A Fast and Robust Method for Global Topological Functional Optimization

Understand

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data.

• The mapping from data structures to persistence diagrams is almost everywhere differentiable, allowing for topological gradients to be backpropagated to ordinary gradients.
• However, as a method for optimizing a topological functional, this backpropagation method is expensive, unstable, and produces very fragile optima.
• Our contribution is to introduce a novel backpropagation scheme that is significantly faster, more stable, and produces more robust optima.