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Probabilistic classifiers induce a similarity metric at each location in the space of the data. This is measured by the Fisher Information Matrix. Pairwise distances in this Riemannian space, calculated along geodesic paths, can be used to generate a similarity map of the data. The novelty in the paper is twofold; to improve the methodology for visualisation of data structures in low-dimensional manifolds, and to illustrate the value of inferring the structure from a probabilistic classifier by metric learning, through application to music data. This leads to the discovery of new structures and song similarities beyond the original genre classification labels. These similarities are not directly observable by measuring Euclidean distances between features of the original space, but require the correct metric to reflect similarity based on genre. The results quantify the extent to which music from bands typically associated with one particular genre can, in fact, crossover strongly to another genre.

Breast cancer is the most commonly diagnosed female malignancy globally, with better survival rates if diagnosed early. Mammography is the gold standard in screening programmes for breast cancer, but despite technological advances, high error rates are still reported. Machine learning techniques, and in particular deep learning (DL), have been successfully used for breast cancer detection and classification. However, the added complexity that makes DL models so successful reduces their ability to explain which features are relevant to the model, or whether the model is biased. The main aim of this study is to propose a novel visualisation to help characterise breast cancer patients using Fisher Information Networks on features extracted from mammograms using a DL model. In the proposed visualisation, patients are mapped out according to their similarities and can be used to study new patients as a ‘patient-like-me’ approach. When applied to the CBIS-DDSM dataset, it was shown that it is a competitive methodology that can (i) facilitate the analysis and decision-making process in breast cancer diagnosis with the assistance of the FIN visualisations and ‘patient-like-me’ analysis, and (ii) help improve diagnostic accuracy and reduce overdiagnosis by identifying the most likely diagnosis based on clinical similarities with neighbouring patients.