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,
Stability of persistence diagrams.Discrete & Computational Geometry, 37(1):103–120, Jan 2007
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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,