Sparse approximate solution of fitting surface to scattered points by MLASSO model

作者：Hao, Yongxia; Li, Chongjun^*; Wang, Renhong

来源：Science China Mathematics, 2018, 61(7): 1319-1336.

DOI：10.1007/s11425-016-9087-y

• sparse solution
• principle shift invariant space
• l(1) norm minimization
• alternating direction method of multipliers
• MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant (PSI) space and the l (1) norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO (MLASSO) model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.

• 出版日期2018-7
• 单位大连理工大学; 江苏大学