What is the main purpose of a ROC curve?

The main purpose of a ROC curve, or Receiver Operating Characteristic curve, is to evaluate the performance of a binary classifier system. It provides a graphical representation of the trade-offs between sensitivity (true positive rate) and specificity (1 - false positive rate) as the decision threshold of the classifier is varied. By plotting these two metrics on the axes of the graph, one can visualize how well the classifier distinguishes between the two classes across different thresholds.

This is particularly useful in assessing the classifier's performance in scenarios where there may be an imbalance between the classes (e.g., one class has significantly more instances than the other) and allows for comparison across multiple classification models. The area under the ROC curve (AUC) is often used as a single metric to summarize the model's performance, with a higher value indicating better classification ability.