Similar to supervised learning, a neural network can be used in a way to train on unlabeled data sets. This type of algorithms are categorized under unsupervised learning algorithms and are useful in a multitude of tasks such as clustering.
Convolutional neural networks are generally trained as supervised methods which means both the inputs (i.e. images in an image recognition task) and their labels (i.e. the objects depicted in the images) are available within the training data. On the other hand, specific unsupervised learning methods are developed for convolutional neural networks to pre-train them. These methods were employed in the past in order to overcome the computational limits during the training of the network and are still in use to generally speed up the training process.(1)
 Why does unsupervised pre-training help deep learning? (2010, Dumitru Erhan, Yoshua Bengio, Aaron Courville, Pierre-Antoine Manzagol, Pascal Vincent, & Samy Bengio)
 Learning deep architectures for AI (2009, Yoshua Bengio)