Clustering is widely used in medical imaging to reduce data dimension and discover subgroups in patient pop-ulations. However, most of the current clustering algorithms depend on scale parameters which are especiallydifficult to select. Persistence homology has been introduced to address this issue. This topological data analysisframework analyses a dataset at multiple scales by generating clusters of increasing sizes, similar to single-linkagehierarchical clustering. Because of this approach, however, the results are sensitive to the presence of noise andoutliers. Several strategies have been suggested to fix this issue. In this paper, we support this research effort bydemonstrating how gradient preserving data smoothings, such as total variation regularization, can improve thestability of persistence homology results, and we derive analytical confidence regions for the significance of thepersistence measured for clusters based on Pearson distances. We demonstrate the advantages of our methodsby analysing structural and functional MRI data released by the Human Connectome Project.
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