Robust PCA based method for discovering differentially expressed genes

Abstract

How to identify a set of genes that are relevant to a key biological process is an important issue in current molecular biology. In this paper, we propose a novel method to discover differentially expressed genes based on robust principal component analysis (RPCA). In our method, we treat the differentially and non-differentially expressed genes as perturbation signals S and low-rank matrix A, respectively. Perturbation signals S can be recovered from the gene expression data by using RPCA. To discover the differentially expressed genes associated with special biological progresses or functions, the scheme is given as follows. Firstly, the matrix D of expression data is decomposed into two adding matrices A and S by using RPCA. Secondly, the differentially expressed genes are identified based on matrix S. Finally, the differentially expressed genes are evaluated by the tools based on Gene Ontology. A larger number of experiments on hypothetical and real gene expression data are also provided and the experimental results show that our method is efficient and effective.

Figure 1

The RPCA model of microarray data. The white and yellow blocks denote zero and near-zero in this figure. Red and blue blocks denote the perturbation signals.

Figure 2

The recognition accuracy of matrix $S$ with different $c$. s1 denotes the recognition accuracy series with $rank=5$ and $\mu =0.05$. s2 denotes the recognition accuracy series with $rank=5$ and $\mu =0.1$. s3 denotes the recognition accuracy series with $rank=10$ and $\mu =0.05$. s4 denotes the recognition accuracy series with $rank=10$ and $\mu =0.1$.

Figure 3

The sample frequency of response to abiotic stimulus.