Topological Data Analysis
161 papers with code • 0 benchmarks • 3 datasets
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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
c-hofer/nips2017
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NeurIPS 2017
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems.
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.
CUTS: A Deep Learning and Topological Framework for Multigranular Unsupervised Medical Image Segmentation
Segmenting medical images is critical to facilitating both patient diagnoses and quantitative research.
Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
BorgwardtLab/Neural-Persistence
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ICLR 2019
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data.
Topological Autoencoders
BorgwardtLab/topological-autoencoders
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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
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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
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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
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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
abrochar/pp_syn
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This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window.
