TITLE: High-Dimensional Feature Selection for Genomic Datasets 

ABSTRACT: 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 $\Delta\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
$\Delta\mathbf{x}$ 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
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 $\Delta\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
$\Delta\mathbf{x}$ 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
High-Dimensional Feature Selection for Genomic Datasets
http://arxiv.org/abs/2002.12104v2