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Background  In recent years, identification of differentially expressed genes and sample clustering have become hot topics in bioinformatics. Principal Component Analysis (PCA) is a widely used method in gene expression data. However, it has two limitations: first, the geometric structure hidden in data, e.g., pair-wise distance between data points, have not been explored. This information can facilitate sample clustering; second, the Principal Components (PCs) determined by PCA are dense, leading to hard interpretation. However, only a few of genes are related to the cancer. It is of great significance for the early diagnosis and treatment of cancer to identify a handful of the differentially expressed genes and find new cancer biomarkers.    Results  In this study, a new method gLSPCA is proposed to integrate both graph Laplacian and sparse constraint into PCA. gLSPCA on the one hand improves the clustering accuracy by exploring the internal geometric structure of the data, on the other hand identifies differentially expressed genes by imposing a sparsity constraint on the PCs.    Conclusions  Experiments of gLSPCA and its comparison with existing methods, including Z-SPCA, GPower, PathSPCA, SPCArt, gLPCA, are performed on real datasets of both pancreatic cancer (PAAD) and head & neck squamous carcinoma (HNSC). The results demonstrate that gLSPCA is effective in identifying differentially expressed genes and sample clustering. In addition, the applications of gLSPCA on these datasets provide several new clues for the exploration of causative factors of PAAD and HNSC.

PCA via joint graph Laplacian and sparse constraint: Identification of differentially expressed genes and sample clustering on gene expression data