# Quantifying Correlation and Its Effects on System Performance in Classifier Fusion

## Date of Award

9-2005

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Department of Mathematics and Statistics

## First Advisor

Mark E. Oxley, PhD

## Abstract

In automatic target recognition systems, classifiers are used to determine whether or not a target of interest is of a specific type. These systems also apply beyond military context to engineering and biomedical fields in which, for example, handwriting recognition and disease states, respectively, are of interest. Regardless of the application, multiple classifier systems, each designed to determine the same target-of-interest classification, are often combined in attempts to increase the overall performance of the fused-classifier system. This performance can be viewed as a trade-off between the number of events that the system accurately classifies as targets of interest versus the number of non-target events that the system classifies as targets. In many contexts, the proportion of targets accurately classified is called the hit rate and the proportion of non-targets classified as targets is called the false alarm rate. These rates are estimates of their respective probabilities, the probability of true and false positive. The Receiver Operator Characteristic (ROC) curve is a tool describing the trade-off between these probabilities for the classifier system. Efficiency in testing and comparing the performance of multiple fusion rules can be gained if the individual systems could be combined mathematically, without the need to retest the entire system. Correlation between individual classifier systems, however, is often not explicitly measured and thus, may not be reflected accurately in the mathematically-combined ROC curve for the fused classifier system. The research contained in this dissertation quantifies the correlation between classifier systems and derives equations of the ROC curve for the fused classifier system, incorporating the correlation between the individual systems. Many methods can be used to combine these systems. The one of the interest for this research is the fusion of the resulting classifications, or the labels of the systems. Thus, this research: 1) produces the formula for correlation between classifier systems; and 2) produces equations to compute the correlation-adjusted ROC curve for the fused classifier system using label-fusion rules. Two types of fusion rules, within and across, are defined and formulas are developed for each type. Further, the general correlation expression developed herein can be incorporated into other fusion rules and used to describe the correlation between classifier systems combined using any label-fusion rule of interest. Finally, the methods presented here to produce formulas for ROC curves of fused classifiers lay the ground work to extend these methods to other fusion rules of interest, so that researchers can observe the performance of many different types of fused classifier systems without having to invest large amounts of resources beyond that for the individual classifier systems already tested.

## AFIT Designator

AFIT-DS-ENC-05-01

## Recommended Citation

Schubert, Christine M., "Quantifying Correlation and Its Effects on System Performance in Classifier Fusion" (2005). *Theses and Dissertations*. 3631.

https://scholar.afit.edu/etd/3631