generally, your classification system should give you a confidence score. To get a ROC curve you set a threshold and define everything above as positive and the other as negative. Then you match those decisions to the groundtruth to see how many are true positives, false positives, true negatives and false negatives. From that you compute precision and recall. This gives you one point on the ROC curve. By varying the above mentioned threshold you get the whole curve.

on a side note:

knn is not a clustering method, its a classification method (did you mean kmeans?).

why do you need knn (or kmeans) if you use random forests?

how is it unsupervised? the random forests usually need labeled data, unless you are doing something like density forests.

generally, your classification system should give you a confidence score. To get a ROC curve you set a threshold and define everything above as positive and the other as negative. Then you match those decisions to the groundtruth to see how many are true positives, false positives, true negatives and false negatives. From that you compute precision and recall. This gives you one point on the ROC curve. By varying the above mentioned threshold you get the whole curve.

on a side note:

knn is not a clustering method, its a classification method (did you mean kmeans?).

why do you need knn (or kmeans) if you use random forests?

how is it unsupervised? the random forests usually need labeled data, unless you are doing something like density forests.

I am sorry, I just got a little confused , I am actually using kmeans with random forest for Multi-class problems , the only parameter that I vary is the bagging fraction, the feature fraction and the number of trees and ofcourse initialisation of centroids for kmeans. ROC for multi-class is difficult I guess unless I do one vs all.

You can get your ROC curves for a multiclass problem.

For one parametrization, your classifier (RF) gives you a confidence score. As said Paul, using your ground truth you can calculate TP, FP, TN, FN scores.

Each time, only one parameter, among the four your consider, is varied and you can then plot your ROC curve for that parameter.

If you set up your random forest so that it gives you the fraction of each class in the leaf as output, you can interpret this as probability of class membership for each class. This should easily work for multiclass problems as well. In that setup you do not do any further clustering in the leaf nodes. This probability is the score for which you can vary the threshold for constructing the ROC.

Now for the *kNN*. Of course you could put a kNN into each leaf node of the random forest. However, kNN itself is a highly nonlinear classifier that needs large numbers of training cases. Putting the kNN into the leaf nodes will give (IMHO unnecessarily) unstable output (i.e. even less stable than the decision tree). Like the leaf node fractions of a decision tree, kNN can output the class membership fractions for the k nearest neighbours to the test case, which again can be interpreted as probability for class membership (again: works also for multi-class problems). However, as always exactly k neighbours are involved, exactly k + 1 output values are possible. Therefore your ROC will have k + 1 points (including 0;0 and 1;1).

In addition to Paul Wolhart's excellent questions and your answer: why would you want to do an unsupervised clustering on the output/leaf nodes of a supervised classifier?

*Multiclass ROC*: one vs. all others are a typical setup for ROC in multi-class scenarios. This is closely connected to so-called one-class classification problems(*) but this ROC setup is also used for closed world classification(**).

For other approaches to generalize ROC to closed world classifiers, see e.g. Landgrebe, T. C. and Paclik, P.: The ROC skeleton for multiclass ROC estimation, Pattern Recognition Letters, 31 (2010), 949-958. DOI: 10.1016/j.patrec.2009.12.037

(*)one-class classifier: class membership of the different classes is independent e.g. a patient may have both a tumour and hepatitis

(**)closed world: the memberships always add up to 1, e.g. one given tumour may be may be either lung or breast cancer, but never both.