面向弱监督学习的多标记矩阵补全模型及其扩展研究

As a generalization of compressed sensing theory from vector to matrix, matrix completion theory has attracted much attention in machine learning community. Though the existing research on matrix completion makes great progress, it is still limited to the imputation of missing data and there are few researches on the multi-label matrix completion for weakly supervised learning. At present, the main problems in the study of multi-label matrix completion lie in the poor noise tolerance and weak prior knowledge fusion. In addition, limited by the small stand-alone memory and low computational efficiency, the existing multi-label matrix completion algorithms are difficult to be applied to large-scale problems. In order to address these challenges, we will focus on the three aspects as follows: 1) Constructing a unified framework of enhanced multi-label matrix completion and designing the corresponding solving algorithms, and at the same time, carrying out the strict theoretical analysis about the stability, convergence and complexity for the designed algorithms; 2) Designing and implementing the parallel versions for the enhanced multi-label matrix completion algorithms in cloud computing environment, so as to address more challenging applications; 3) Applying the proposed enhanced multi-label matrix completion algorithms to the large-scale social tags refinement and the complex disease-gene associations prediction. The project has important theoretical and practical significance to expand the application of the existing matrix completion theory.

矩阵补全理论衍生于近年来非常流行的压缩感知技术，是当前备受关注的机器学习研究热点之一。现有的矩阵补全理论研究虽然取得了很大进展，但主要聚焦于数据缺失信息的填补，鲜有面向弱监督学习问题的多标记矩阵补全研究。当前，多标记矩阵补全研究面临的主要问题在于模型的噪声容错性差和先验信息融合性不强，同时所设计的算法受制于单机内存和计算效率约束，难以应用于大规模问题求解。针对这些问题，本项目拟在如下三方面展开研究：1）构建一类鲁棒的增强型多标记矩阵补全模型统一框架并设计相应的求解算法，同时对所设计算法的稳定性、收敛性及计算复杂性展开严格的理论分析；2）展开云计算环境下大规模增强型多标记矩阵补全算法并行拓展研究，以解决更具挑战性的应用问题；3）将所设计的增强型多标记矩阵补全算法实际应用于大规模社交图像标签修正及复杂疾病-基因关联关系预测。本项目对拓展现有矩阵补全理论的应用范围具有重要的理论和实际意义。

矩阵补全理论衍生于近年来非常流行的压缩感知技术，是当前备受关注的机器学习研究热点之一。现有的矩阵补全理论研究虽然取得了很大进展，但主要聚焦于数据缺失信息的填补，鲜有面向弱监督学习问题的多标记矩阵补全研究。当前，多标记矩阵补全研究面临的主要问题在于模型的噪声容错性差、先验信息融合性不强以及算法扩放性受限。针对这些问题，本项目从以下三方面展开研究：（1）面向弱监督学习的鲁棒增强型多标记矩阵补全模型及其统一框架构建；（2）并行计算环境下可扩展的增强型多标记数据补全模型设计；（3）面向弱监督学习的增强型多标记矩阵补全模型应用。基于本项目研究，提出了一系列先验信息融合的噪声容错多标记矩阵/张量补全模型，构建了面向弱监督学习的鲁棒增强型标记分布模型统一框架，设计了深度学习架构下可扩展的生成式增强型多标记数据补全模型。此外，项目也针对图像标签修正、疾病-基因关联关系预测、无线传感网节点定位、阿尔兹海默症疾病进程预测等多个应用问题展开了探索研究，其中，基于项目研究成果（增强型矩阵补全的无线传感网节点定位）的应用示范项目（苏通GIL管廊施工机具防碰撞技术）获得了2020-2021年度中国安装协会科学技术进步奖三等奖。本项目对拓展现有矩阵补全理论的应用范围具有重要的理论和实际意义。