Best sparse rank-1 approximation to higher-order tensors via a truncated exponential induced regularizer
作者：
Highlights：
• The best sparse tensor best rank-1 approximation problem is considered, with a truncated exponential induced regularizer introduced to encourage the sparsity, which has the unbiasedness property for a large true parameter estimation.
• The reweighted property of the regularizer is exploited, based on which, an iteratively reweighted algorithm is developed, with convergence guarantee given without any assumption; in particular, the support of the iterates will not change after finitely many steps provided that the parameter is small enough.
• Lower bounds for nonzero entries and upper bounds for the number of nonzero entries of the stationary points are studied.
• Numerical experiments on synthetic as well as real data are conducted to show the effectiveness and efficiency of the developed algorithm and model.
摘要
•The best sparse tensor best rank-1 approximation problem is considered, with a truncated exponential induced regularizer introduced to encourage the sparsity, which has the unbiasedness property for a large true parameter estimation.•The reweighted property of the regularizer is exploited, based on which, an iteratively reweighted algorithm is developed, with convergence guarantee given without any assumption; in particular, the support of the iterates will not change after finitely many steps provided that the parameter is small enough.•Lower bounds for nonzero entries and upper bounds for the number of nonzero entries of the stationary points are studied.•Numerical experiments on synthetic as well as real data are conducted to show the effectiveness and efficiency of the developed algorithm and model.
论文关键词：Tensor,Sparse,Rank-1 approximation,Reweighted algorithms
论文评审过程：Received 9 September 2021, Revised 29 June 2022, Accepted 18 July 2022, Available online 28 July 2022, Version of Record 28 July 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127433
