An Extension of Fisher's Criterion: Theoretical Results with a Neural Network Realization

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.