ROC Curve

Author:
Victor Hui

Receiver Operating Characteristic Curve

Correspondence between score distributions and the ROC curve (https://en.wikipedia.org/wiki/Receiver_operating_characteristic)
• d (x-axis) is the score returned by a binary classifier﻿
• The red and blue hatchings are distributions of the scores of the positive and negative truths
• Let the distributions be normal, move "<-->" to adjust the location and scale
• d* is a threshold setting to separate the mixing of the positive and negative classifications
• The blue shaded region (d < d*) is the distribution of false positive (FP) scores
• The red shaded region (d > d*) is the distribution of false negative (FN) scores
• The area of the blue shaded region yields the false positive rate FPR
• The area of the red hatching less the area of the red shade yields the truth positive rate TPR
• The ROC curve is the plot of TPR vs FPR as function of the threshold setting d*
• Move d* on Graph to trace the ROC curve on Graph2
Question: Find an optimal threshold setting d*