统计与决策2024，Vol.40Issue(5)：39-44,6.DOI:10.13546/j.cnki.tjyjc.2024.05.007
局部线性下的函数型主成分聚类算法
Functional Principal Component Clustering Algorithm Under Local Linearity
摘要
Abstract
Function-based clustering analysis has garnered widespread attention in the field of statistics,with its analysis typically conducted after achieving the goal of dimensionality reduction.In order to effectively address the problem of functional principal component clustering,this paper combines the applicability of the Locally Linear Embedding(LLE)algorithm in nonlin-ear spaces to propose an LLE Function Principal Component Analysis(LFPCA)model under local linearity.Initially,the function-al principal component analysis is adopted as the target method of dimensionality reduction;the algorithm model of FPCA is im-proved;a clustering algorithm suitable for nonlinear spaces is constructed by integrating the weight coefficient matrix of the LLE algorithm with the definition of functional principal components.Then,in the process of solving the algorithm,the functional prin-cipal component score is defined,and the GMM model is constructed by combining the EM algorithm to approximate the probabili-ty density function of the functional algorithm,making model more efficient and more applicable.Finally,the random simulation experiment and application analysis are conducted to verify that the LFPCA algorithm model has a good clustering performance on the real data set.关键词
函数型主成分聚类/局部线性嵌入算法/EM算法/GMM模型Key words
functional principal component clustering/locally linear embedding algorithm/EM algorithm/GMM model分类
数理科学引用本文复制引用
陈海龙,胡晓雪..局部线性下的函数型主成分聚类算法[J].统计与决策,2024,40(5):39-44,6.基金项目
新疆维吾尔自治区自然科学基金资助项目(2021D01A55) （2021D01A55）
