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Suppose I would like to train and test the MNIST dataset in Keras.

The required data can be loaded as follows:

from keras.datasets import mnist

digits_data = mnist.load_data()

Is there any way in keras to split this data into three sets namely: training_data, test_data, and cross_validation_data?

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From the Keras documentation, you can load the data into Train and Test sets like this

(X_train, y_train), (X_test, y_test) = mnist.load_data()

As for cross validation, you could follow this example from https://github.com/fchollet/keras/issues/1711

from sklearn.model_selection import StratifiedKFold

def load_data():
    # load your data using this function

def create model():
    # create your model using this function

def train_and_evaluate__model(model, data_train, labels_train, data_test, labels_test):
    model.fit...
    # fit and evaluate here.

if __name__ == "__main__":
    n_folds = 10
    data, labels, header_info = load_data()
    skf = StratifiedKFold(labels, n_folds=n_folds, shuffle=True)

    for i, (train, test) in enumerate(skf):
        print "Running Fold", i+1, "/", n_folds
        model = None # Clearing the NN.
        model = create_model()
        train_and_evaluate_model(model, data[train], labels[train], data[test], labels[test])
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Not in keras. I normally just use sklearn's train_test_split function:

from sklearn.model_selection import train_test_split

train, test = train_test_split(data, train_size=0.8)

Keras also has sklearn wrappers that might be useful later on:

http://keras.io/scikit-learn-api/

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