3
Three-Dimensional Receiver Operating Characteristics (3D ROC) Analysis
Receiver operating characteristics (ROC) analysis is a widely used performance evaluation tool in signal processing, communications, and medical diagnosis. It utilizes two-dimensional (2D) curves plotted between detection rate (PD) and false alarm rate (PF) to assess effectiveness of a detector or sensor/device for detection. However, PD and PF are actually dependent parameters resulting from a more crucial but implicit parameter hidden in the ROC curves, that is, threshold τ, which is determined by the cost of implementing a detector or sensor/device except the case when the Bayes theory is used for detection, where τ is completely determined by the Bayes cost. This chapter extends the traditional ROC analysis for single-signal detection to multiple-signal detection and classification. It also explores the relationship among the three parameters, PD, PF, and τ, and further develops a new concept of three-dimensional ROC (3D ROC) analysis that uses 3D ROC curves plotted with PD, PF, and τ to evaluate detection effectiveness rather than only PD and PF used by 2D ROC analysis. As a result of using the 3D ROC curves, three 2D ROC curves can also be derived, the conventional 2D ROC curve plotted by PD versus PF and two new 2D ROC curves plotted by PD versus τ and PF versus τ. To demonstrate the utility of 3D ROC analysis, four applications are considered: hyperspectral target detection, medical diagnosis, chemical/biological ...
