tSSNALM: A fast two-stage semi-smooth Newton augmented Lagrangian method for sparse CCA
作者：
Highlights：
• We are the first to solve the dual formulation rather than itself. This is very important in high-dimensional problems. For example, XTX and YYY are of size p × p and q × q. For the dual optimization problem, we only need XXT and YYT of size n × n. Thus, the cost is reduced from O(p3) and O(q3) to O(n3)(n ≪ max (p, q)).
• We develop a fast two-stage semi-smooth Newton augmented Lagrangian method (tSSNALM) to optimize SCCA model, and the resulting subproblems either have closed-form solutions or can be solved by fast solvers. In addition, we prove that the sequence generated by tSSNALM converges to a local optimum.
• We conduct a variety of simulated examples to demonstrate that our proposed tSSNALM can achieve better performance than the existing state-of-the-art solvers CoLaR and AMA.
摘要
•We are the first to solve the dual formulation rather than itself. This is very important in high-dimensional problems. For example, XTX and YYY are of size p × p and q × q. For the dual optimization problem, we only need XXT and YYT of size n × n. Thus, the cost is reduced from O(p3) and O(q3) to O(n3)(n ≪ max (p, q)).•We develop a fast two-stage semi-smooth Newton augmented Lagrangian method (tSSNALM) to optimize SCCA model, and the resulting subproblems either have closed-form solutions or can be solved by fast solvers. In addition, we prove that the sequence generated by tSSNALM converges to a local optimum.•We conduct a variety of simulated examples to demonstrate that our proposed tSSNALM can achieve better performance than the existing state-of-the-art solvers CoLaR and AMA.
论文关键词：Sparse canonical correlation analysis,Semi-smooth Newton,Augmented Lagrangian method,Duality
论文评审过程：Received 17 May 2019, Revised 7 February 2020, Accepted 29 March 2020, Available online 21 May 2020, Version of Record 21 May 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125272
