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Topic · Computational Theory and Mathematics

Topological and Geometric Data Analysis

Topological and Geometric Data Analysis is a research topic within Computational Theory and Mathematics. Science Explorer counts 12k research works in it since 1950. 10.3% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of topological data analysis in various scientific and engineering domains. It covers topics such as persistent homology, shape analysis, statistical topology, machine learning, and spatial data.

  • Persistent Homology
  • Topological Methods
  • Data Analysis
  • Complex Networks
  • Shape Analysis
  • Statistical Topology
  • Morse Theory
  • Point Cloud Data
  • Machine Learning
  • Spatial Data
Research works
12k
fractional, since 1950
In the world top 10%
1.2k
per year above
Top-10% rate
10.3%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+36%
the tick is no change
Largest producer
United States
32% of the 10 largest, 2022-now
Topological and Geometric Data Analysis

Which countries lead Topological and Geometric Data Analysis research?

By volume, the United States and China publish the most (688 and 424 works in 2022-now).

By volume, 2022-now

  1. 1 United States 688 works
  2. 2 China 424 works
  3. 3 France 180 works
  4. 4 India 157 works
  5. 5 Germany 157 works
  6. 6 United Kingdom 141 works
  7. 7 Japan 134 works
  8. 8 Italy 94 works
  9. 9 Russia 87 works
  10. 10 Spain 74 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 32.2%China: 19.9%France: 8.4%India: 7.4%6 others listed: 32.1%32%largest
United States688 · 32.2%China424 · 19.9%France180 · 8.4%India157 · 7.4%6 others listed686 · 32.1%

Shares of the rows listed above, not of the whole node.

Which institutions lead Topological and Geometric Data Analysis research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Topological and Geometric Data Analysis research, followed by University of Oxford and Max Planck Society.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 75 works
  2. 2 University of OxfordUnited Kingdom 23 works
  3. 3 Max Planck SocietyGermany 22 works
  4. 4 Russian Academy of SciencesRussia 20 works
  5. 5 Michigan State UniversityUnited States 19 works
  6. 6 Faculdades GuarulhosBrazil 18 works
  7. 7 Guarulhos UniversityBrazil 16 works
  8. 8 Chinese Academy of SciencesChina 16 works
  9. 9 National Research University Higher School of EconomicsRussia 13 works
  10. 10 Purdue University West LafayetteUnited States 12 works

Who are the leading researchers in Topological and Geometric Data Analysis?

The most-cited researchers publishing on Topological and Geometric Data Analysis include Karl John Friston, Yann LeCun and Albert-Ĺaszló Barabási.

  1. 1 Karl John Friston United Kingdom 310k citations
  2. 2 Yann LeCun United States 256k citations
  3. 3 Albert-Ĺaszló Barabási United States 223k citations
  4. 4 Stephen M. Smith United Kingdom 214k citations
  5. 5 Harry Eugene Stanley United States 198k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Topological and Geometric Data Analysis?

The most cited paper in Topological and Geometric Data Analysis is "Finding and evaluating community structure in networks" (Michelle Gayle Newman, Michelle Girvan, 2004), with 14,307 citations. Next come "Gephi: An Open Source Software for Exploring and Manipulating Networks" (11,573) and "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation" (7,818).

Most cited papers
#PaperReleasedCitations
1 Finding and evaluating community structure in networks Michelle Gayle Newman, Michelle Girvan · Physical Review E Open access 26 Feb 2004 14,307
2 Gephi: An Open Source Software for Exploring and Manipulating Networks Mathieu Bastian, Sébastien Heymann, Mathieu Jacomy · Proceedings of the International AAAI Conference on Web and Social Media Conference paperOpen access 19 Mar 2009 11,573
3 Laplacian Eigenmaps for Dimensionality Reduction and Data Representation Mikhail Belkin, Partha Niyogi · Neural Computation 21 May 2003 7,818
4 Graph drawing by force‐directed placement Thomas M. J. Fruchterman, Edward M. Reingold · Software Practice and Experience Nov 1991 6,481
5 Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering Mikhail Belkin, Partha Niyogi · The MIT Press eBooks Book chapter 8 Nov 2002 4,552
All 100 most cited papers, with filters and sorting

Where is Topological and Geometric Data Analysis research done?

The largest centres of Topological and Geometric Data Analysis research in 2022-now are Beijing (China), Paris (France), Moscow (Russia) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Guarulhos.

Largest cities, 2022-now

  1. 1 BeijingChina 73 works
  2. 2 ParisFrance 65 works
  3. 3 MoscowRussia 43 works
  4. 4 TokyoJapan 40 works
  5. 5 GuarulhosBrazil 34 works
  6. 6 LondonUnited Kingdom 33 works
  7. 7 ShanghaiChina 32 works
  8. 8 New YorkUnited States 30 works
  9. 9 Mexico CityMexico 25 works
  10. 10 OxfordUnited Kingdom 24 works

Where it is the local speciality

  1. GuarulhosBR · 33.7 works121×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Topological and Geometric Data Analysis than the world average.

See Topological and Geometric Data Analysis on the map

Where is the best place to study Topological and Geometric Data Analysis?

Among universities, judged by research, Michigan State University, University of Oxford and Stanford University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 18.65%fractional works in this field (log) →share of work in the world top 10% →Stanford UniversityMichigan State Unive…École Polytechnique …University of Oxford
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Michigan State UniversityUnited States 82.828.6%10.3×19 +53.7%
2University of OxfordUnited Kingdom 73.211.9%6.4×23 +76.7%
3Stanford UniversityUnited States 59.529.4%2.6×10 +13.6%
4École Polytechnique Fédérale de LausanneSwitzerland 57.524.7%8.2×8 +35.9%
5ETH ZurichSwitzerland 46.213.5%5.1×9 +109.6%
6Massachusetts Institute of TechnologyUnited States 46.022.9%5.6×10 -23.5%
7Tsinghua UniversityChina 45.718.6%2.0×12 +116.3%
8Sapienza University of RomeItaly 45.211.5%4.1×12 +61.2%
9Zhejiang UniversityChina 44.715.7%1.7×12 +137.4%
10National University of SingaporeSingapore 44.49.7%3.5×10 +385.0%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Topological and Geometric Data Analysis, country by country

Is Topological and Geometric Data Analysis research growing?

Output in 2022-2025 was 36% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Topological and Geometric Data Analysis.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Topological and Geometric Data Analysis as a percentage of every work published that year, 0.011% in 2024.

still counting0.0050%0.010%0.015%Topological and Geometric Data Analysis0.013% in 202519801990200020102020

Fractional works of Topological and Geometric Data Analysis over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Topological and Geometric Data Analysis10.3% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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