Pattern classification is a common technique used in a variety of applications. From simple tasks, such as password acceptance, to more complex tasks, such as identication by biometrics, speech recognition, and text recognition. As a result, a large number of pattern classification algorithms have emerged, allowing computers to perform these tasks. However, these techniques become less eective when excessive data on a given object is provided in comparison to the number of samples required to train. As a result, much research has been placed in nding ecient methods of reducing the dimensionality of the data while maintaining maximum classification accuracy. Dimensionality reduction aims to maximize the spread between samples of dierent classes, and mimimumize the spread between samples of the same class. A variety of methods aiming to do this have been reported in the literature. The most common methods of dimensionality reduction are Linear Discriminant Analysis and its variants. These typically focus on the spread of all the data, without regard to how spread out sections of the data already are. Few methods disregard the spread of data that is already spread out, but these are not so commonly accepted. While the classication accuracy is often better using these techniques, the computational time is often a large obstacle. This thesis will investigate several methods of dimensionality reduction, and then discuss algorithms to improve upon the existing algorithms. These algorithms utilize techniques that can be implemented on any hardware, making them suitable for any form of hardware.