Abstract
BackgroundPrincipal component analysis (PCA) has gained popularity as a method for the analysis of high-dimensional genomic data. However, it is often difficult to interpret the results because the principal components are linear combinations of all variables, and the coefficients (loadings) are typically nonzero. These nonzero values also reflect poor estimation of the true vector loadings; for example, for gene expression data, biologically we expect only a portion of the genes to be expressed in any tissue, and an even smaller fraction to be involved in a particular process. Sparse PCA methods have recently been introduced for reducing the number of nonzero coefficients, but these existing methods are not satisfactory for high-dimensional data applications because they still give too many nonzero coefficients.ResultsHere we propose a new PCA method that uses two innovations to produce an extremely sparse loading vector: (i) a random-effect model on the loadings that leads to an unbounded penalty at the origin and (ii) shrinkage of the singular values obtained from the singular value decomposition of the data matrix. We develop a stable computing algorithm by modifying nonlinear iterative partial least square (NIPALS) algorithm, and illustrate the method with an analysis of the NCI cancer dataset that contains 21,225 genes.ConclusionsThe new method has better performance than several existing methods, particularly in the estimation of the loading vectors.
Highlights
Principal component analysis (PCA) has gained popularity as a method for the analysis of highdimensional genomic data
We provide some simulation studies that indicate that these sparse PCA (SPCA) methods perform better than existing ones, and illustrate their use using a cancer gene-expression dataset with 21,225 genes
We first perform small simulation studies in order to assess the performance of the proposed sparse PCA methods and compare them against other methods
Summary
Principal component analysis (PCA) has gained popularity as a method for the analysis of highdimensional genomic data. It is often difficult to interpret the results because the principal components are linear combinations of all variables, and the coefficients (loadings) are typically nonzero These nonzero values reflect poor estimation of the true vector loadings; for example, for gene expression data, biologically we expect only a portion of the genes to be expressed in any tissue, and an even smaller fraction to be involved in a particular process. Principal component analysis (PCA) or its equivalent singular-value decomposition (SVD) is widely used for the analysis of high-dimensional data. For such gene expression data with an enormous number of variables, PCA is a useful technique for visualization, analyses and interpretation [1,2,3,4]. In this paper our focus on the PCA methodology is constrained to produce sparse loadings
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