  Fisher's criterion is a widely used tool in machine learning for feature
selection. For large search spaces, Fisher's criterion can provide a scalable
solution to select features. A challenging limitation of Fisher's criterion,
however, is that it performs poorly when mean values of class-conditional
distributions are close to each other. Motivated by this challenge, we propose
an extension of Fisher's criterion to overcome this limitation. The proposed
extension utilizes the available heteroscedasticity of class-conditional
distributions to distinguish one class from another. Additionally, we describe
how our theoretical results can be casted into a neural network framework, and
conduct a proof-of-concept experiment to demonstrate the viability of our
approach to solve classification problems.
