High-Dimensional Feature Selection for Genomic Datasets

A central problem in machine learning and pattern recognition is the process of recognizing the most important features. In this paper, we provide a new feature selection method (DRPT) that consists of first removing the irrelevant features and then detecting correlations between the remaining features. Let $D=[A\mid \mathbf{b}]$ be a dataset, where $\mathbf{b}$ is the class label and $A$ is a matrix whose columns are the features. We solve $A\mathbf{x} = \mathbf{b}$ using the least squares method and the pseudo-inverse of $A$. Each component of $\mathbf{x}$ can be viewed as an assigned weight to the corresponding column (feature). We define a threshold based on the local maxima of $\mathbf{x}$ and remove those features whose weights are smaller than the threshold. To detect the correlations in the reduced matrix, which we still call $A$, we consider a perturbation $\tilde A$ of $A$. We prove that correlations are encoded in $Δ\mathbf{x}=\mid \mathbf{x} -\tilde{\mathbf{x}}\mid $, where $\tilde{\mathbf{x}}$ is the least quares solution of $\tilde A\tilde{\mathbf{x}}=\mathbf{b}$. We cluster features first based on $Δ\mathbf{x}$ and then using the entropy of features. Finally, a feature is selected from each sub-cluster based on its weight and entropy. The effectiveness of DRPT has been verified by performing a series of comparisons with seven state-of-the-art feature selection methods over ten genetic datasets ranging up from 9,117 to 267,604 features. The results show that, over all, the performance of DRPT is favorable in several aspects compared to each feature selection algorithm. \e