Fisher's Pioneering work on Discriminant Analysis and its Impact on AI

TL;DR

Fisher's foundational work on discriminant analysis significantly influenced AI, with ongoing developments from classical methods to modern machine learning techniques, demonstrating its enduring importance in supervised learning.

Contribution

This paper revisits Fisher's original discriminant analysis, tests its assumptions on iris data, and discusses its evolution alongside modern AI methods.

Findings

Fisher's discriminant analysis is still relevant in AI.

The iris data hypothesis of multivariate normality was tested.

Modern methods like SVMs and neural networks build on Fisher's principles.

Abstract

Fisher opened many new areas in Multivariate Analysis, and the one which we will consider is discriminant analysis. Several papers by Fisher and others followed from his seminal paper in 1936 where he coined the name discrimination function. Historically, his four papers on discriminant analysis during 1936-1940 connect to the contemporaneous pioneering work of Hotelling and Mahalanobis. We revisit the famous iris data which Fisher used in his 1936 paper and in particular, test the hypothesis of multivariate normality for the data which he assumed. Fisher constructed his genetic discriminant motivated by this application and we provide a deeper insight into this construction; however, this construction has not been well understood as far as we know. We also indicate how the subject has developed along with the computer revolution, noting newer methods to carry out discriminant analysis, such as kernel classifiers, classification trees, support vector machines, neural networks, and deep learning. Overall, with computational power, the whole subject of Multivariate Analysis has changed its emphasis but the impact of this Fisher's pioneering work continues as an integral part of supervised learning in Artificial Intelligence.