Influence functions for Linear Discriminant Analysis: Sensitivity analysis and efficient influence diagnostics

TL;DR

This paper derives influence functions for Linear Discriminant Analysis (LDA) with multiple groups, enabling robustness analysis and influential observation detection, by leveraging the relationship between LDA and Sliced Inverse Regression (SIR).

Contribution

It introduces influence functions for LDA in multi-group settings, extending previous single-group results through a novel connection with SIR.

Findings

Influence functions for multi-group LDA are derived.

The methods help identify influential data points in LDA.

Application to real data demonstrates practical utility.

Abstract

Whilst influence functions for linear discriminant analysis (LDA) have been found for a single discriminant when dealing with two groups, until now these have not been derived in the setting of a general number of groups. In this paper we explore the relationship between Sliced Inverse Regression (SIR) and LDA, and exploit this relationship to develop influence functions for LDA from those already derived for SIR. These influence functions can be used to understand robustness properties of LDA and also to detect influential observations in practice. We illustrate the usefulness of these via their application to a real data set.