# Topological Data Analysis

126 papers with code • 0 benchmarks • 3 datasets

## Benchmarks

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## Libraries

Use these libraries to find Topological Data Analysis models and implementations## Most implemented papers

# Persistence Images: A Stable Vector Representation of Persistent Homology

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

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

# 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.

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

Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints.

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

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data.

# Topological Autoencoders

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

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

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

# Markov-Lipschitz Deep Learning

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.

# Particle gradient descent model for point process generation

This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window.