---
_id: '14739'
abstract:
- lang: eng
  text: Attempts to incorporate topological information in supervised learning tasks
    have resulted in the creation of several techniques for vectorizing persistent
    homology barcodes. In this paper, we study thirteen such methods. Besides describing
    an organizational framework for these methods, we comprehensively benchmark them
    against three well-known classification tasks. Surprisingly, we discover that
    the best-performing method is a simple vectorization, which consists only of a
    few elementary summary statistics. Finally, we provide a convenient web application
    which has been designed to facilitate exploration and experimentation with various
    vectorization methods.
acknowledgement: "The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel
  Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia
  e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part
  by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028.
  The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la
  Universidad de Sevilla para la recualificacion del sistema universitario español,
  2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda
  was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR
  under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON
  developers, for their work and their support. We are also grateful to Streamlit
  for providing extra resources to deploy the web app\r\nonline on Streamlit community
  cloud. We thank the anonymous referees for their helpful suggestions."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Dashti
  full_name: Ali, Dashti
  last_name: Ali
- first_name: Aras
  full_name: Asaad, Aras
  last_name: Asaad
- first_name: Maria-Jose
  full_name: Jimenez, Maria-Jose
  last_name: Jimenez
- first_name: Vidit
  full_name: Nanda, Vidit
  last_name: Nanda
- first_name: Eduardo
  full_name: Paluzo-Hidalgo, Eduardo
  last_name: Paluzo-Hidalgo
- first_name: Manuel
  full_name: Soriano Trigueros, Manuel
  id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
  last_name: Soriano Trigueros
  orcid: 0000-0003-2449-1433
citation:
  ama: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M.
    A survey of vectorization methods in topological data analysis. <i>IEEE Transactions
    on Pattern Analysis and Machine Intelligence</i>. 2023;45(12):14069-14080. doi:<a
    href="https://doi.org/10.1109/tpami.2023.3308391">10.1109/tpami.2023.3308391</a>
  apa: Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., &#38; Soriano
    Trigueros, M. (2023). A survey of vectorization methods in topological data analysis.
    <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE. <a
    href="https://doi.org/10.1109/tpami.2023.3308391">https://doi.org/10.1109/tpami.2023.3308391</a>
  chicago: Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo,
    and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological
    Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>.
    IEEE, 2023. <a href="https://doi.org/10.1109/tpami.2023.3308391">https://doi.org/10.1109/tpami.2023.3308391</a>.
  ieee: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano
    Trigueros, “A survey of vectorization methods in topological data analysis,” <i>IEEE
    Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12.
    IEEE, pp. 14069–14080, 2023.
  ista: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros
    M. 2023. A survey of vectorization methods in topological data analysis. IEEE
    Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.
  mla: Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data
    Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>,
    vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:<a href="https://doi.org/10.1109/tpami.2023.3308391">10.1109/tpami.2023.3308391</a>.
  short: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano
    Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023)
    14069–14080.
date_created: 2024-01-08T09:59:46Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-08T10:11:46Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1109/tpami.2023.3308391
file:
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  date_created: 2024-01-08T10:09:14Z
  date_updated: 2024-01-08T10:09:14Z
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file_date_updated: 2024-01-08T10:09:14Z
has_accepted_license: '1'
intvolume: '        45'
issue: '12'
keyword:
- Applied Mathematics
- Artificial Intelligence
- Computational Theory and Mathematics
- Computer Vision and Pattern Recognition
- Software
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 14069-14080
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_identifier:
  eissn:
  - 1939-3539
  issn:
  - 0162-8828
publication_status: published
publisher: IEEE
quality_controlled: '1'
status: public
title: A survey of vectorization methods in topological data analysis
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2023'
...