Two Regularized Polynomial Regressions And Its Application To Microarray Classification

The problem with "small sample, high dimension"’characteristic of microarray data classi-fication is a hot topic in the research of multidisciplinary such as matheatics, biology, computer science and so on.According to the multi-class classification problem of microarray data, and starting from the regularization theory of statistical machine learning. We propose two regularized polyno-mial regression learning machines that can simultaneously classification and gene selection by introducing two kinds of penalty function. And then applying the two machines in the rat liver regeneration related gene screening. The main work and innovations are as follows:(1) By combining polynomial likelihood loss function and multi-class elastic network penalty function with grouped gene selection performance, a new regularized polynomial regression learning machine was proposed.(2) By combining polynomial likelihood loss function and the multi-class adaptive elastic network penalty function with adaptive grouped gene selection performance, an adaptive poly-nomial regression learning machine was proposed.(3)Applying the two kinds of polynomial regression learning machines to rat liver regenera-tion gene chip data, the genes associated with liver regeneration wasselected; Useing the pathway Studio8software to analyze the selected channel relationship between genes, and then verified the biological rationality of the selected genes.