Existing automated approaches to classifying galaxies in astronomical images typically use supervised machine learning algorithms. The most high profile example is the Galaxy Zoo machine learning project which successfully classifies images of galaxies from the Sloan Digital Sky Survey. However, this required very detailed classification data consisting of over 67,000 galaxies that had previously been classified by citizen scientists. A significant effort over a period of years by a large number of people was required in order to gather the data used to train the supervised learning algorithm. The alternative approach is to use an unsupervised learning algorithm to identify the latent structure within the data. We investigate possible methods to automatically segment and classify galaxies in astronomical images using an unsupervised learning algorithm known as Growing Neural Gas. We demonstrate the effectiveness of the approach using data from the Hubble Space Telescope Frontier Field observations.