基于相同稀疏模式的稀疏主成分分析算法  

Sparse Principal Component Analysis Algorithm Based on Same Sparse Pattern

作　　者：邵剑飞[1] 浦蓉 黄伟 季建杰 郭鹏 SHAO Jianfei;PU Rong;HUANG Wei;JI Jianjie;GUO Peng(Faculty of Information Engineering and Automation,Kunming University of Science and Technology,Kunming 650500,China;Honghe Power Supply Bureau,Yunnan Power Grid Co.,Ltd.,Honghe 661100,China)

机构地区：[1]昆明理工大学信息工程与自动化学院,昆明650500 [2]云南电网有限责任公司红河供电局,红河661100

出　　处：《数据采集与处理》2022年第5期1084-1091,共8页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(61763020)。

摘　　要：稀疏主成分分析是一种用于降维和特征选择的无监督方法。由于计算多个主成分时主载荷向量间不具有相同的稀疏模式,导致难以从原始特征空间中确定出对主成分贡献最大的小部分变量,为解决此问题,提出一种自适应稀疏主成分分析(Adaptive sparse principal component analysis,ASPCA)算法。首先使用组套索模型,通过在载荷向量上施加块稀疏约束得出自适应稀疏主成分分析公式,随后对稀疏矩阵的不同列使用不同的调整参数获得自适应惩罚,最后运用块坐标下降法对自适应稀疏主成分分析公式进行两阶段优化,从而找到稀疏载荷矩阵和正交矩阵,实现降维的最优化。对稀疏主成分分析(Sparse principal component analysis,SPCA)算法、结构化且稀疏的主成分分析(Structured and sparse principal component analysis,SSPCA)算法和ASPCA算法进行仿真比较,结果表明ASPCA算法的降维性能更优,能提取更有价值的特征,从而显著提高了分类模型的平均分类准确率。Sparse principal component analysis is an unsupervised method for dimensionality reduction and feature selection.An adaptive sparse principal component analysis(ASPCA) algorithm is proposed,because the principal load vectors do not have the same sparse pattern when calculating multiple principal components,and it is difficult to determine a small number of the variables that contribute the most to the principal components from the original feature space.Firstly,the group lasso model is used,and the ASPCA formula is obtained by applying block sparse constraints on the load vector.Subsequently,different adjustment parameters are used for different columns of the sparse matrix to obtain adaptive penalty.Finally,the block-coordinate descent method is used to optimize the adaptive sparse principal component analysis formula in two stages,so as to find the sparse load matrix and the orthogonal matrix and achieve the optimization of dimensionality reduction.The comparison results of the sparse principal component analysis(SPCA)algorithm,the structured and sparse principal component analysis(SSPCA)algorithm and the ASPCA algorithm show that the ASPCA algorithm has better dimensionality reduction performance and can extract more valuable features,thereby effectively improving the average classification accuracy of the classification model.

关 键 词：稀疏主成分分析 稀疏模式 主载荷向量 调整参数 块坐标下降法 降维 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]