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Persistent homology of complex networks for dynamic state detection

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Using persistent homology and dynamical distances to analyze protein binding

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Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis

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Topological data analysis of single-trial electroencephalographic signals

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The shape of things to come: Topological data analysis and biology, from molecules to organisms

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Functional summaries of persistence diagrams

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Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

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A Survey of Vectorization Methods in Topological Data Analysis

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Hypothesis testing for topological data analysis

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Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

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The Persistence Landscape and Some of Its Properties

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On the topology of random complexes built over stationary point processes

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Topological consistency via kernel estimation

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Probabilistic Fréchet means for time varying persistence diagrams

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Statistical Topological Data Analysis - a Kernel Perspective

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A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

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Topological data analysis in investment decisions

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A smeary central limit theorem for manifolds with application to high-dimensional spheres

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Learning Representations of Persistence Barcodes

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The Euler characteristic: A general topological descriptor for complex data

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Progressive Wasserstein Barycenters of Persistence Diagrams

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Geometric Inference on Kernel Density EstimatesPreprint

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A Comparative Study of Machine Learning Methods for Persistence Diagrams

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Topological Machine Learning with Persistence Indicator Functions

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Persistence Atlas for Critical Point Variability in Ensembles

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Wasserstein Distances, Geodesics and Barycenters of Merge Trees

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A Riemannian Framework for Statistical Analysis of Topological Persistence Diagrams

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Modeling and replicating statistical topology and evidence for CMB nonhomogeneity

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A survey of Optimal Transport for Computer Graphics and Computer Vision

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Topological spaces of persistence modules and their properties

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Topological feature vectors for chatter detection in turning processes

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Signal classification with a point process distance on the space of persistence diagrams

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Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology

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Computational topology-based characterization of pore space changes due to chemical dissolution of rocks

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On Wasserstein Barycenters and MMOSPA Estimation

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Approximating Continuous Functions on Persistence Diagrams Using Template Functions

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Topological learning for brain networks

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An Overview of the Topology ToolKit

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Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

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Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

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The density of expected persistence diagrams and its kernel based estimationPreprint

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Applications of Persistent Homology to Time Varying Systems

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A novel approach for wafer defect pattern classification based on topological data analysis

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Tropical Sufficient Statistics for Persistent Homology

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Same But Different: Distance Correlations Between Topological Summaries

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Homological persistence in time series: an application to music classification

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Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study

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Persistent Homology for Breast Tumor Classification Using Mammogram Scans

Asaad, A., Ali, D., Majeed, T. F., & Rashid, R. D. (2022) · Mathematics · doi:10.3390/math10214039 · Cited by 17

Multiparameter Persistence Image for Topological Machine Learning

Carrière, M., & Blumberg, A. J. (2020) · neural information processing systems · Cited by 16

Medians of populations of persistence diagrams

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Persistent topology of the reionization bubble network – II. Evolution and classification

Elbers, W., & van de Weygaert, R. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad120 · Cited by 14

The promises of persistent homology, machine learning, and deep neural networks in topological data analysis of democracy survival

Arfi, B. (2023) · Quality & Quantity · doi:10.1007/s11135-023-01708-6 · Cited by 14

Investigation of Indian stock markets using topological data analysis and geometry-inspired network measures

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Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport

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K−means clustering on the space of persistence diagrams

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Modelling persistence diagrams with planar point processes, and revealing topology with bagplots

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Limit theorems for Fréchet mean sets

Evans, S. N., & Jaffe, A. Q. (2023) · Bernoulli · doi:10.3150/23-bej1603 · Cited by 11

Topological data analysis assisted automated sleep stage scoring using airflow signals

Chung, Y.-M., Huang, W. K., & Wu, H. (2023) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2023.105760 · Cited by 11

Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance

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Statistical Parameter Selection for Clustering Persistence Diagrams

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An LP-based, strongly-polynomial 2-approximation algorithm for sparse Wasserstein barycenters

Borgwardt, S. (2020) · Operational Research · doi:10.1007/s12351-020-00589-z · Cited by 17

The (homological) persistence of gerrymandering

Duchin, M., Needham, T., & Weighill, T. (2021) · Foundations of Data Science · doi:10.3934/fods.2021007 · Cited by 10

An algebraic Wasserstein distance for generalized persistence modulesPreprint

Bubenik, P., Scott, J., & Stanley, D. (2018) · arXiv (Cornell University) · Cited by 10

Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations

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Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

Pont, M., Vidal, J., & Tierny, J. (2022) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2022.3215001 · Cited by 9

Metric geometry of spaces of persistence diagrams

Che, M., Galaz‐García, F., Guijarro, L., & Solis, I. M. (2024) · Journal of Applied and Computational Topology · doi:10.1007/s41468-024-00189-2 · Cited by 9

Higher Interpolation and Extension for Persistence Modules

Bubenik, P., de Silva, V., & Nanda, V. (2017) · SIAM Journal on Applied Algebra and Geometry · doi:10.1137/16m1100472 · Cited by 9

Topological Data Analysis: Developments and Applications

Motta, F. C. (2017) · Springer eBooks · doi:10.1007/978-3-319-58895-7_19 · Cited by 9

Computing persistent homology under random projection

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Nonparametric Estimation of Probability Density Functions of Random Persistence DiagramsPreprint

Mike, J. L., & Maroulas, V. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1803.02739 · Cited by 9

Topology Data Analysis Using Mean Persistence Landscapes in Financial Crashes

Aguilar, A., & Ensor, K. B. (2020) · Journal of Mathematical Finance · doi:10.4236/jmf.2020.104038 · Cited by 8

k-means clustering for persistent homology

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Optimization of Spectral Wavelets for Persistence-Based Graph Classification

Yim, K. M., & Leygonie, J. (2021) · Frontiers in Applied Mathematics and Statistics · doi:10.3389/fams.2021.651467 · Cited by 8

An Overview of the Topology ToolKit

Falk, M., Favelier, G., Gueunet, C., Guillou, P., Kamakshidasan, A., Klacansky, P., Levine, J. A., Lukasczyk, J., Sakurai, D., Soler, M., et al. (2019) · HAL · Cited by 8

A random persistence diagram generator

Papamarkou, T., Nasrin, F., Lawson, A., Gong, N., Rios, O. R., & Maroulas, V. (2022) · Statistics and Computing · doi:10.1007/s11222-022-10141-y · Cited by 8

Convergence of persistence diagram in the sparse regime

Owada, T. (2022) · The Annals of Applied Probability · doi:10.1214/22-aap1800 · Cited by 8

Topological data analysis reveals differences between simulated galaxies and dark matter haloes

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Functional Data Analysis using a Topological Summary Statistic: the Smooth Euler Characteristic TransformPreprint

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Characterizing Reaction Route Map of Realistic Molecular Reactions Based on Weight Rank Clique Filtration of Persistent Homology

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Association-Free Direct Filtering of Multi-Target Random Finite Sets with Set Distance Measures

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Frechet means for distributions of persistence diagrams. Discrete and Computational Geometry

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Probabilistic Frechet means and statistics on vineyards, 2013. arXiv 1307.6530Preprint

Munch, E., Bendich, P. L., Turner, K., Mukherjee, S., Mattingly, J. C., & Harer, J. (2016)

A lower bound for estimating Fréchet means

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