Gaussian Mixture Model Cross Validation

I want to perform cross validation on my Gaussian mixture model. Currently, my cross_validationapproach using sklearn is as follows.

clf = GaussianMixture(n_components=len(np.unique(y)), covariance_type='full')
cv_ortho = cross_validate(clf, parameters_train, y, cv=10, n_jobs=-1, scoring=scorer)

I see that cross_validation is training my classifier y_trainto be a supervised classifier.

try:
    if y_train is None:
        estimator.fit(X_train, **fit_params)
    else:
        estimator.fit(X_train, y_train, **fit_params)

However, I would like to cross-validate an unsupervised classifier clf.fit(parameters_train). I know that classifiers assign their own class labels. Since, I have two different clusters (see picture), yI can decrypt the corresponding labels. Then cross-validate. Are there routines sklearn?

A routine similar to this example : https://scikit-learn.org/stable/auto_examples/mixture/plot_gmm_covariances.html