receiver operating characteristic (roc) and area under the curve (AUC) in matlab

You want to use a classifier, for example a support vector machine, to distinguish between different classes. When making binary decisions you want to make sure that your decision criterion is sensitive to your target class and that it is specific to the target class. Say you want to detect cancer, but only cancer. That's why there are roc curves and the area under the curve.

I searched for implementations in matlab for calculating areas under the curve (auc) and found several, unfortunately, they had shortcomings. Some were incorrect. Most of them took the outcome of the decision criterion, Y, and the target vector, T, as input, which doesn't make sense, because the auc is a summary statistics not over just two vectors Y and T. The idea is that you take true positive rate (TPR) and false positive rate (FPR) from each {Y,T} pair and summarize over several runs of the decision criterion with different parameters.

Here is my implementation corresponding to Tom Fawcett's algorithm 3 in "roc graphs: notes and practical considerations for researchers, " 2004.

Code snippet - area under the curve (AUC) on Snipplr

Here is how you get true positive rate and false positive rate (i assume you have T,Y element of {-1,1}:

Code snippet - true positive rate and false positive rate for receiver operating characteristics (ROC) and area under the curve on Snipplr

Enjoy. Please comment below for any questions or suggestions.