  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.
