离散感知矩阵补全：基于凸化 $\u2113_0$-范数逼近
Discrete Aware Matrix Completion via Convexized $\ell_0$-Norm Approximation
AI总结：
本文提出一种改进的离散感知矩阵补全算法，用连续可微函数逼近$\u2113_0$-范数正则化器，在近端梯度框架下求解，仿真显示性能优于现有最先进方法。
摘要：
我们考虑一种新颖算法，用于在结构化设置中补全部分观测的低秩矩阵，其中每个条目可以从有限离散字母表中选择，例如常见的推荐系统。所提出的低秩矩阵补全（MC）方法是我们先前提出的最先进（SotA）离散感知矩阵补全方法的改进变体，其中离散性通过 $\u2113_0$-范数正则化器强制实现，而非用 $\u2113_1$-范数替代，而是通过分数规划（FP）在近端梯度（PG）框架下归一化的连续可微函数逼近。仿真结果表明，与SotA技术以及早期基于$\u2113_1$-范数的离散感知矩阵补全方法相比，新方法具有优越性能。
英文摘要：
We consider a novel algorithm, for the completion of partially observed low-rank matrices in a structured setting where each entry can be chosen from a finite discrete alphabet set, such as in common recommender systems. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method which we previously proposed, in which discreteness is enforced by an $\ell_0$-norm regularizer, not by replaced with the $\ell_1$-norm, but instead approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework. Simulation results demonstrate the superior performance of the new method compared to the SotA techniques as well as the earlier $\ell_1$-norm-based discrete-aware matrix completion approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
