Linear Discriminant

Definition

A discriminant is a function that takes an input variable x and outputs a class label y for it. A linear discriminant is a discriminant that uses a linear function of the input variables and more generally a linear function of some vector function of the input variables f(x).

This entry focuses on one such linear discriminant function called Fisher’s linear discriminant. Fisher’s discriminant works by finding a projection of input variables to a lower dimensional space while maintaining a class separability property.

Motivation and Background

The curse of dimensionality (Curse of Dimensionality) is an ongoing problem in applying statistical techniques to pattern recognition problems. Techniques that are computationally tractable in low-dimensional spaces can become completely impractical in high-dimensional spaces. Consequently, various methods have been proposed to reduce the dimensionality of the input or feature space in the hope of obtaining a more manageable problem....