Research And Application Of Sparse Principal Component Analysis Algorithm

Principal component analysis(PCA)is a popular data processing and dimensional-ity reduction technique,which has many applications in engineering,biology and social sciences.However,a significant disadvantage of principal component analysis is that principal components are usually linear combinations of all variables.This is very unfa-vorable for the interpretation of the results.Therefore,in recent years,there have been many researches on sparse principal component analysis(Sparse PCA)algorithm.The article proposes a new sparse PCA method by introducing the norm of L0 to replace the norm of L1 in the traditional sparse PCA problem.Using this method,we can effectively obtain sparse principal components,and achieve the purpose of ex-plaining high percentage changes with sparse linear combinations.In addition,we have established some theoretical results to prove our method.Based on the success of the original dual active set algorithm in the selection of the best subset,we propose an effi-cient iterative algorithm with convergence guarantee.Experimental results for synthetic data and real data show that our approach obtains more competitive results compared with some existing alternatives.In order to compare with the classic PCA method,we applied BessPCA to the 1000 genome data set,and successfully separated the popu-lation structure with a small number of SNPs.On the other hand,in order to explore the application effects of the sparse PCA algorithm in multiple fields,we respectively select the Olivetti face recognition data set in computer vision,the CSI300 data set in the stock market,and the drug mechanism of action(MoA)in the field of drug discov-ery.These data set are applied and compared with the traditional principal component analysis.Experiments in the three fields have shown that the sparse PCA algorithm can achieve results equivalent to or better than PCA,but it has stronger interpretability.