Abstract and concrete categories
Abstract and concrete categories
Conceptual mathematics: a first introduction to categories
Conceptual mathematics: a first introduction to categories
Elementary categories, elementary toposes
Elementary categories, elementary toposes
Robust classification systems for imprecise environments
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Robust Classification for Imprecise Environments
Machine Learning
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Random Processes: Filtering, Estimation, and Detection
Random Processes: Filtering, Estimation, and Detection
Category Theory Applied to Neural Modeling and Graphical Representations
IJCNN '00 Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN'00)-Volume 3 - Volume 3
The evaluation of competing classifiers
The evaluation of competing classifiers
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Improving the Practice of Classifier Performance Assessment
Neural Computation
The ROC manifold for classification systems
Pattern Recognition
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A mathematical description of fusion is presented using category theory. A category of fusion rules is developed. The category definition is derived for a model of a classification system beginning with an event set and leading to the final labeling of the event. Functionals on receiver operating characteristic (ROC) curves are developed to form a partial ordering of families of classification systems. The arguments of these functionals point to specific ROCs and, under various choices of input data, correspond to the Bayes optimal threshold (BOT) and the Neyman-Pearson threshold of the families of classification systems. The functionals are extended for use over ROC curves and ROC manifolds where the number of classes of interest in the fusion system exceeds two and the parameters used are multi-dimensional. Choosing a particular functional, therefore, provides the qualitative requirements to define a fusor and choose the best competing classification system.