I am fairly new to the machine learning, and I have been going over all the great posts about cross-validation today and I have a question regarding PCA and cross-validation, I don't have enough points to comment on the PCA and train/test split so I thought maybe I should post a new question.

My understanding is the most correct procedure is the following which I saw in an earlier post:

for each fold:
    split data
    conduct PCA on the 90% used for training
    pick the number of components
    fit linear regression
    predict the 10% held out
end

My main question is, if I want to do eigenfaces with PCA and SVM I would split up my set of images into my training and validation sets, and then apply the PCA to each new split in my cross-validation and optimization? My confusion comes because I was following an example on Scikit-learn where they divide the data, and then proceed to caluclate the PCA for the split data. Next, they run GridSearchCV which I understand is doing a cross-validation to tune the parameters. Does this tuning introduce a bias because it preprocessed the data or is it okay for some reason? I have attached the relevant sections of the example below.

###############################################################################
# Split into a training set and a test set using a stratified k fold

# split into a training and testing set
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25)


###############################################################################
# Compute a PCA (eigenfaces) on the face dataset (treated as unlabeled
# dataset): unsupervised feature extraction / dimensionality reduction
n_components = 150

print("Extracting the top %d eigenfaces from %d faces"
      % (n_components, X_train.shape[0]))
t0 = time()
pca = RandomizedPCA(n_components=n_components, whiten=True).fit(X_train)
print("done in %0.3fs" % (time() - t0))

eigenfaces = pca.components_.reshape((n_components, h, w))

print("Projecting the input data on the eigenfaces orthonormal basis")
t0 = time()
X_train_pca = pca.transform(X_train)
X_test_pca = pca.transform(X_test)
print("done in %0.3fs" % (time() - t0))


###############################################################################
# Train a SVM classification model

print("Fitting the classifier to the training set")
t0 = time()
param_grid = {'C': [1e3, 5e3, 1e4, 5e4, 1e5],
              'gamma': [0.0001, 0.0005, 0.001, 0.005, 0.01, 0.1], }
clf = GridSearchCV(SVC(kernel='rbf', class_weight='auto'), param_grid)
clf = clf.fit(X_train_pca, y_train)
print("done in %0.3fs" % (time() - t0))
print("Best estimator found by grid search:")
print(clf.best_estimator_)