Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify, and classically represent, their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states - which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.