计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (2): 100-106.doi: 10.11896/jsjkx.230300040

• 数据库&大数据&数据科学 • 上一篇    下一篇

基于Lp范数的非负矩阵分解并行优化算法

黄路路1, 唐舒宇2, 张伟3, 代祥光3   

  1. 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
  • 收稿日期:2023-03-06 修回日期:2023-06-15 出版日期:2024-02-15 发布日期:2024-02-22
  • 通讯作者: 张伟(cqec126@126.com)
  • 作者简介:(huangllu0@163.com)
  • 基金资助:
    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)

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

HUANG Lulu1, TANG Shuyu2, ZHANG Wei 3, DAI Xiangguang3   

  1. 1 School of Electronics and Information Engineering,Chongqing Three Gorges University,Chongqing 404100,China
    2 School of Computer Science and Engineering,Chongqing Three Gorges University,Chongqing 404100,China
    3 Key Laboratory of Intelligent Information Processing and Control,Chongqing Three Gorges University,Wanzhou,Chongqing 404100,China
  • Received:2023-03-06 Revised:2023-06-15 Online:2024-02-15 Published:2024-02-22
  • About author:HUANG Lulu,born in 1997,postgra-duate.Her main research interests include computer vision and algorithm optimization.ZHANG Wei,born in 1970,Ph.D,professor.His main research interests include information security and computational intelligence.
  • Supported by:
    Science and Technology Research Project of Chongqing Municipal Education Commission(KJZD-M202201204,KJZD-K202201205) and Science and Technology Innovation Smart Agriculture Project of Science and Technology Department,Wanzhou District of Chongqing(2022-17).

PDF (PC)

981

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。

关键词: 非负矩阵分解, Lp范数, 聚类, 并行优化, 收敛速度

Abstract: 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.

Key words: Non-negative matrix factorization, Lp-norm, Clustering, Parallel optimization, Rate of convergence

中图分类号: 

  • TP391
[1]LEE D D,SEUNG H S.Learning the parts of objects by non-negative matrix factorization[J].Nature,1999,401(6755):788-791.
[2]ADDI H,WILLIAMS L J.Principal component analysis[J].Wiley Interdisciplinary Reviews:Computational Statistics,2010,2(4):433-459.
[3]PAATEROP P,TAPPER U.Positive matrix factorization:Anon-negative factor model with optimal utilization of error estimates of data values[J].Environmetrics,1994,5(2):111-126.
[4]LI X L,JIA M X.Nonnegative Matrix Factor-ization Algorithmwith Hypergraph Based on pertreatments[J].Computer Science,2020,47(7):71-77.
[5]JAIN A K,DUIN R P W,MAO J.Statistical pattern recognition:A review[J].IEEE Transactions on pattern analysis and machine intelligence,2000,22(1):4-37.
[6]MITCHELL T,BUCHANAN B,DEJONG G,et al.Machinelearning[J].Annual Review of Computer Science,1990,4(1):417-433.
[7]GUAN N,TAO D,LUO Z,et al.MahNMF:Manhattan Non-negative Matrix Factorization[J].Journal of Machine Learning Research,2012,1050:14-59.
[8]NESTEROV Y.Smooth minimization of non-smooth functions[J].Mathematical Programming,2005,103(1):127-152.
[9]DING C,HE X,SIMON H D.On the equivalence of non-negative matrix factorization and spectral clustering[C]//Procee-dings of the 2005 SIAM International Conference on Data Mi-ning.Society for Industrial and Applied Mathematics,2005:606-610.
[10]WANG S,CHANG T H,CUI Y,et al.Clustering by orthogonal NMF model and non-convex penalty optimization[J].IEEE Transactions on Signal Processing,2021,69:5273-5288.
[11]NAGAYAMA M,ARITAKE T,HINO H,et al.Detecting cell assemblies by NMF-based clustering from calcium imaging data[J].Neural Networks,2022,149:29-39.
[12]KONG D,DING C,HUANG H.Robust non-negative matrixfactorization using L2,1-norm[C]//The 20th ACM InternationalConference on Information and Knowledge Management.2011:673-682.
[13]HOYER P O.Non-negative matrix factorization with sparseness constraints[J].Journal of Machine Learning Research,2004,5(9):1457-1469.
[14]NAKAMURA T,KAMEOKA H.Lp-norm non-negative matrix factorization and its application to singing voice enhancement[C]//2015 IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP).IEEE,2015:2115-2119.
[15]ZHANG L,CHEN Z,ZHENG M,et al.Robust non-negativematrix factorization[J].Frontiers of Electrical and Electronic Engineering in China,2011,6:192-200.
[16]LANGE K.MM optimization algorithms[M].Society for Industrial and Applied Mathematics,2016.
[17]YAO Y,LI Z,LIU H,et al.Robust Transceiver OptimizationAgainst Echo Eclipsing Via Majorization-Minimization[J].IEEE Transactions on Aerospace and Electronic Systems,2022,59(3):2464-2479.
[18]PANWAR K,KATWE M,BABU P,et al.A Majorization-Minimization Algorithm for Hybrid T-OA-RSS Based Localization in NLOS Environment[J].IEEE Communications Letters,2022,26(5):1017-1021.
[19]LIU F,SHANG X,ZHU H.Efficient majorization-minimization-based channel estimation for onebit massive MIMO systems[J].IEEE Transactions on Wireless Communications,2021,20(6):3444-3457.
[20]XU J,LANGE K.Power k-means clustering[C]//International Conference On Machine Learning. PMLR,2019:6921-6931.
[21]NESTEROV Y E.A method for solving the convex program-ming problem with convergence rate O(1/k∧2) [J].Dokl.Akad.Nauk SSSR269,1983,269(3):543-547.
[22]QU L C,LYU J,QU Y H,et al.Intelligent Assignment and Positioning Algorithm of Moving Target Based on Fuzzy Neural Network[J].Computer Science,2021,48(8):246-252.
[23]YU M,LI G,JIANG D,et al.Application of PSO-RBF neuralnetwork in gesture recognition of continuous surface EMG signals[J].Journal of Intelligent & Fuzzy Systems,2020,38(3):2469-2480.
[24]QABOUCHE H,SAHEL A,BADRI A,et al.Energy efficient PSO-based routing protocol for large WSN[C]//2022 2nd International Conference on Innovative Research in Applied Science,Engineering and Technology(IRASET). IEEE,2022:1-7.
[25]LI Y.An Improved Particle Swarm Optimization AlgorithmBased on Simulated Annealing for Large-Scale Node Location of WSN[C]//2022 IEEE 4th International Conference on Civil Aviation Safety and Information Technology(ICCASIT).IEEE,2022:971-974.
[26]ALHAJ Y A,DAHOU A,ALQANESS M A,et al.A novel text classification technique using im-proved particle swarm optimization:A case study of Arabic language[J].Future Internet,2022,14(7):194-211.
[27]WANG L Z,MU X D,LIU H L.Using SVM Method Optimized by Improved Particle Swarm O-ptimization to Analyze Emotion of Chinese Text[J].Computer Science,2020,47(1):231-236.
[28]PAN Y,WU Y,LAM H K.Security based fuzzy control for nonlinear networked control systems with DoS attacks via a resilient event-triggered scheme[J].IEEE Transactions on Fuzzy Systems,2022,30(10):4359-4368.
[29]LEE D D,SEUNGH S.Algorithms for non-negative matrix factorization[J].Advances in Neural Information Processing Systems,2000,13:556-562.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
渝ICP备16013121号-4
地址：重庆市渝北区洪湖西路18号    邮编：401121  
电话：023-63500828（编辑部） 023-67039612（会议/专题） 023-67039623（财务/发票）
E-mail：jsjkx12@163.com
本系统由北京玛格泰克科技发展有限公司设计开发