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Sparse principal component analysis is an important technique for simultaneous dimensionality reduction and variable selection with high-dimensional data. In this work we combine the unique geometric structure of the sparse principal component analysis problem with recent advances in convex optimization to develop novel gradient-based sparse principal component analysis algorithms. These algorithms enjoy the same global convergence guarantee as the original alternating direction method of multipliers, and can be more efficiently implemented with the rich toolbox developed for gradient methods from the deep learning literature. Most notably, these gradient-based algorithms can be combined with stochastic gradient descent methods to produce efficient online sparse principal component analysis algorithms with provable numerical and statistical performance guarantees. The practical performance and usefulness of the new algorithms are demonstrated in various simulation studies. As an application, we show how the scalability and statistical accuracy of our method enable us to find interesting functional gene groups in high-dimensional RNA sequencing data.

 

Abstract Motivation Marker genes, defined as genes that are expressed primarily in a single-cell type, can be identified from the single-cell transcriptome; however, such data are not always available for the many uses of marker genes, such as deconvolution of bulk tissue. Marker genes for a cell type, however, are highly correlated in bulk data, because their expression levels depend primarily on the proportion of that cell type in the samples. Therefore, when many tissue samples are analyzed, it is possible to identify these marker genes from the correlation pattern. Results To capitalize on this pattern, we develop a new algorithm to detect marker genes by combining published information about likely marker genes with bulk transcriptome data in the form of a semi-supervised algorithm. The algorithm then exploits the correlation structure of the bulk data to refine the published marker genes by adding or removing genes from the list. Availability and implementation We implement this method as an R package markerpen, hosted on CRAN (https://CRAN.R-project.org/package=markerpen). Supplementary information Supplementary data are available at Bioinformatics online.