse and low-rank PARAFAC decompositions for tensors with missing values by deriving a Bayesian model using the elastic net, which robustly identifies true rank and sparse factor matrices. They demonstrated its effectiveness on simulation and real data, showing it is powerful for large-scale problems.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and admax stochastic block coordinate descent algorithm to solve it, which can be used to solve the large scale problem. To choose the appropriate rank and sparsity in PARAFAC decomposition, we will give a solution path by gradually increasing the regularization to increase the sparsity and decrease the rank. When we find the sparse structure of the factor matrix, we can fixed the sparse structure, using a small to regularization to decreasing the recovery error, and one can choose the proper decomposition from the solution path with sufficient sparse factor matrix with low recovery error. We test the power of our algorithm on the simulation data and real data, which show it is powerful.