Topological Data Analysis

69 papers with code • 0 benchmarks • 2 datasets

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Use these libraries to find Topological Data Analysis models and implementations

Most implemented papers

Persistence Images: A Stable Vector Representation of Persistent Homology

CSU-TDA/PersistenceImages 22 Jul 2015

We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs.

Deep Learning with Topological Signatures

c-hofer/nips2017 NeurIPS 2017

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems.

Mapper on Graphs for Network Visualization

USFDataVisualization/MapperOnGraphs 3 Apr 2018

We propose to apply the mapper construction--a popular tool in topological data analysis--to graph visualization, which provides a strong theoretical basis for summarizing network data while preserving their core structures.

Approximating Continuous Functions on Persistence Diagrams Using Template Functions

lizliz/teaspoon 19 Feb 2019

Specifically, we begin by characterizing relative compactness with respect to the bottleneck distance, and then provide explicit theoretical methods for constructing compact-open dense subsets of continuous functions on persistence diagrams.

Topological Autoencoders

BorgwardtLab/topological-autoencoders ICML 2020

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders.

Scalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications

rushilanirudh/icf-jag-cycleGAN 19 Jul 2019

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization.

Mapper Based Classifier

asgeorges/mapper-classifier 17 Oct 2019

We propose a classifier based on applying the Mapper algorithm to data projected onto a latent space.

Markov-Lipschitz Deep Learning

westlake-cairi/Markov-Lipschitz-Deep-Learning 15 Jun 2020

We propose a novel framework, called Markov-Lipschitz deep learning (MLDL), to tackle geometric deterioration caused by collapse, twisting, or crossing in vector-based neural network transformations for manifold-based representation learning and manifold data generation.

Visualizing the Effects of a Changing Distance on Data Using Continuous Embeddings

ginagruenhage/cmdsr 8 Nov 2013

The right scale is hard to pin down and it is preferable when results do not depend too tightly on the exact value one picked.

A Riemannian Framework for Statistical Analysis of Topological Persistence Diagrams

rushilanirudh/pdsphere 28 May 2016

This paper concerns itself with one popular topological feature, which is the number of $d-$dimensional holes in the dataset, also known as the Betti$-d$ number.