
Learning Simplicial Complexes from Persistence Diagrams
Topological Data Analysis (TDA) studies the shape of data. A common topo...
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Persistence Weighted Gaussian Kernel for Probability Distributions on the Space of Persistence Diagrams
A persistence diagram characterizes robust geometric and topological fea...
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Topological Regularization via PersistenceSensitive Optimization
Optimization, a key tool in machine learning and statistics, relies on r...
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Robust Topological Feature Extraction for Mapping of Environments using BioInspired Sensor Networks
In this paper, we exploit minimal sensing information gathered from biol...
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The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platfo...
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Bayesian Topological Learning for Classifying the Structure of Biological Networks
Actin cytoskeleton networks generate local topological signatures due to...
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Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams
We introduce a nonparametric way to estimate the global probability dens...
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A Fast and Robust Method for Global Topological Functional Optimization
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. Moreover, this scheme can also be used to produce a stable visualization of dots in a persistence diagram as a distribution over critical, and nearcritical, simplices in the data structure.
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