论文标题
列$ \ ell_ {2,0} $ - 低率矩阵恢复及其计算的规范正规化分解模型
Column $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation
论文作者
论文摘要
本文关注的是$ \ ell_ {2,0} $ - 低率矩阵恢复问题及其计算的正则分解模型。列$ \ ell_ {2,0} $ - 引入因子矩阵的规范，以促进因子和低级别解决方案的列稀疏性。对于这个非凸的不连续优化问题，我们开发了一种交替的多数式最小化（AMM）方法，并具有外推性，并提出了一种混合AMM，其中提出了一种主要的交替交替近端方法，以寻求一种具有较少非零列的初始因子对，然后使用伸出额的AMM来最小化，以最大程度地减少非conconve损失。我们为提出的AMM方法提供了全局收敛分析，并将其应用于非均匀抽样方案的矩阵完成问题。数值实验是通过合成和真实数据示例进行的，并与核定 - 正规化分解模型进行了比较结果，最大值正则化凸模型表明，列$ \ ell_ {2,0} $ - 正则化分解模型在提供较低误差和较小时间的解决方案方面具有优势。
This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and low-rank solutions. For this nonconvex discontinuous optimization problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is proposed to seek an initial factor pair with less nonzero columns and the AMM with extrapolation is then employed to minimize of a smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model show that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.
