A Robust Principal Component Analysis via Alternating Direction Method of Multipliers to Gene-Expression Prediction

Gene expression is the main process responsible for the function of every living cell. Thousands of genes expressed in a specific cell determine what that cell can do. Gene expression values can be measured by measuring the amount of messenger RNA (mRNA) molecules. There are biological methods to measure gene expression in biological samples so researchers can find genes responsible for each disease. Some example methods are Reporter gene, Microarray, and RNA sequencing. These methods however are very costly and time consuming. Computational methods have the potential to help these studies by identifying reliable directions using prediction techniques on incomplete data; so novel and efficient techniques and algorithms to predict gene expressions are in high demand. In this paper, we describe a method to recover gene expression dataset based on robust principal component analysis (RPCA). We treat the differentially expressed genes as sparse noise S and non-differentially expressed genes as low-rank matrix Y. We show how S and Y can be recovered from gene expression data using RPCA. We also used existing implementations of three other iterative optimization based matrix completion methods to provide a comparative analysis of their performances. We show that this approach consistently outperforms the other methods with reaching improvement factors beyond 7.9 in measured mean squared error.