Topological Data Analysis

Benchmarks archive 2025-07-28

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Libraries

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Datasets archive 2025-07-28

3 datasets whose archive record lists this task, ordered by the archive's paper count.

Subtasks archive 2025-07-28

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Parent tasks archive 2025-07-28

Most implemented papers archive 2025-07-28

30 shown of 166 papers with code (498 tagged with this task in all), ordered by repositories listed in the archive, not by stars (the archive holds no stars, so PwC's “Social” and “Latest” sorts cannot be reproduced). Papers without a page here are shown as plain text.

• Deep Learning with Topological Signatures
  13 Jul 2017 4 repositories listed
  Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems.
• Persistence Images: A Stable Vector Representation of Persistent Homology
  22 Jul 2015 4 repositories listed
  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.
• CUTS: A Deep Learning and Topological Framework for Multigranular Unsupervised Medical Image Segmentation
  23 Sep 2022 3 repositories listed Syntology ran 3 of 3 samples · 0 unverified · 3 pointer-only (licence)
  Segmenting medical images is critical to facilitating both patient diagnoses and quantitative research.
• Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs
  3 Apr 2018 3 repositories listed Syntology ran 1 of 1 samples · 0 unverified · 1 pointer-only (licence)
  Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints.
• Stability for Inference with Persistent Homology Rank Functions
  6 Jul 2023 2 repositories listed
  In this paper, we revisit the persistent homology rank function, which is mathematically equivalent to a barcode and persistence diagram, as a tool for statistics and machine learning.
• GRIL: A $2$-parameter Persistence Based Vectorization for Machine Learning
  11 Apr 2023 2 repositories listed
  We show that this vector representation is $1$-Lipschitz stable and differentiable with respect to underlying filtration functions and can be easily integrated into machine learning models to augment encoding…
• Can BERT eat RuCoLA? Topological Data Analysis to Explain
  4 Apr 2023 2 repositories listed
  Our results contribute to understanding the behavior of monolingual LMs in the acceptability classification task, provide insights into the functional roles of attention heads, and highlight the advantages of TDA-based…
• Multiscale topology classifies and quantifies cell types in subcellular spatial transcriptomics
  13 Dec 2022 2 repositories listed
  Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues.
• Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems
  3 Dec 2022 2 repositories listed
  While being a weaker invariant in one dimension, we show that Euler Characteristic based approaches do not possess some handicaps of persistent homology; we show efficient algorithms to compute them in a distributed…
• Fast Topological Signal Identification and Persistent Cohomological Cycle Matching
  30 Sep 2022 2 repositories listed
  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.
• Neural Approximation of Graph Topological Features
  28 Jan 2022 2 repositories listed Syntology ran 3 of 4 samples · 1 unverified · 4 pointer-only (licence)
  Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods.
• Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest
  1 Jan 2022 2 repositories listed
  We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest.
• Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks
  25 Nov 2021 2 repositories listed Syntology ran 4 of 7 samples · 3 unverified
  Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters.
• Artificial Text Detection via Examining the Topology of Attention Maps
  10 Sep 2021 2 repositories listed Syntology ran 9 of 9 samples · 0 unverified · 9 pointer-only (licence)
  The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content.
• Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
  4 Apr 2021 2 repositories listed
  Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the…
• Particle gradient descent model for point process generation
  27 Oct 2020 2 repositories listed
  This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window.
• Markov-Lipschitz Deep Learning
  15 Jun 2020 2 repositories listed Syntology ran 0 of 7 samples · 7 unverified
  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…
• Mapper Based Classifier
  17 Oct 2019 2 repositories listed
  We propose a classifier based on applying the Mapper algorithm to data projected onto a latent space.
• Scalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications
  19 Jul 2019 2 repositories listed
  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.
• Topological Autoencoders
  3 Jun 2019 2 repositories listed Syntology ran 0 of 4 samples · 4 unverified
  We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders.
• Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
  23 Dec 2018 2 repositories listed Syntology ran 2 of 13 samples · 11 unverified · 2 pointer-only (licence)
  While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data.
• Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging
  29 May 2025 1 repository listed
  In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models.
• Topological Machine Learning for Protein-Nucleic Acid Binding Affinity Changes Upon Mutation
  28 May 2025 1 repository listed
  Understanding how protein mutations affect protein-nucleic acid binding is critical for unraveling disease mechanisms and advancing therapies.
• Topology across Scales on Heterogeneous Cell Data
  5 May 2025 1 repository listed
  Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data.
• Short-PHD: Detecting Short LLM-generated Text with Topological Data Analysis After Off-topic Content Insertion
  1 Apr 2025 1 repository listed
  Short-PHD stabilizes the estimation of the previous PHD method for short texts by inserting off-topic content before the given input text and identifies LLM-generated text based on an established detection threshold.
• A Topological Data Analysis Framework for Quantifying Necrosis in Glioblastomas
  21 Mar 2025 1 repository listed
  In this paper, we introduce a shape descriptor that we call "interior function".
• Persistent Homology-induced Graph Ensembles for Time Series Regressions
  18 Mar 2025 1 repository listed
  The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures.
• Dimension reduction methods, persistent homology and machine learning for EEG signal analysis of Interictal Epileptic Discharges
  18 Feb 2025 1 repository listed
  The reduced data are examined using topological data analysis (TDA), specifically using a persistent homology algorithm.
• Persistent Sheaf Laplacian Analysis of Protein Flexibility
  12 Feb 2025 1 repository listed
  Protein flexibility, measured by the B-factor or Debye-Waller factor, is essential for protein functions such as structural support, enzyme activity, cellular communication, and molecular transport.
• Towards Fast Graph Generation via Autoregressive Noisy Filtration Modeling
  4 Feb 2025 1 repository listed Syntology ran 1 of 14 samples · 13 unverified
  We introduce Autoregressive Noisy Filtration Modeling (ANFM), a novel approach that addresses both challenges.

Syntology lines on 9 of the papers shown; no Syntology record for the others (a paper without an arXiv id cannot be joined to the graph, and absence from the graph layer is not a recorded non-run). “Ran” means the sample executed on a synthesized fixture, not that the paper's result was reproduced. Read from the graph 2026-09-24.