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....