局部线性下的函数型主成分聚类算法

Functional Principal Component Clustering Algorithm Under Local Linearity

函数型聚类分析在统计学领域被广泛关注,其分析过程通常在降维目标实现后进行。为了有效解决函数型主成分聚类问题,文章结合局部线性嵌入算法(Locally Linear Embedding,LLE)在非线性空间下的适用性,提出了一种局部线性下的函数型主成分分析模型(LLE Function Principle Component Analysis,LFPCA)。首先,采用函数型主成分分析法作为降维目标方法,改进了FPCA的算法模型,通过将LLE算法的权重系数矩阵与函数型主成分定义相结合,构建出一个适用于非线性空间下的聚类算法;其次,在求解算法的过程中定义了函数型主成分得分,并结合EM算法构建出GMM模型来近似函数型算法的概率密度函数,使模型更高效且适用性更强;最后,通过随机模拟实验及应用分析验证了LFPCA算法模型在真实数据集上具有良好的聚类效能。

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 nonlinear spaces to propose an LLE Function Principal Component Analysis(LFPCA)model under local linearity.Initially,the functional principal component analysis is adopted as the target method of dimensionality reduction;the algorithm model of FPCA is improved;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 principal component score is defined,and the GMM model is constructed by combining the EM algorithm to approximate the probability 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.