Part-based image classification aims at representing categories by small sets of learned discriminative parts, upon which an image representation is built. Considered as a promising avenue a decade ago, this direction has been neglected since the advent of deep neural networks. In this context, this paper brings two contributions: first, this work proceeds one step further compared to recent part-based models (PBM), focusing on how to learn parts without using any labeled data. Instead of learning a set of parts per class, as generally performed in the PBM literature, the proposed approach both constructs a partition of a given set of images into visually similar groups, and subsequently learns a set of discriminative parts per group in a fully unsupervised fashion. This strategy opens the door to the use of PBM in new applications where labeled data are typically not available, such as instance-based image retrieval. Second, this paper shows that despite the recent success of end-to-end models, explicit part learning can still boost classification performance. We experimentally show that our learned parts can help building efficient image representations, which outperform state-of-the art Deep Convolutional Neural Networks (DCNN) on both classification and retrieval tasks.