How to use a deep learning algorithm to cluster image *styles* in an unlabeled data set?
You can use a pretrained model, extract features, and try to cluster images based on these features. The success will be contingent on the "style" you want to distinguish (and if the derived features represent the different styles). I had a similar problem and used Kerans and VGG16 features to cluster images using KNN. Find my Python code on Github.