基于Lp范数的非负矩阵分解并行优化算法  

Non-negative Matrix Factorization Parallel Optimization Algorithm Based on Lp-norm

作　　者：黄路路 唐舒宇 张伟[3] 代祥光 HUANG Lulu;TANG Shuyu;ZHANG Wei;DAI Xiangguang(School of Electronics and Information Engineering,Chongqing Three Gorges University,Chongqing 404100,China;School of Computer Science and Engineering,Chongqing Three Gorges University,Chongqing 404100,China;Key Laboratory of Intelligent Information Processing and Control,Chongqing Three Gorges University,Wanzhou,Chongqing 404100,China)

机构地区：[1]重庆三峡学院电子与信息工程学院,重庆404100 [2]重庆三峡学院计算机科学与工程学院,重庆404100 [3]重庆三峡学院智能信息处理与控制重庆高校市级重点实验室,重庆404100

出　　处：《计算机科学》2024年第2期100-106,共7页Computer Science

基　　金：重庆市教委科学技术研究项目(KJZD-M202201204,KJZD-K202201205);重庆万州区科学技术局科技创新智慧农业项目(2022-17)。

摘　　要：非负矩阵分解算法可以从高维数据中提取出低维和稀疏的有用信息,是处理图像聚类、数据压缩和特征提取等问题的重要手段。传统非负矩阵分解算法大多采用欧几里得距离来度量重构误差,尽管其在许多任务中已经显示出有效性,但在解决实际应用问题时仍面临着聚类效果欠佳、收敛速度慢、稳定性较差等问题。为解决这些问题,文中采用Lp范数作为非负矩阵分解的损失函数,通过调节系数p来获得更好的聚类结果。基于协同优化理论和Majorization-Minimization算法,使用粒子群优化算法来并行求解基于Lp范数的非负矩阵分解问题,并在多个真实数据集上验证了所提方法的可行性和有效性。实验结果表明所提算法明显提升了程序的执行效率且一系列评价指标均优于传统非负矩阵分解算法。Non-negative matrix factorization algorithm is an important tool for image clustering,data compression and feature extraction.Traditional non-negative matrix factorization algorithms mostly use Euclidean distance to measure reconstruction error,which has shown its effectiveness in many tasks,but still has the problems of suboptimal clustering results and slow convergence.To solve these problems,the loss function of non-negative matrix factorization is reconstructed by Lp-norm to obtain better clustering results by adjusting the coefficient p.Based on the collaborative optimization theory and Majorization-Minimization algorithm,this paper uses the particle swarm optimization to solve the non-negative matrix factorization problem of reconstruction in parallel.The feasibility and effectiveness of the proposed method is verified in real datasets,and the experimental results show that the proposed algorithm significantly improves program execution efficiency and outperforms the traditional non-negative matrix decomposition algorithm in a series of evaluation metrics.

关 键 词：非负矩阵分解 LP范数 聚类 并行优化 收敛速度 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]