# Topological Data Analysis

69 papers with code • 0 benchmarks • 2 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.

# Mapper on Graphs for Network Visualization

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

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

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.

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

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

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.