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In this thesis, I demonstrate a novel and efficient unsupervised clustering and data exploration method with the combination of a Self-Organising Map (SOM) and a Convolutional Autoencoder, applied to radio-astronomical images from the Radio Galaxy Zoo (RGZ) dataset. The rapidly increasing volume and complexity of radio-astronomical data have ushered in a new era of big-data astronomy which has increased the demand for Machine Learning (ML) solutions. In this era, the sheer amount of image data produced with modern instruments and has resulted in a significant data deluge. Furthermore, the morphologies of objects captured in these radio-astronomical images are highly complex and challenging to classify conclusively due to their intricate and indiscrete nature. Additionally, major radio-astronomical discoveries are unplanned and found in the unexpected, making unsupervised ML highly desirable by operating with few assumptions and without labelled training data. In this thesis, I developed a novel unsupervised ML approach as a practical solution to these astronomy challenges. Using this system, I demonstrated the use of convolutional autoencoders and SOM’s as a dimensionality reduction method to delineate the complexity and volume of astronomical data. My optimised system shows that the coupling of these methods is a powerful method of data exploration and unsupervised clustering of radio-astronomical images. The results of this thesis show this approach is capable of accurately separating features by complexity on a SOM manifold and unified distance matrix with neighbourhood similarity and hierarchical clustering of the mapped astronomical features. This method provides an effective means to explore the high-level topological relationships of image features and morphology in large datasets automatically with minimal processing time and computational resources. I achieved these capabilities with a new and innovative method of SOM training using the autoencoder compressed latent feature vector representations of radio-astronomical data, rather than raw images. Using this system, I successfully investigated SOM affine transformation invariance and analysed the true nature of rotational effects on this manifold using autoencoder random rotation training augmentations. Throughout this thesis, I present my method as a powerful new approach to data exploration technique and contribution to the field. The speed and effectiveness of this method indicates excellent scalability and holds implications for use on large future surveys, large-scale instruments such as the Square Kilometre Array and in other big-data and complexity analysis applications.