A novel low-rank representation method for identifying differentially expressed genes

Low-rank representation (LRR) has attracted lots of attentions in recent years. However, LRR has a chief shortcoming, which uses the nuclear norm to approximate the non-convex rank function. This approximation minimises all singular values, thus the nuclear norm may not approximate to the rank function well. In this paper, we propose a novel low-rank method that replaces the nuclear norm with the truncated nuclear norm to approximate the rank function. And it is applied to identifying differentially expressed genes. The truncated nuclear norm is defined as the sum of some smaller singular values which may be a better measure to approximate the rank function than the nuclear norm. In order to achieve the convergence of our method, the optimisation problem of our method is solved by the augmented Lagrange multiplier method that has the property of convergence. The experimental results demonstrate that our method exceeds LLRR, TRPCA and RPCA methods.