graphs-5

Topological Data Analysis

3260 papers • 126 benchmarks • 313 datasets

This task has no description! Would you like to contribute one?

(Image credit: Papersgraph)

Benchmarks

These leaderboards are used to track progress in topological-data-analysis-5

Trend

Dataset

Best Model

Actions

No benchmarks available.

Libraries

i

Use these libraries to find topological-data-analysis-5 models and implementations

MathieuCarriere/perslay

2 papers 78

Datasets

REDDIT-5K

REDDIT-12K

Subtasks

No subtasks available.

Most implemented papers

Deep Learning with Topological Signatures

Christoph Hofer, R. Kwitt, M. Niethammer, A. Uhl•Wed Jul 12 2017

This work proposes a technique that enables us to input topological signatures to deep neural networks and learn a task-optimal representation during training, realized as a novel input layer with favorable theoretical properties.

266

Content

0

Paper Graph

Persistence Images: A Stable Vector Representation of Persistent Homology

Henry Adams, T. Emerson, M. Kirby, R. Neville, C. Peterson, Patrick D. Shipman, Sofya Chepushtanova, Eric M. Hanson, Francis C. Motta, Lori Ziegelmeier•Tue Jul 21 2015

This work converts a PD to a finite-dimensional vector representation which it is called a persistence image, and proves the stability of this transformation with respect to small perturbations in the inputs.

783 0

Paper Graph

Fast topological signal identification and persistent cohomological cycle matching

In'es Garc'ia-Redondo, Anthea Monod, Anna Song•Thu Sep 29 2022

This paper harnesses the state-of-the-art for persistent homology computation by studying the problem of determining topological prevalence and cycle matching using a cohomological approach, which increases their feasibility and applicability to a wider variety of applications and contexts.

9 0

Paper Graph

Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs

P. Rosen, Mustafa Hajij, Bei Wang•Mon Apr 02 2018

A variation of the mapper construction targeting weighted, undirected graphs is developed, called mapper on graphs, which generates homology-preserving skeletons of graphs, and how the adjustment of a single parameter enables multi-scale skeletonization of the input graph is shown.

8 0

Paper Graph

Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology

Thomas Gumbsch, Christian Bock, Max Horn, Michael Moor, Karsten M. Borgwardt, Bastian Alexander Rieck, Matteo Togninalli•Sat Dec 22 2018

This work proposes neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs and derives a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

125 0

Paper Graph

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

Shusen Liu, B. V. Essen, Rushil Anirudh, Jayaraman J. Thiagarajan, P. Bremer, Di Wang, D. Maljovec, S. A. Jacobs, D. Hysom, Jae-Seung Yeom, J. Gaffney, L. Peterson, Peter B. Robinson, H. Bhatia, Valerio Pascucci, B. Spears•Thu Jul 18 2019

This work presents the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline by combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes.

14 0

Paper Graph

Mapper Based Classifier

J. Cyranka, A. Georges, David A. Meyer•Wed Oct 16 2019

A classifier based on applying the Mapper algorithm to data projected onto a latent space is proposed, which is immune to any gradient based attack, and improves robustness over traditional CNNs.

2 0

Paper Graph

Markov-Lipschitz Deep Learning

S. Li, Lirong Wu, Zelin Zhang•Sun Jun 14 2020

This work proposes 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.

17 0

Paper Graph

Particle gradient descent model for point process generation

Sixin Zhang, B. Błaszczyszyn, Antoine Brochard, S. Mallat•Mon Oct 26 2020

A statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window, inspired by recent works on gradient descent algorithms for sampling maximum-entropy models, that allows for fast sampling of new configurations reproducing the statistics of the given observation.

3 0

Paper Graph

Adding a benchmark result helps the community track progress.