Don't understand why I get an inverse ROC curve for SVM (Python)

For any classification problem if AUC<0.5, you are not performing better than random(0.5).

Reason could be:

• Your classifier is over-fitted on the training set and performs very poorly on the test set.
• Your test sample might be very small.
• Your classifier is giving you the probability that the class is -1. Thus, you get a prediction (close to) 0 for a class 1, and 1 for a class -1 prediction. If your ROC method expects positive (+1) predictions to be higher than negative (-1) ones, you get a reversed curve.

A valid strategy is to simply invert the predictions as:

invert_prob=1-prob 

Reference: ROC

One potential fix is to remove max_iter = 12 (which would set it to the scikit learn default of max_iter=-1). Using such a low value can lead to bad scores as you can see from the following example:

from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.metrics import plot_roc_curve
from sklearn.datasets import load_breast_cancer

data = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(data.data, data.target, test_size=0.2)

model = SVC(max_iter=12, probability = True)
model.fit(X_train, y_train)

plot_roc_curve(model, X_test, y_test)

results in

However, executing exactly the same code (max_iter=12 still) again gives a totally different result:

After removing max_iter=12 the code consistently produces higher AUCs around $0.95$ to $0.99$.