Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 61

An ROC point is a point in the ROC space with x and y values where x is the probability of false alarm and y is the probability of detection. Each of the x and y axes spans from 0 to 1. Let us use an example of ROC curves in the ROC space where we simplify the curves by linearly connecting adjacent points. Let us assume that for an example dataset as explained above, we have four possibilities to classify the dataset:

1 Achieve a probability of detection equal to zero at a probability of false alarm equal to zero.

2 Achieve a probability of detection equal to 0.5 at a probability of false alarm equal to 0.25.

3 Achieve a probability of detection equal to 0.75 at a probability of false alarm equal to 0.5.

4 Achieve a probability of detection equal to 1 at a probability of false alarm equal to 1.

These four possibilities become four points in a ROC curve in the ROC space as shown in Figure 3A.4. Notice that each point constitutes a threshold that can be used to hypothesize the dataset value classification. In the ROC space, each point on a ROC curve can become a decision threshold. The key here is to decide an acceptable probability of false alarm and live with the associated probability of detection.

Figure 3A.4 An example of a ROC curve in the ROC space.