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Topic · Computational Mathematics

Tensor decomposition and applications

Tensor decomposition and applications is a research topic within Computational Mathematics. Science Explorer counts 7.4k research works in it since 1951. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the theory and applications of tensor decompositions, particularly in the context of multilinear algebra. It covers various decomposition methods such as Singular Value Decomposition, Parallel Factor Analysis, Canonical Polyadic Decomposition, and Tucker Decomposition, along with their applications in signal processing and machine learning.

  • Tensor Decomposition
  • Multilinear Algebra
  • Singular Value Decomposition
  • Parallel Factor Analysis
  • Canonical Polyadic Decomposition
  • Tucker Decomposition
  • Nonnegative Tensor Factorization
  • Higher-Order Tensors
  • Signal Processing
  • Machine Learning
Research works
7.4k
fractional, since 1951
In the world top 10%
756
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+24%
the tick is no change
Largest producer
China
48% of the 10 largest, 2022-now
Tensor decomposition and applications

Which countries lead Tensor decomposition and applications research?

By volume, China and the United States publish the most (934 and 454 works in 2022-now).

By volume, 2022-now

  1. 1 China 934 works
  2. 2 United States 454 works
  3. 3 Germany 94 works
  4. 4 Japan 88 works
  5. 5 India 82 works
  6. 6 France 79 works
  7. 7 Italy 66 works
  8. 8 United Kingdom 63 works
  9. 9 Canada 48 works
  10. 10 Russia 40 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.

China: 47.9%United States: 23.3%Germany: 4.8%Japan: 4.5%6 others listed: 19.4%48%largest
China934 · 47.9%United States454 · 23.3%Germany94 · 4.8%Japan88 · 4.5%6 others listed379 · 19.4%

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

Which institutions lead Tensor decomposition and applications research?

By volume in 2022-now, Chinese Academy of Sciences publishes the most Tensor decomposition and applications research, followed by Centre National de la Recherche Scientifique and University of Electronic Science and Technology of China.

By volume, 2022-now

  1. 1 Chinese Academy of SciencesChina 35 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 29 works
  3. 3 University of Electronic Science and Technology of ChinaChina 25 works
  4. 4 Southwest UniversityChina 21 works
  5. 5 Fudan UniversityChina 18 works
  6. 6 Shanghai UniversityChina 17 works
  7. 7 Xi'an Jiaotong UniversityChina 16 works
  8. 8 KU LeuvenBelgium 15 works
  9. 9 National University of Defense TechnologyChina 14 works
  10. 10 Russian Academy of SciencesRussia 14 works

Who are the leading researchers in Tensor decomposition and applications?

The most-cited researchers publishing on Tensor decomposition and applications include Trevor Hastie, Peter M. Bentler and Nicholas G. Martin.

  1. 1 Trevor Hastie United States 301k citations
  2. 2 Peter M. Bentler United States 233k citations
  3. 3 Nicholas G. Martin Australia 228k citations
  4. 4 Kai You Wang China 224k citations
  5. 5 Paul M. Thompson United States 196k citations
  6. 6 Michael I. Jordan United States 182k 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 Tensor decomposition and applications?

The most cited paper in Tensor decomposition and applications is "Tensor Decompositions and Applications" (Tamara G. Kolda, Brett W. Bader, 2009), with 10,717 citations. Next come "Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions" (4,178) and "Generalized Procrustes Analysis" (3,317).

Most cited papers
#PaperReleasedCitations
1 Tensor Decompositions and Applications Tamara G. Kolda, Brett W. Bader · SIAM Review 5 Aug 2009 10,717
2 Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions Nathan Halko, Per‐Gunnar Martinsson, Joel A. Tropp · SIAM Review 2011 4,178
3 Generalized Procrustes Analysis J. C. Gower · Psychometrika Mar 1975 3,317
4 Matrix multiplication via arithmetic progressions Don Coppersmith, Shmuel Winograd · Journal of Symbolic Computation Open access Mar 1990 2,313
5 On the distribution of the largest eigenvalue in principal components analysis Iain M. Johnstone · The Annals of Statistics Open access Apr 2001 2,059
All 99 most cited papers, with filters and sorting

Where is Tensor decomposition and applications research done?

The largest centres of Tensor decomposition and applications research in 2022-now are Beijing (China), Shanghai (China), Xi'an (China) and Chengdu (China).

Largest cities, 2022-now

  1. 1 BeijingChina 120 works
  2. 2 ShanghaiChina 74 works
  3. 3 Xi'anChina 54 works
  4. 4 ChengduChina 48 works
  5. 5 GuangzhouChina 45 works
  6. 6 ChongqingChina 44 works
  7. 7 ChangshaChina 35 works
  8. 8 TokyoJapan 34 works
  9. 9 NanjingChina 31 works
  10. 10 HangzhouChina 28 works
See Tensor decomposition and applications on the map

Where is the best place to study Tensor decomposition and applications?

Among universities, judged by research, Southwest University, University of Electronic Science and Technology of China and Fudan 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%10%20%30%mean 20.42%fractional works in this field (log) →share of work in the world top 10% →Southwest UniversityFudan UniversityUniversity of Electr…Xi'an Jiaotong Unive…
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
1Southwest UniversityChina 86.324.7%19.0×21 +492.1%
2University of Electronic Science and Technology of ChinaChina 80.220.4%11.2×25 -12.1%
3Fudan UniversityChina 73.522.1%5.6×18 +59.8%
4Xi'an Jiaotong UniversityChina 64.616.3%4.6×16 +135.1%
5University of Hong KongChina 63.222.0%6.3×12 -2.0%
6City University of Hong KongChina 57.316.8%7.3×8 +20.4%
7Guangdong University of TechnologyChina 55.319.2%8.3×9 +12.2%
8Shanghai UniversityChina 54.911.9%11.4×17 +15.0%
9Southeast UniversityChina 54.825.5%2.7×8 +85.6%
10Northwestern Polytechnical UniversityChina 52.325.3%5.4×12 -35.4%

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 Tensor decomposition and applications, country by country

Is Tensor decomposition and applications research growing?

Output in 2022-2025 was 24% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Tensor decomposition and applications.

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 Tensor decomposition and applications as a percentage of every work published that year, 0.0084% in 2024.

still counting0.0050%0.010%0.015%Tensor decomposition and applications0.010% in 202519801990200020102020

Fractional works of Tensor decomposition and applications 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%Tensor decomposition and applications10.1% 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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