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Found 10 papers, 3 papers with code
Rapid and Precise Topological Comparison with Merge Tree Neural Networks
To address this challenge, we introduce the merge tree neural networks (MTNN), a learned neural network model designed for merge tree comparison.
The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning
We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques.
Visualizing Topological Importance: A Class-Driven Approach
This paper presents the first approach to visualize the importance of topological features that define classes of data.
A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering
In this paper, we propose a persistence diagram hashing framework that learns a binary code representation of persistence diagrams, which allows for fast computation of distances.
Functional Summaries of Persistence Diagrams
First, we review the various functional summaries in the literature and propose a unified framework for the functional summaries.
Methodology
Introduction to the R package TDA
The salient topological features of the sublevel sets (or superlevel sets) of these functions can be quantified with persistent homology.
Mathematical Software Computational Geometry Computation
Subsampling Methods for Persistent Homology
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.
Algebraic Topology Computational Geometry Applications
Stochastic Convergence of Persistence Landscapes and Silhouettes
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram.
Statistics Theory Computational Geometry Algebraic Topology Statistics Theory
On the Bootstrap for Persistence Diagrams and Landscapes
Persistent homology probes topological properties from point clouds and functions.
Algebraic Topology Computational Geometry Applications
Confidence sets for persistence diagrams
Persistent homology is a method for probing topological properties of point clouds and functions.
