{'fraction_non_alphanumeric': 0.03400503778337532, 'fraction_numerical': 0.011335012594458438, 'mean_word_length': 4.977443609022556, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Robust Shape Clustering : Computing 1-medians on Riemannian Manifolds

Propelled by advances in medical imaging technology, clinicians and researchers are generating vast amounts of complex 2D and 3D shape data describing the brain, the heart, and other critical organs in both diseased and normal patients. Such shape data is often modelled as points on manifolds. Thus, characterizing such data requires us to extend statistical notions of centrality to manifold-valued data. In previous work [2, 6, 13], the notion of centrality of empirical data was defined via the Fréchet mean [7], which was first developed for manifold-valued data by Karcher [8]. Although the mean is an obvious central representative, one of its major drawbacks is its lack of robustness, i.e. sensitivity to outliers.