Research map / Learning theory and algorithms / Clustering
Clustering approximation algorithms
Design provable algorithms for hierarchical and general clustering objectives, often via convex relaxation.
150 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Clustering, keyword cluster “correlation clustering · hierarchical · spectral clustering”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Few recent reports The tracked benchmarks have at most one report from 2025–26 that could beat the old record, too few to say whether they are still moving.
26 papers in 2023–24 and 23 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 18.6% to 11.2%.
No longer reported by papers here: MNIST (NMI, last in 2023); MNIST (ACC, last in 2023).
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Fast and accurate spike sorting of high-channel count probes with KiloSort (NeurIPS 2016 · 356 citations)
- 2017 · Optimal Neighborhood Kernel Clustering with Multiple Kernels (AAAI 2017 · 124 citations)
- 2018 · Word Co-Occurrence Regularized Non-Negative Matrix Tri-Factorization for Text Data Co-Clustering (AAAI 2018 · 42 citations)
- 2019 · Nearest-Neighbour-Induced Isolation Similarity and Its Impact on Density-Based Clustering (AAAI 2019 · 48 citations)
- 2020 · Deep Embedded Non-Redundant Clustering (AAAI 2020 · 18 citations)
- 2021 · Objective-Based Hierarchical Clustering of Deep Embedding Vectors (AAAI 2021 · 18 citations)
- 2022 · DeepDPM: Deep Clustering With an Unknown Number of Clusters (CVPR 2022 · 75 citations)
- 2023 · DivClust: Controlling Diversity in Deep Clustering (CVPR 2023 · 29 citations)
- 2024 · Low-Distortion Clustering with Ordinal and Limited Cardinal Information (AAAI 2024 · 4 citations)
- 2025 · k-HyperEdge Medoids for Clustering Ensemble (AAAI 2025 · 7 citations)
- 2026 · Break the Tie: Learning Cluster-Customized Category Relationships for Categorical Data Clustering (AAAI 2026 · 4 citations)
Earliest papers here
- Fast and accurate spike sorting of high-channel count probes with KiloSort (NeurIPS 2016 · 356 citations)
- Multiple Model Fitting as a Set Coverage Problem (CVPR 2016 · 76 citations)
- Crowdsourced Clustering: Querying Edges vs Triangles (NeurIPS 2016 · 34 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
Iris · NMI (higher is better)
5 papers, 2020–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2020 | 0.889 | A Three-Level Optimization Model for Nonlinearly Separable Clustering (AAAI 2020 · 7 citations) |
| 2024 | 0.901 | SEC: More Accurate Clustering Algorithm via Structural Entropy (AAAI 2024 · 3 citations) |
MNIST · NMI (higher is better)
5 papers, 2019–2023 · not reported since 2023
| Year | Best so far | Set by |
|---|---|---|
| 2019 | 0.339 | The SpectACl of Nonconvex Clustering: A Spectral Approach to Density-Based Clustering (AAAI 2019 · 31 citations) |
| 2020 | 0.663 | A Three-Level Optimization Model for Nonlinearly Separable Clustering (AAAI 2020 · 7 citations) |
| 2022 | 0.962 | Amortized Mixing Coupling Processes for Clustering (NeurIPS 2022 · 0 citations) |
USPS · ACC (higher is better)
5 papers, 2022–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2022 | 0.89 | DeepDPM: Deep Clustering With an Unknown Number of Clusters (CVPR 2022 · 75 citations) |
| 2023 | 0.952 | UEQMS: UMAP Embedded Quick Mean Shift Algorithm for High Dimensional Clustering (AAAI 2023 · 5 citations) |
MNIST · ACC (higher is better)
4 papers, 2022–2023 · not reported since 2023
| Year | Best so far | Set by |
|---|---|---|
| 2022 | 0.98 | DeepDPM: Deep Clustering With an Unknown Number of Clusters (CVPR 2022 · 75 citations) |
wine · NMI (higher is better)
4 papers, 2020–2025 · one report since 2024, not better
| Year | Best so far | Set by |
|---|---|---|
| 2020 | 0.908 | A Three-Level Optimization Model for Nonlinearly Separable Clustering (AAAI 2020 · 7 citations) |
| 2024 | 0.947 | SEC: More Accurate Clustering Algorithm via Structural Entropy (AAAI 2024 · 3 citations) |
What has been tried
130 papers here report 1,060 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 9%, hurt 16%, mixed 7%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use Wasserstein-2 instead of Euclidean distance | Pavement · ARI | 23.11 -> 77.64 | Helped | MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations (ICML 2024 · 1 citation) |
| Use DC tree instead of Cover tree | Boxes, D31, airway, lactate, HAR, letterrec., PenDigits, COIL20, COIL100, cmu_faces, OptDigits, USPS, MNIST · ARI | Helped | Ultrametric Cluster Hierarchies: I Want ‘em All! (NeurIPS 2025 · 0 citations) | |
| Retain the two equality constraints in NLR rather than relaxing them to the NMF formulation | clustering experiments · classification accuracy | Helped | Statistically Optimal $K$-means Clustering via Nonnegative Low-rank Semidefinite Programming (ICLR 2024 · 0 citations) | |
| Use a rank-t Masked Sketch instead of the full covariance matrix | ANN benchmark datasets, larger k · recall | Hurt | Optimistic Query Routing in Clustering-based Approximate Maximum Inner Product Search (NeurIPS 2025) |
What reviewers will expect
Datasets and baselines named in the 11 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- iris · 2 of 11 papers
- wine · 2 of 11 papers
- Digits · 2 of 11 papers
- Pendigits · 2 of 11 papers
- USPS · 2 of 11 papers
Baselines
- k-means · 4 of 11 papers
- single linkage · 2 of 11 papers
- average linkage · 2 of 11 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 49 papers; from OpenAlex and the papers' affiliations).
- University of Illinois, Urbana Champaign · 3 papers
- Aarhus University · 2 papers
- Google · 2 papers
- Meta · 2 papers
- Pontificia Universidade Catolica · 2 papers
- Stanford University · 2 papers
- McMaster University · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Correlation clustering (102 papers)
- Subspace clustering (102 papers)
- Fairness-constrained clustering (19 papers)
- Incomplete multi-view clustering (125 papers)
- Spectral clustering algorithms (43 papers)
Elsewhere in the topic
- Coresets and dynamic clustering (77 papers)
- k-means++ seeding analysis (76 papers)
- Fair clustering approximation (31 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).