Luo Xin, Zhou Mengchu, Li Shuai, Hu Lun, Shang Mingsheng
IEEE Trans Cybern. 2020 May;50(5):1844-1855. doi: 10.1109/TCYB.2019.2894283. Epub 2019 Feb 27.
High-dimensional and sparse (HiDS) matrices are commonly seen in big-data-related industrial applications like recommender systems. Latent factor (LF) models have proven to be accurate and efficient in extracting hidden knowledge from them. However, they mostly fail to fulfill the non-negativity constraints that describe the non-negative nature of many industrial data. Moreover, existing models suffer from slow convergence rate. An alternating-direction-method of multipliers-based non-negative LF (AMNLF) model decomposes the task of non-negative LF analysis on an HiDS matrix into small subtasks, where each task is solved based on the latest solutions to the previously solved ones, thereby achieving fast convergence and high prediction accuracy for its missing data. This paper theoretically analyzes the characteristics of an AMNLF model, and presents detailed empirical studies regarding its performance on nine HiDS matrices from industrial applications currently in use. Therefore, its capability of addressing HiDS matrices is justified in both theory and practice.
高维稀疏（HiDS）矩阵在推荐系统等与大数据相关的工业应用中很常见。潜在因子（LF）模型已被证明在从这些矩阵中提取隐藏知识方面准确且高效。然而，它们大多无法满足描述许多工业数据非负性质的非负性约束。此外，现有模型收敛速度慢。一种基于乘子交替方向法的非负LF（AMNLF）模型将HiDS矩阵上的非负LF分析任务分解为小的子任务，其中每个任务都基于先前已解决任务的最新解来求解，从而实现对其缺失数据的快速收敛和高预测精度。本文从理论上分析了AMNLF模型的特性，并针对其在目前正在使用的来自工业应用的九个HiDS矩阵上的性能进行了详细的实证研究。因此，其处理HiDS矩阵的能力在理论和实践上都得到了验证。
