Multiparameter Receiver Operating Characteristic Analysis for Signal Detection and Classification

Receiver operating characteristic (ROC) analysis is a widely used evaluation tool in signal processing and communications, and medical diagnosis for performance analysis. It utilizes 2-D curves plotted by detection rate (
P

_D
) against false alarm rate (
P

_F
) to assess effectiveness of a detector, sensor/device for detection. However,
P

_D
and
P

_F
are actually dependent parameters resulting from a more crucial but implicit parameter hidden in the ROC curves, threshold ¿ , which is determined by the cost of implementing a detector or sensor/device, except only the case that when the Bayes theory is used for detection, ¿ is completely determined by the Bayes cost. This paper extends the traditional ROC analysis for single-signal detection to detection and classification of multiple signals. It also explores relationships among the three parameters,
P

_D
,
P

_F
, and ¿ , and further develops a new concept of multiparameter ROC analysis, which uses 3-D ROC curves plotted by three parameters,
P

_D
,
P

_F
, and ¿, to evaluate effectiveness of detection performance based on interrelationship among
P

_D
,
P

_F
, and ¿, rather then only
P

_D
and
P

_F
used by 2-D ROC analysis. As a result of a 3-D ROC curve, three 2-D ROC curves can be also derived: the conventional 2-D ROC curve plotted by
P

_D
versus
P

_F
and two new 2-D ROC curves plotted based on
P

_D
versus ¿ and
P

_F
versus ¿. In order to demonstrate the utility of 3-D ROC analysis, four applications are considered: hyperspectral target detection, medical diagnosis, chemical/biological agent detection, and biometric recognition.