基于多视角学习的非负函数型矩阵填充算法  

Non-negative Functional Matrix Completion Algorithm Based on Multi-view Learning

作　　者：薛娇 傅德印 韩海波 高海燕 Xue Jiao;Fu Deyin;Han Haibo;Gao Haiyan(School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]兰州财经大学统计学院,兰州730020

出　　处：《统计与决策》2022年第7期5-11,共7页Statistics & Decision

基　　金：国家社会科学基金资助项目(18BTJ038);兰州财经大学博士研究生科研创新项目(2021D02);兰州财经大学校级科研项目(Lzufe2018D-04);兰州财经大学统计学习与大数据分析科研创新团队支持计划项目(Lzufe-SRT202001)。

摘　　要：随着数据采集密集化程度的提高,不同领域产生了大量具备曲线特征的函数型数据。这类数据具有多源性和多态性特征,且其离散采样点通常呈现大规模缺失、取值非负的特点。文章针对非负函数型数据的缺失处理展开讨论:在梳理了单视角和多视角数据插补方法的基础上,引入非负约束,采用函数型数据分析方法,试图将非负矩阵分解、多视角学习以及矩阵填充进行融合,构造一种基于多视角学习的非负函数型矩阵填充算法,并给出了交替迭代更新求解算法。模拟和实例数据修复表明,与现有的单视角函数型数据填充方法相比,新方法不仅具有较好的数据修复效果,而且具备明显的计算时间优势。With the increasing density of data collection, a large number of functional data with curve characteristics have been generated in different fields. This kind of data has the characteristics of multi-source and polymorphism, and its discrete sampling points usually show the characteristics of large-scale missing and non-negative values. This paper discusses the missing processing of non-negative functional data. On the basis of sorting out data completion methods of single view and multi-view,non-negative constraint is introduced, and functional data analysis method is adopted to integrate non-negative matrix factorization, multi-view learning and matrix completion to construct a non-negative functional matrix completion algorithm based on multi-view learning, and finally, an alternate iteration algorithm is presented. Simulation and example data restoration show that compared with the existing single-view functional data completion method, the new method not only has better data restoration effect, but also has an obvious advantage in computing time.

关 键 词：多视角学习 矩阵填充 非负矩阵分解 函数型数据分析 

分 类 号：O212[理学—概率论与数理统计]