Date of Award


Document Type


Degree Name

Master of Science in Applied Mathematics


Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD


Classification systems are abundant in modern-day life. The United States Air Force uses classification systems across many applications such as radar, satellite, and infrared sensing just to name a few. Combining classification systems allows an opportunity to get more accurate results. Using the known information from already built and tested systems that can be mathematically combined can give insight into the performance of the fused system without having to build a combined system. Leveraging this can save time, resources, and money. This work examines the correlation effects of fusing two classifier systems, each with only two labels, using the Boolean AND and OR rule. We examine the correlation caused by fusion and its relation to the dependency effects of the fused system in the event set. We also examine the fixed correlation fusion formulas developed for the AND and OR rules as well as expand the formulas to a less restrictive case. The results demonstrate how the feature set correlation affects the induced correlation on the ROC curve and the relation between the dependency effects, existing in the pre-images projected back to the event set and the correlation. Using this information, we were able to define the correlation term in the fixed correlation fusion formula as the induced correlation from label fusion not the correlation in the feature space. We were also able to remove the restriction of independence in the false positives of the fused system fixed correlation formula and validated the revised formula using correlated features in the feature space from which the systems were fused. From these findings we have discovered fusing systems induces a correlation, which may alter the algebraic properties when fusing two or more systems such as for ensemble classifiers. Future work will derive conclusively the algebraic properties of label fusion. Further, defining the mapping between the correlation of the features and the induced correlation between the fused ROC curves implies the ability to reverse engineer properties of the individual systems and mathematically derive the optimal settings (and adjust settings) to improve performance in a dynamic environment.

AFIT Designator



PA cleared, 88ABW-2023-0255

Included in

Mathematics Commons