2022
A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis
Wang Z, Liu B, Chen S, Ma S, Xue L, Zhao H. A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis. INFORMS Journal On Optimization 2022, 4: 200-214. DOI: 10.1287/ijoo.2021.0064.Peer-Reviewed Original ResearchSparse spectral clusteringOptimization problemSpectral clusteringLinear methodsIteration complexity resultsNonconvex objectiveNonsmooth objectiveConvex relaxationStiefel manifoldSingle-cell RNA sequencing data setsSSC problemComplexity resultsSmoothing techniquesRNA sequencing data analysisData setsOriginal formulationUnsupervised learning methodData analysisNonsmoothProblemAlgorithmFormulationManifoldClusteringConvergence
2017
Structured subcomposition selection in regression and its application to microbiome data analysis
Wang T, Zhao H. Structured subcomposition selection in regression and its application to microbiome data analysis. The Annals Of Applied Statistics 2017, 11: 771-791. DOI: 10.1214/16-aoas1017.Peer-Reviewed Original ResearchRegularization methodLinear log contrast modelGeneralized lasso problemLog-contrast modelNovel penalty functionMicrobiome data analysisCompositional covariatesOptimization problemLasso problemHigher dimensionsStatistical challengesPenalty functionPractical problemsSymmetric versionTree structure informationSubtree levelProblemPrior knowledgeTree structureSubcompositionsCompositional dataSuch dataStructure informationData analysisNodes
2012
Sparse principal component analysis by choice of norm
Qi X, Luo R, Zhao H. Sparse principal component analysis by choice of norm. Journal Of Multivariate Analysis 2012, 114: 127-160. PMID: 23524453, PMCID: PMC3601508, DOI: 10.1016/j.jmva.2012.07.004.Peer-Reviewed Original ResearchHigh-dimensional situationsSparse principal component analysisReal gene expression dataEfficient iterative algorithmHigh-dimensional dataSparse principal component analysis methodEigenvalue problemOptimization problemIterative methodChoice of normDimensional situationTheoretical resultsTraditional eigenvalue problemIterative algorithmStrict convexityLinear combinationSingle-component modelExpensive computationSparse linear combinationDimensional dataUsual normExistence of correlationsGene expression dataPractical applicationsCompetitive results