提出可扩展的深度学习矩阵补全方法，高效处理大规模低秩数据中的缺失值和异常值。
Deeply Learned Robust Matrix Completion for Large-scale Low-rank Data Recovery
- 基于深度展开设计混合前馈-循环神经网络，实现无限迭代优化
- 线性收敛且计算复杂度低，在合成与真实数据上优于现有方法
- 适用于视频去背景、超声成像、人脸识别等实际场景
鲁棒矩阵补全（RMC）是解决低秩数据分析中缺失数据与极端异常值的常用机器学习工具。本文提出一种新型可扩展、可学习的非凸方法——学习型鲁棒矩阵补全（LRMC），适用于大规模RMC问题。LRMC具有线性收敛特性且计算复杂度低。基于所提出的定理，其自由参数可通过深度展开有效学习以达到最优性能。此外，本文设计了一种灵活的前馈-循环混合神经网络框架，将深度展开从固定迭代次数拓展至无限迭代。通过大量实验验证，LRMC在合成数据集及真实应用（包括视频背景分割、超声成像、人脸建模、卫星图像云层去除）中均显著优于当前最先进方法。
原文摘要 · Abstract (English)
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fix-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.
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