Strong regulations in the financial industry mean that any decisions based on machine learning need to be explained. This precludes the use of powerful supervised techniques such as neural networks. In this study we propose a new unsupervised and semi-supervised technique known as the topological hierarchical decomposition (THD). This process breaks a dataset down into ever smaller groups, where groups are associated with a simplicial complex that approximate the underlying topology of a dataset. We apply THD to the FICO machine learning challenge dataset, consisting of anonymized home equity loan applications using the MAPPER algorithm to build simplicial complexes. We identify different groups of individuals unable to pay back loans, and illustrate how the distribution of feature values in a simplicial complex can be used to explain the decision to grant or deny a loan by extracting illustrative explanations from two THDs on the dataset.