统计与决策2024，Vol.40Issue(15)：46-52,7.DOI:10.13546/j.cnki.tjyjc.2024.15.008
基于非负矩阵分解的函数型聚类算法改进与比较
Improvement and Comparison of Functional Clustering Algorithms Based on Nonnegative Matrix Factorization
摘要
Abstract
Nonnegative function data can be observed at unequal intervals,which is widely used in theory and practice,and clustering them can better explore objective laws.This paper uses location integral transformation to convert the function data into high-dimensional vector,then transforms it into low-dimensional vectors by nonnegative matrix factorization(NMF),and con-structs functional clustering algorithms.For the functional spectral clustering algorithm based on NMF,two methods are offered to determine the number of clusters K:K is determined according to the eigenvalue of Laplacian matrix,and K is determined by constructing some new evaluation indexes.Numerical experiment results are shown as follows:The functional clustering algorithms based on location integral transformation and NMF are effective,and the requirement of function structure is relaxed,but the value of function should be restricted to be positive.The rank of the NMF can be determined by the cophenetic correlation coefficient,and a smaller value is recommended to eliminate the redundant features of the class.In time of determining K for spectral clus-tering,it is recommended to standardize the data after dimensionality reduction to reduce the range of distance variation between samples.The change point plot of the cluster number is intuitive and effective,and it is of great reference value to determine K by combining with the eigenvalue difference method,with the threshold value[0.05,0.08]recommended to take.The method of de-termining K based on coincidence degree and similarity ratio is effective and easy to understand关键词
函数型数据/非负矩阵分解/谱聚类/聚类个数Key words
functional data/nonnegative matrix factorization/spectral clustering/number of clusters分类
数理科学引用本文复制引用
王丙参,魏艳华,李旭..基于非负矩阵分解的函数型聚类算法改进与比较[J].统计与决策,2024,40(15):46-52,7.基金项目
山西省自然科学基金青年项目(202203021222223) （202203021222223）
天水师范学院高层次人才科研项目(KYQ2023-13) （KYQ2023-13）
