trouble understanding roc curve

Question

I'm not sure if I can consider three different land cover maps "classifiers" but I have several pairs of TPRs and FPRs for these 3 land cover maps which look like this.

For A(corine):

 cities        TPR           FPR

Bristol     0.6894999    0.08716076    
Brussel     0.8065292    0.18621056   
Amsterdam   0.8234692    0.07085285   
Berlin      0.6944172    0.05507682  
Manchester  0.6360882    0.11037915  
...........

For B(globcover):

 cities      TPR         FPR

Bristol    0.3830600 0.02031096  
Brussel    0.7203415 0.09221805    
Amsterdam  0.5984948 0.03149400    
Berlin     0.3902973 0.01440764     
Manchester 0.7105581 0.02429963
..........

For C(grump):

 cities      TPR         FPR

Bristol    0.3830600 0.02031096  
Brussel    0.7203415 0.09221805    
Amsterdam  0.5984948 0.03149400    
Berlin     0.3902973 0.01440764     
Manchester 0.7105581 0.02429963
..........

with these datas, I plotted FPR vs TPR with a random classifier without having any threshold. And the plot looks like this:

Can it still be considered an ROC Curve or am I missing something or have I not understood what an roc curve is?

Any help is much appreciated.

Thanks!

Answer 1

No, it is not correct because each combination of classifier and city should have its own ROC curve that is obtained by changing the classifier's threshold. What you can do is compute ROC area for each (city, classifier) combination and then average by city to compare classifiers. You could also plot those ROC values using three boxplots, one for each classifier.