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Found 10 papers, 8 papers with code
Computable Stability for Persistence Rank Function Machine Learning
In this paper, we revisit the persistent homology rank function -- an invariant measure of ``shape" that was introduced before barcodes and persistence diagrams and captures the same information in a form that is more amenable to data and computation.
$k$-Means Clustering for Persistent Homology
Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful applications to many domains.
Fast Topological Signal Identification and Persistent Cohomological Cycle Matching
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications.
Learning Linear Non-Gaussian Polytree Models
In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees.
Rewiring Networks for Graph Neural Network Training Using Discrete Geometry
Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks.
Approximating Persistent Homology for Large Datasets
We show that the mean of the persistence diagrams of subsamples -- taken as a mean persistence measure computed from the subsamples -- is a valid approximation of the true persistent homology of the larger dataset.
Curved Markov Chain Monte Carlo for Network Learning
We present a geometrically enhanced Markov chain Monte Carlo sampler for networks based on a discrete curvature measure defined on graphs.
Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in a hierarchy-preserving manner using a variety of metrics.
Tropical Optimal Transport and Wasserstein Distances
We study the problem of optimal transport in tropical geometry and define the Wasserstein-$p$ distances in the continuous metric measure space setting of the tropical projective torus.
Optimization and Control Metric Geometry Statistics Theory Statistics Theory
Functional Data Analysis using a Topological Summary Statistic: the Smooth Euler Characteristic Transform
We introduce a novel statistic, the smooth Euler characteristic transform (SECT), which is designed to integrate shape information into regression models by representing shapes and surfaces as a collection of curves.
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