A persistence-augmented neural network framework encodes local gradient flow regions and their hierarchy via the Morse-Smale complex to retain multi-scale localized topological information, outperforming global TDA descriptors on histopathology classification and 3D porous material regression while,
Clique topology reveals intrinsic geometric structure in neural correlations.Proceedings of the National Academy of Sciences, 112(44):13455–13460, 2015
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Faster algorithms compute the integral bottleneck distance between PHTs in Õ(n^5) time and the max version in Õ(n^3) time for R^2 and Õ(n^5) for R^3.
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Persistence-Augmented Neural Networks
A persistence-augmented neural network framework encodes local gradient flow regions and their hierarchy via the Morse-Smale complex to retain multi-scale localized topological information, outperforming global TDA descriptors on histopathology classification and 3D porous material regression while,
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Computing the Bottleneck Distance between Persistent Homology Transforms
Faster algorithms compute the integral bottleneck distance between PHTs in Õ(n^5) time and the max version in Õ(n^3) time for R^2 and Õ(n^5) for R^3.