Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

Density Estimation for Statistics and Data Analysis

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Nonlinear Dimensionality Reduction by Locally Linear Embedding

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A Global Geometric Framework for Nonlinear Dimensionality Reduction

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Algorithms for Clustering Data

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Hierarchical Clustering Schemes

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The Sorcerer II Global Ocean Sampling Expedition: Northwest Atlantic through Eastern Tropical Pacific

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The Sorcerer II Global Ocean Sampling Expedition: Expanding the Universe of Protein Families

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The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics

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Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization

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Topological estimation using witness complexes

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Data: A Collection of Problems from Many Fields for the Student and Research Worker

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The Nonlinear Statistics of High-Contrast Patches in Natural Images

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On the use of Gromov-Hausdorff Distances for Shape Comparison

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Nonmetric multidimensional scaling

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Extended Reeb Graphs for Surface Understanding and Description

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Metric multidimensional scaling

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Discussion: Projection Pursuit

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Topology and data

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PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells

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A roadmap for the computation of persistent homology

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Stereotypic Immune System Development in Newborn Children

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Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival

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Visualizing high-dimensional data: advances in the past decade

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A blood atlas of COVID-19 defines hallmarks of disease severity and specificity

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Spatiotemporal genomic architecture informs precision oncology in glioblastoma

Lee, J., Wang, J., Sa, J. K., Ladewig, E., Lee, H., Lee, I., Kang, H. J., Rosenbloom, D. I. S., Cámara, P. G., Liu, Z., et al. (2017) · Nature Genetics · doi:10.1038/ng.3806 · Cited by 276 · see citing works

EMG Pattern Recognition in the Era of Big Data and Deep Learning

Phinyomark, A., & Scheme, E. (2018) · Big Data and Cognitive Computing · doi:10.3390/bdcc2030021 · Cited by 272 · see citing works

A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching

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Towards a new approach to reveal dynamical organization of the brain using topological data analysis

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Topological pattern recognition for point cloud data

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Knowledge Discovery and interactive Data Mining in Bioinformatics - State-of-the-Art, future challenges and research directions

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The Topology ToolKit

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The 2019 mathematical oncology roadmap

Rockne, R. C., Hawkins-Daarud, A. J., Swanson, K. R., Sluka, J. P., Glazier, J. A., Macklin, P., Hormuth, D. A., Jarrett, A. M., Lima, E. A. B. F., Oden, J. T., et al. (2019) · Physical Biology · doi:10.1088/1478-3975/ab1a09 · Cited by 215 · see citing works

An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

Chazal, F., & Michel, B. (2021) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2021.667963 · Cited by 780 · see citing works

An artificial niche preserves the quiescence of muscle stem cells and enhances their therapeutic efficacy

Quarta, M., Brett, J. O., DiMarco, R. L., de Morrée, A., Boutet, S. C., Chacon, R., Gibbons, M. C., Garcia, V. A., Su, J., Shrager, J. B., et al. (2016) · Nature Biotechnology · doi:10.1038/nbt.3576 · Cited by 196 · see citing works

A metabolic function of FGFR3-TACC3 gene fusions in cancer

Frattini, V., Pagnotta, S. M., Tala, Fan, J. J., Russo, M. V., Lee, S. B., Garofano, L., Zhang, J., Shi, P., Lewis, G., et al. (2018) · Nature · doi:10.1038/nature25171 · Cited by 189 · see citing works

Analysis of Big Data in Gait Biomechanics: Current Trends and Future Directions

Phinyomark, A., Petri, G., Ibáñez‐Marcelo, E., Osis, S. T., & Ferber, R. (2017) · Journal of Medical and Biological Engineering · doi:10.1007/s40846-017-0297-2 · Cited by 175 · see citing works

Big data analytics for smart factories of the future

Gao, R., Wang, L.-H., Helu, M., & Teti, R. (2020) · Cirp Annals-manufacturing Technology · doi:10.1016/j.cirp.2020.05.002 · Cited by 150 · see citing works

A Survey of Topology‐based Methods in Visualization

Heine, C., Leitte, H., Hlawitschka, M. W., Iuricich, F., Floriani, L. D., Scheuermann, G., Hagen, H., & Garth, C. (2016) · Computer Graphics Forum · doi:10.1111/cgf.12933 · Cited by 165 · see citing works

A User’s Guide to Topological Data Analysis

Munch, E. (2017) · Journal of Learning Analytics · doi:10.18608/jla.2017.42.6 · Cited by 163 · see citing works

Tracking Resilience to Infections by Mapping Disease Space

Torres, B. Y., Oliveira, J. H. M., Tate, A. T., Rath, P., Cumnock, K., & Schneider, D. S. (2016) · PLoS Biology · doi:10.1371/journal.pbio.1002436 · Cited by 144 · see citing works

Head and neck cancer subtypes with biological and clinical relevance: Meta-analysis of gene-expression data

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Topological methods for exploring low-density states in biomolecular folding pathways

Yao, Y., Sun, J. Z., Huang, X., Bowman, G. R., Singh, G., Lesnick, M., Guibas, L. J., Pande, V. S., & Carlsson, G. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3103496 · Cited by 129 · see citing works

Modeling and interpreting mesoscale network dynamics

Khambhati, A. N., Sizemore, A. E., Betzel, R. F., & Bassett, D. S. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.06.029 · Cited by 128 · see citing works

Manifold learning-based methods for analyzing single-cell RNA-sequencing data

Moon, K. R., Stanley, J. S., Burkhardt, D. B., van Dijk, D., Wolf, G., & Krishnaswamy, S. (2017) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2017.12.008 · Cited by 127 · see citing works

EXplainable Artificial Intelligence (XAI)—From Theory to Methods and Applications

Ortigossa, E. S., Gonçalves, T., & Nonato, L. G. (2024) · IEEE Access · doi:10.1109/access.2024.3409843 · Cited by 124 · see citing works

How Many Parameters Does It Take to Describe Disease Tolerance?

Louie, A., Song, K. H., Hotson, A. G., Tate, A. T., & Schneider, D. S. (2016) · PLoS Biology · doi:10.1371/journal.pbio.1002435 · Cited by 108 · see citing works

Topological data analysis reveals genotype–phenotype relationships in primary ciliary dyskinesia

Shoemark, A., Rubbo, B., Legendre, M., Fassad, M. R., Haarman, E. G., Best, S. K., Bon, I., Brandsma, J., Burgel, P., Carlsson, G., et al. (2021) · European Respiratory Journal · doi:10.1183/13993003.02359-2020 · Cited by 108 · see citing works

Three-dimensional point cloud recognition via distributions of geometric distances

Mahmoudi, M., & Sapiro, G. (2008) · Graphical Models · doi:10.1016/j.gmod.2008.10.002 · Cited by 108 · see citing works

Topological analysis of data

Patania, A., Vaccarino, F., & Petri, G. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0104-x · Cited by 105 · see citing works

Measuring Distance between Reeb Graphs

Bauer, U., Ge, X., & Wang, Y. (2014) · Annual Symposium on Computational Geometry (SoCG) · doi:10.1145/2582112.2582169 · Cited by 103 · see citing works

Principal Graph and Structure Learning Based on Reversed Graph Embedding

Mao, Q., Wang, L., Tsang, I. W.-H., & Sun, Y. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2635657 · Cited by 92 · see citing works

Emergent Experience and the Connected Consumer in the Smart Home Assemblage and the Internet of ThingsPreprint

Hoffman, D. L., & Novak, T. P. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2648786 · Cited by 96 · see citing works

Kepler Mapper: A flexible Python implementation of the Mapper algorithm.

van Veen, H. J., Saul, N., Eargle, D., & Mangham, S. (2019) · The Journal of Open Source Software · doi:10.21105/joss.01315 · Cited by 91 · see citing works

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

Yan, L., Masood, T. B., Sridharamurthy, R., Rasheed, F., Natarajan, V., Hotz, I., & Wang, B. (2021) · Computer Graphics Forum · doi:10.1111/cgf.14331 · Cited by 81 · see citing works

Topological methods for data modelling

Carlsson, G. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-00249-3 · Cited by 79 · see citing works

MIMA: MAPPER-Induced Manifold Alignment for Semi-Supervised Fusion of Optical Image and Polarimetric SAR Data

Hu, J., Hong, D., & Zhu, X. X. (2019) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2019.2924113 · Cited by 78 · see citing works

Topology of deep neural networksPreprint

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Navigating features: a topologically informed chart of electromyographic features space

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Algebraic stability of zigzag persistence modules

Botnan, M. B., & Lesnick, M. (2018) · Algebraic & Geometric Topology · doi:10.2140/agt.2018.18.3133 · Cited by 73 · see citing works

Crowdsourcing digital health measures to predict Parkinson’s disease severity: the Parkinson’s Disease Digital Biomarker DREAM Challenge

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Tropical Coordinates on the Space of Persistence Barcodes

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SFCM: A Fuzzy Clustering Algorithm of Extracting the Shape Information of Data

Bui, Q., Vo, B., Snåšel, V., Pedrycz, W., Hong, T., Nguyên, N. T., & Chen, M. (2020) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2020.3014662 · Cited by 60 · see citing works

Topological Approaches to Deep Learning

Carlsson, G., & Gabrielsson, R. B. (2020) · Abel symposia · doi:10.1007/978-3-030-43408-3_5 · Cited by 60 · see citing works

CONSTRUCTING MULTI-RESOLUTION MARKOV STATE MODELS (MSMS) TO ELUCIDATE RNA HAIRPIN FOLDING MECHANISMS

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Generating dynamical neuroimaging spatiotemporal representations (DyNeuSR) using topological data analysis

Geniesse, C., Sporns, O., Petri, G., & Saggar, M. (2019) · Network Neuroscience · doi:10.1162/netn_a_00093 · Cited by 57 · see citing works

Statistical Analysis and Parameter Selection for MapperPreprint

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Land consumption in cities: A comparative study across the globe

Hu, J., Wang, Y., Taubenböck, H., & Zhu, X. X. (2021) · Cities · doi:10.1016/j.cities.2021.103163 · Cited by 58 · see citing works

Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest

Saggar, M., Shine, J. M., Liégeois, R., Dosenbach, N. U. F., & Fair, D. A. (2022) · Nature Communications · doi:10.1038/s41467-022-32381-2 · Cited by 60 · see citing works

Topological methods for genomics: Present and future directions

Cámara, P. G. (2016) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2016.12.007 · Cited by 56 · see citing works

Persistent Homology for the Evaluation of Dimensionality Reduction Schemes

Rieck, B., & Leitte, H. (2015) · Computer Graphics Forum · doi:10.1111/cgf.12655 · Cited by 55 · see citing works

Resting-State fMRI Functional Connectivity: Big Data Preprocessing Pipelines and Topological Data Analysis

Phinyomark, A., Ibáñez‐Marcelo, E., & Petri, G. (2017) · IEEE Transactions on Big Data · doi:10.1109/tbdata.2017.2734883 · Cited by 54 · see citing works

Topological clustering of multilayer networks

Yuvaraj, M., Dey, A. K., Lyubchich, V., Gel, Y. R., & Poor, H. V. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2019994118 · Cited by 54 · see citing works

Explainable reinforcement learning (XRL): a systematic literature review and taxonomy

Bekkemoen, Y. (2023) · Machine Learning · doi:10.1007/s10994-023-06479-7 · Cited by 58 · see citing works

Robust and interpretable PAM50 reclassification exhibits survival advantage for myoepithelial and immune phenotypes

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Structure and Stability of the One-Dimensional Mapper

Carrière, M., & Oudot, S. (2017) · HAL · Cited by 54 · see citing works

Persistent homology of attractors for action recognition

Venkataraman, V., Ramamurthy, K. N., & Turaga, P. K. (2016) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2016.7533141 · Cited by 53 · see citing works

A Structural Average of Labeled Merge Trees for Uncertainty Visualization

Yan, L., Wang, Y., Munch, E., Gasparovic, E., & Wang, B. (2019) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2019.2934242 · Cited by 50 · see citing works

Sputum microbiomic clustering in asthma and chronic obstructive pulmonary disease reveals a Haemophilus‐predominant subgroup

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Distinct genomic profile and specific targeted drug responses in adult cerebellar glioblastoma

Cho, H. J., Zhao, J., Jung, S. W., Ladewig, E., Kong, D., Suh, Y., Lee, Y., Kim, D., Ahn, S. H., Bordyuh, M., et al. (2018) · Neuro-Oncology · doi:10.1093/neuonc/noy123 · Cited by 49 · see citing works

Generalized persistence diagrams for persistence modules over posets

Kim, W., & Mémoli, F. (2021) · Journal of Applied and Computational Topology · doi:10.1007/s41468-021-00075-1 · Cited by 49 · see citing works

Interpatient Similarities in Cardiac Function

Tokodi, M., Shrestha, S., Bianco, C. M., Kagiyama, N., Casaclang‐Verzosa, G., Narula, J., & Sengupta, P. P. (2020) · JACC. Cardiovascular imaging · doi:10.1016/j.jcmg.2019.12.018 · Cited by 49 · see citing works

BitcoinHeist: Topological Data Analysis for Ransomware Detection on the Bitcoin BlockchainPreprint

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Cytokine systems approach demonstrates differences in innate and pro-inflammatory host responses between genetically distinct MERS-CoV isolates

Selinger, C., Tisoncik-Go, J., Menachery, V. D., Agnihothram, S., Law, G. L., Chang, J., Kelly, S. M., Sova, P., Baric, R. S., & Katze, M. G. (2014) · BMC Genomics · doi:10.1186/1471-2164-15-1161 · Cited by 47 · see citing works

Refining understanding of corporate failure through a topological data analysis mapping of Altman’s Z-score model

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Graph-based representations of point clouds

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Application of Aligned-UMAP to Longitudinal Biomedical Studies

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Intersectionality of Non-normative Identities in the Cultures of Engineering

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F-Mapper: A Fuzzy Mapper clustering algorithm

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Malaria intensity in Colombia by regions and populations

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Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures

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Identification of key features using topological data analysis for accurate prediction of manufacturing system outputs

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A Genomic Multiprocess Survey of Machineries that Control and Link Cell Shape, Microtubule Organization, and Cell-Cycle Progression

Graml, V. M., Studera, X. E., Lawson, J., Chessel, A., Geymonat, M., Bortfeld‐Miller, M., Walter, T., Wagstaff, L., Piddini, E., & Salas, R. E. C. (2014) · Developmental Cell · doi:10.1016/j.devcel.2014.09.005 · Cited by 41 · see citing works

Topology of Learning in Feedforward Neural Networks

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Functional coordination of non-myocytes plays a key role in adult zebrafish heart regeneration

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Simplicial Models and Topological Inference in Biological Systems

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Topological data analysis and machine learning

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Topological gene expression networks recapitulate brain anatomy and function

Patania, A., Selvaggi, P., Veronese, M., Dipasquale, O., Expert, P., & Petri, G. (2019) · Network Neuroscience · doi:10.1162/netn_a_00094 · Cited by 38 · see citing works

Unveiling patterns of international communities in a global city using mobile phone data

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Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

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Predicting associations among drugs, targets and diseases by tensor decomposition for drug repositioning

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Exploring hyperspectral imaging data sets with topological data analysis

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