Awesome Dimensionality Reduction

Last updated 18.06.2025.

NOTE: This is an open-ended list. If you feel some method is missing or some new one is around, you are more than welcome to contribute 😄

Contents

• Awesome Dimensionality Reduction
  • Contents
  • Surveys
  • Methods
  • Frameworks and codebases
  • Metrics
    • Datasets

Surveys

Year	Authors	Title	Venue	Methods Covered	Publication Link
2002	Fodor, Imola K.	A survey of dimension reduction techniques	Lawrence Livermore National Lab	12 methods	Link
2009	Van Der Maaten, Laurens, Eric O. Postma, and H. Jaap Van Den Herik	Dimensionality reduction: A comparative review	Journal of machine learning research	14 methods	Link
2014	Sorzano, Carlos Oscar Sánchez, Javier Vargas, and A. Pascual Montano	A survey of dimensionality reduction techniques	arXiv preprint	19 methods	Link
2018	Nonato and Aupetit	Multidimensional projection for visual analytics: Linking techniques with distortions, tasks, and layout enrichment	IEEE Transactions on visualization and computer graphics	27 methods	Link
2019	Espadoto, Mateus, et al.	Toward a quantitative survey of dimension reduction techniques	IEEE Transactions on visualization and computer graphics	44 methods	Link
2020	Ghojogh, Benyamin, et al.	Multidimensional scaling, sammon mapping, and isomap: Tutorial and survey	arXiv preprint arXiv:2009.08136	MDS, Sammon Mapping, Isomap	Link
2020	S Ayesha, MK Hanif, R Talib	Overview and comparative study of dimensionality reduction techniques for high dimensional data	Information Fusion	PCA, t-SNE, LDA, AE, UMAP	Link
2021	Wang, Yingfan, et al.	Understanding how dimension reduction tools work: an empirical approach to deciphering t-SNE, UMAP, TriMAP, and PaCMAP for data visualization	Journal of Machine Learning Research	t-SNE, UMAP, TriMAP, PaCMAP	Link
2021	Xia, Jiazhi, et al.	Revisiting dimensionality reduction techniques for visual cluster analysis: An empirical study	IEEE Transactions on visualization and computer graphics	12 methods	Link
2025	Jeon, Hyeon, et al.	Unveiling high-dimensional backstage: A survey for reliable visual analytics with dimensionality reduction	2025 ACM CHI Conference on Human Factors in Computing Systems	48 methods	Link

Methods

Year	Authors	Title	Venue	Method Abbreviation	Publication Link	Code Link
1901	Pearson, Karl	On lines and planes of closest fit to systems of points in space	The London, Edinburgh, and Dublin philosophical magazine and journal of science	PCA	Link	Code
1904	C. Spearman	General intelligence objectively determined and measured	American Journal of Psychology	FA	Link	Code
1933	Hotelling, Harold	Analysis of a complex of statistical variables into principal components	Journal of educational psychology	PCA	Link	Code
1936	R.A. Fisher	The use of multiple measurements in taxonomic problems	Annals of human genetics	LDA	Link	Code
1969	Sammon, John W.	A nonlinear mapping for data structure analysis	IEEE Transactions on Computers	Sammon Mapping	Link	Code
1978	Kruskal, Joseph B., and Myron Wish	Multidimensional scaling	Sage	MDS	Link	Code
1989	Hastie, Trevor, and Werner Stuetzle	Principal curves	Journal of the American Statistical Association		Link	Code
1990	Kohonen, Teuvo	The Self-organizing Map	IEEE Proceedings	SOM	Link	Code
1997	Schölkopf, Bernhard, Alexander Smola, and Klaus-Robert Müller	Kernel principal component analysis	International Conference on Artificial Neural Networks	KPCA	Link	Code
1997	Tenenbaum, Joshua	Mapping a manifold of perceptual observations	Advances in Neural Information Processing Systems		Link
1999	Tipping, Michael E., and Christopher M. Bishop	Probabilistic principal component analysis	Journal of the Royal Statistical Society Series B: Statistical Methodology	PPCA	Link	Code
2000	Hyvärinen, Aapo, and Erkki Oja	Independent component analysis: algorithms and applications	Neural Networks	ICA	Link	Code
2000	Roweis, Sam T., and Lawrence K. Saul.	Nonlinear dimensionality reduction by locally linear embedding	Science	LLE	Link	Code
2000	Tipping, Michael	Sparse kernel principal component analysis	Advances in Neural Information Processing Systems	SKPCA	Link
2000	Tenenbaum, Joshua B., Vin de Silva, and John C. Langford	A global geometric framework for nonlinear dimensionality reduction	Science	Isomap	Link	Code
2002	Brand, Matthew	Charting a manifold	Advances in neural information processing systems		Link
2002	Hinton, Geoffrey E., and Sam Roweis	Stochastic neighbor embedding	Advances in Neural Information Processing Systems	SNE	Link	Code
2002	Bach, Francic, and Jordan, Michael	Kernel independent component analysis	Journal of machine learning research	kICA	Link	Code
2003	Zhang, Zhenyue, and Hongyuan Zha	Nonlinear dimension reduction via local tangent space alignment	International Conference on Intelligent Data Engineering and Automated Learning	LTSA	Link	Code (call with method = "ltsa")
2003	Belkin, Mikhail, and Niyogi, Partha	Laplacian eigenmaps for dimensionality reduction and data representation	IEEE journal of neural computation	LE	Link	Code
2003	Dohono, David, and Grimes, Carrie	Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data	Proceedings of National Academy of Science	HE	Link	Code (call with method = "hessian")
2004	Weinberger, Kilian, Sha, Fei, and Saul, Lawrence	Learning a kernel matrix for nonlinear dimensionality reduction	ICCV	MVU	Link	Code
2006	Yu, Shipeng, et al.	Supervised probabilistic principal component analysis	Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining	SPPCA	Link
2007	Choi, Heeyoul, and Seungjin Choi	Robust kernel isomap	Pattern Recognition	RKI	Link
2007	Hoffmann, Heiko	Kernel PCA for novelty detection	Pattern Recognition	KPCA	Link	Code
2007	Singh, Gurjeet, Facundo Mémoli, and Gunnar E. Carlsson	Topological methods for the analysis of high dimensional data sets and 3d object recognition	Eurographics Symposium on Point-Based Graphics	Mapper	Link	Code
2008	Paulovich, Fernando, et al.	Least Square Projection: A Fast High-Precision Multidimensional Projection Technique and Its Application to Document Mapping	IEEE Transactions on Visualization and Computer Graphics	LSP	Link	Code
2008	Van der Maaten, Laurens, and Geoffrey Hinton	Visualizing data using t-SNE	Journal of Machine Learning Research	t-SNE	Link	Code
2009	Van Der Maaten, Laurens	Learning a parametric embedding by preserving local structure	Artificial Intelligence and Statistics		Link	Code
2010	Venna, Jarkko, et al.	Information retrieval perspective to nonlinear dimensionality reduction for data visualization	Journal of Machine Learning Research		Link
2010	Yang, Zhirong, Chiwei Wang, and Erkki Oja	Multiplicative updates for t-SNE	IEEE International Workshop on Machine Learning for Signal Processing	t-SNE	Link
2011	Joia, Paulo, et al.	Local affine multidimensional projection	IEEE Transactions on visualization and computer graphics	LMAP	Link	Code
2011	Halko, Nathan, Per-Gunnar Martinsson, and Joel A. Tropp.	Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions	SIAM review	Randomized PCA	Link	Code (with method = "randomized")
2012	Van der Maaten, Laurens, and Geoffrey Hinton	Visualizing non-metric similarities in multiple maps	Machine Learning		Link
2013	Amir, El-ad David, et al.	viSNE enables visualization of high dimensional single-cell data and reveals phenotypic heterogeneity of leukemia	Nature Biotechnology	viSNE	Link	Code
2014	Van Der Maaten, Laurens	Accelerating t-SNE using tree-based algorithms	The Journal of Machine Learning Research	t-SNE	Link	Code (with method = "barnes_hut")
2015	Fadel, Samuel, et al.	Loch: A neighborhood-based multidimensional projection technique for high-dimensional sparse spaces	Neurocomputing	LoCH	Link
2016	Wei, Chihang, Junghui Chen, and Zhihuan Song	Developments of two supervised maximum variance unfolding algorithms for process classification	Chemometrics and Intelligent Laboratory Systems	SMVU	Link
2017	Pezzotti, Nicola, et al.	Approximated and User Steerable tSNE for Progressive Visual Analytics	IEEE Transactions on Visualization and Computer Graphics	A-tSNE	Link	Code
2018	Jo, Jaemin, et al.	PANENE: A Progressive Algorithm for Indexing and Querying Approximate k-Nearest Neighbors	IEEE Transactions on Visualization and Computer Graphics	Responsive t-SNE	Link	Code
2018	McInnes, Leland, John Healy, and James Melville	Umap: Uniform manifold approximation and projection for dimension reduction	arXiv preprint arXiv:1802.03426	UMAP	Link	Code
2019	Amid, Ehsan, and Manfred K. Warmuth	TriMap: Large-scale dimensionality reduction using triplets	arXiv preprint arXiv:1910.00204	TriMap	Link	Code
2019	Fu, Cong, et al.	Atsne: Efficient and robust visualization on gpu through hierarchical optimization	ACM SIGKDD International Conference on Knowledge Discovery & Data Mining	AtSNE	Link	Code
2019	Linderman, George C., et al.	Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data	Nature Methods	t-SNE	Link
2020	Ko, Hyung-Kwon, et al.	Progressive Uniform Manifold Approximation and Projection	VGTC/EG Conference on Visualization (EuroVis)	PUMAP	Link	Code
2021	Damrich, Sebastian, and Fred A. Hamprecht	On UMAP's true loss function	Advances in Neural Information Processing Systems	UMAP	Link
2021	Narayan, Ashwin, Bonnie Berger, and Hyunghoon Cho	Assessing single-cell transcriptomic variability through density-preserving data visualization	Nature Biotechnology	DensMap	Link	Code (with densemap = True)
2021	Sainburg, Tim, Leland McInnes, and Timothy Q. Gentner	Parametric UMAP embeddings for representation and semisupervised learning	Neural Computation	parametric UMAP	Link	Code
2022	Damrich, Sebastian, et al.	From $ t $-SNE to UMAP with contrastive learning	arXiv preprint arXiv:2206.01816	t-SNE, UMAP	Link	Code
2022	M. Saquib Sarfraz, Marios Koulakis, Constantin Seibold, Rainer Stiefelhagen	Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction	CVF Conference on Computer Vision and Pattern Recognition	h-NNE	Link	Code
2022	Jeon, Hyeon, et al.	Uniform manifold approximation with two-phase optimization	IEEE Visualization and Visual Analytics	UMATO	Link	Code
2023	Van Assel, Hugues, et al.	Snekhorn: Dimension reduction with symmetric entropic affinities	Advances in Neural Information Processing Systems	Snekhorn	Link	Code
2024	Wang, Yingfan, et al.	Dimension Reduction with Locally Adjusted Graphs	arXiv preprint arXiv:2412.15426		Link	Code
2024	Yang, Deliang, and Hou-Duo Qi	Supervised maximum variance unfolding	Machine Learning	SMVU	Link	Code
2018	Minshuo Chen, Lin Yang, Mengdi Wang, Tuo Zhao	Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization	NeurIPS
2018	Kry Lui, Gavin Weiguang Ding, Ruitong Huang, Robert McCann	Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds	NeurIPS
2018	Mikio Aoi, Jonathan W Pillow	Model-based targeted dimensionality reduction for neuronal population data	NeurIPS
2019	Michela Meister, Tamas Sarlos, David Woodruff	Tight Dimensionality Reduction for Sketching Low Degree Polynomial Kernels	NeurIPS
2019	Yair Bartal, Nova Fandina, Ofer Neiman	Dimensionality reduction: theoretical perspective on practical measures	NeurIPS
2019	Chieh Wu, Jared Miller, Yale Chang, Mario Sznaier, Jennifer Dy	Solving Interpretable Kernel Dimensionality Reduction	NeurIPS
2019	Guan Zhang, Jiaxin Zhang, Jacob Hinkle	Learning nonlinear level sets for dimensionality reduction in function approximation	NeurIPS
2019	Uthaipon Tantipongpipat, Samira Samadi, Mohit Singh, Jamie H Morgenstern, Santosh Vempala	Multi-Criteria Dimensionality Reduction with Applications to Fairness	NeurIPS
2020	Benoît Colange, Jaakko Peltonen, Michael Aupetit, Denys Dutykh, Sylvain Lespinats	Steering Distortions to Preserve Classes and Neighbors in Supervised Dimensionality Reduction	NeurIPS
2020	Dimitris Fotakis, Thanasis Lianeas, Georgios Piliouras, Stratis Skoulakis	Efficient Online Learning of Optimal Rankings: Dimensionality Reduction via Gradient Descent	NeurIPS
2021	Zachary Izzo, Sandeep Silwal, Samson Zhou	Dimensionality Reduction for Wasserstein Barycenter	NeurIPS
2021	Ines Chami, Albert Gu, Dat P Nguyen, Christopher Re	HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections	ICML		http://proceedings.mlr.press/v139/chami21a/chami21a-supp.pdf
2021	Zhili Feng, Praneeth Kacham, David Woodruff	Dimensionality Reduction for the Sum-of-Distances Metric	ICML		http://proceedings.mlr.press/v139/feng21a/feng21a-supp.pdf
2021	Aditi Jha, Michael J. Morais, Jonathan W Pillow	Factor-analytic inverse regression for high-dimension, small-sample dimensionality reduction	ICML		http://proceedings.mlr.press/v139/jha21b/jha21b-supp.pdf
2022	Marius Memmel, Puze Liu, Davide Tateo, Jan Peters	Dimensionality Reduction and Prioritized Exploration for Policy Search	AISTATS		https://proceedings.mlr.press/v151/memmel22a/memmel22a.pdf
2022	Saquib Sarfraz, Marios Koulakis, Constantin Seibold, Rainer Stiefelhagen	Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction	CVPR
2022	Yunhui Guo, Haoran Guo, Stella X. Yu	CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data	CVPR
2022	Xiran Fan, Chun-Hao Yang, Baba C. Vemuri	Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Design	CVPR
2022	Alex R. Dytso, Mario Goldenbaum, H. Vincent Poor, Shlomo Shamai	A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence	AISTATS		https://proceedings.mlr.press/v151/dytso22a/dytso22a.pdf
2023	Guillaume Huguet, Alexander Tong, Edward De Brouwer, Yanlei Zhang, Guy Wolf, Ian Adelstein, Smita Krishnaswamy	A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction	NeurIPS
2023	Xinyu Luo, Christopher Musco, Cas Widdershoven	Dimensionality Reduction for General KDE Mode Finding	ICML		https://proceedings.mlr.press/v202/luo23c/luo23c.pdf
2024	Ziwei Li, Xiaoqi Wang, Hong-You Chen, Han Wei Shen, Wei-Lun (Harry) Chao	FedNE: Surrogate-Assisted Federated Neighbor Embedding for Dimensionality Reduction	NeurIPS
2024	Mikael Møller Høgsgaard, Lior Kamma, Kasper Green Larsen, Jelani Nelson, Chris Schwiegelshohn	Sparse Dimensionality Reduction Revisited	ICML		https://raw.githubusercontent.com/mlresearch/v235/main/assets/hogsgaard24a/hogsgaard24a.pdf
2024	Prarabdh Shukla, Gagan Raj Gupta, Kunal Dutta	DiffRed: Dimensionality reduction guided by stable rank	AISTATS		https://proceedings.mlr.press/v238/shukla24a/shukla24a.pdf
2024	Charbel Sakr, Brucek Khailany	ESPACE: Dimensionality Reduction of Activations for Model Compression	NeurIPS
2024	Haiyang Huang, Yingfan Wang, Cynthia Rudin	Navigating the Effect of Parametrization for Dimensionality Reduction	NeurIPS
2024	Haiyang Huang, Yingfan Wang, Cynthia Rudin	Navigating the Effect of Parametrization for Dimensionality Reduction	NeurIPS	ParamRepulsor	Link	Code
2024	Wang, Yingfan, et al.	Dimension Reduction with Locally Adjusted Graphs	arXiv preprint arXiv:2412.15426	LocalMAP	Link	Code
2025	Thomas Dagès, Simon Weber, Ya-Wei Eileen Lin, Ronen Talmon, Daniel Cremers, Michael Lindenbaum, Alfred M. Bruckstein, Ron Kimmel	Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding	CVPR

Frameworks and codebases

Name	Type	Language	Methods	Documentation	Code
scikit-learn	Method	python	PCA, t-SNE, Kernel PCA, FA, ICA, Isomap, LLE, LTSA, MDS and more	Docs	Code
umap-learn	Method	python	UMAP, Parametric UMAP, DensMap	Docs	Code
matlab toolbox for dim reduction	Method	matlab	PCA, SNE, t-SNE, FA, MDS, Sammon mapping, LDA, Isomap, LLE, LTSA, Kernel PCA, and more	Docs	Code
scikit-tda	Method	python	Mapper, Eilenberg-MacLane Coordinates	Docs	Code
sammon	Method	python	Sammon mapping	Docs	Code
trimap	Method	python	TriMap	Docs	Code
hnne	Method	python	h-NNE	Docs	Code
zadu	Metric	python	19 Evaluation metrics	Docs	Code
tf-projection-qm	Metric	python	17 Evaluation metrics	Docs	Code

Metrics

Name	Optimality	Range	Optimum	Source
Average Local Error	↓	[0, +∞)	0	Martins et al., 2014
Trustworthiness & Continuity	↑	[0.5, 1]	1	Venna & Kaski, 2006
Mean Relative Rank Errors	↑	[0, 1]	1	Lee & Verleysen, 2009
Local Continuity Meta-Criteria	↑	[0, 1]	1	Chen & Buja, 2009
Neighborhood Hit	↑	[0, 1]	1	Paulovich et al., 2011
Neighbor Dissimilarity	↓	[0, +∞)	0	Fujiwara et al., 2023
Class-Aware Trustworthiness & Continuity	↑	[0.5, 1]	1	Colange et al., 2020
Procrustes Measure	↓	[0, +∞)	0	Goldberg & Ritov, 2009
Steadiness & Cohesiveness	↑	[0, 1]	1	Jeon et al., 2021
Distance Consistency	↑	[0.5, 1]	0.5	Sips et al., 2009
Label Trustworthiness & Continuity	↑	[0, 1]	1	Jeon et al., 2023
Stress	↓	[0, +∞)	0	Kruskal, 1964
Non-metric Stress	↓	[0, +∞)	0	Kruskal, 1964
Scale-normalized Stress	↓	[0, +∞)	0	Smelser et al., 2024
Kullback-Leibler Divergence	↓	[0, +∞)	0	Hinton & Roweis, 2002
Distance-to-Measure	↓	[0, +∞)	0	Chazal et al., 2011
Topographic Product	↓	(-∞, +∞)	0	Bauer and Pawelzik, 1992
Pearson's Correlation Coefficient	↑	[-1, 1]	1	Geng et al., 2005
Spearman's Rank Correlation Coefficient	↑	[-1, 1]	1	Sidney, 1957
Jaccard	↑	[0, 1]	1	Jaccard, 2001
Shepard Goodness	↑	[-1, 1]	1	Siegel and Castellan, 1988
Procrustes Statistic	↓	[0, +∞)	0	Goldberg and Ritov

Datasets

Year	Authors	Title	Venue	Name	Data type	Publication Link	Dataset Link
2017	Han Xiao, Kashif Rasul, and Roland Vollgraf	Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms	arXiv Preprint	FMNIST	Images	Link	Dataset (or from torchvision)
2014	Pierre Baldi, Peter Sadowski, and Daniel Whiteson	Searching for exotic particles in high-energy physics with deep learning	Nature Communications	HIGGS	Tabular - Physics features	Link	Dataset
2013	Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean	Distributed representations of words and phrases and their compositionality	Advances in Neural Information Processing Systems	Google News	Word embeddings	Link	Dataset
2013	Martin Bäuml, Makarand Tapaswi, and Rainer Stiefelhagen	Semi-supervised Learning with Constraints for Person Identification in Multimedia Data	CVPR	BBT	Images	Link	—
2013	Martin Bäuml, Makarand Tapaswi, and Rainer Stiefelhagen	Semi-supervised Learning with Constraints for Person Identification in Multimedia Data	CVPR	Buffy	Images	Link	—
2009	Alex Krizhevsky, Geoffrey Hinton, et al.	Learning multiple layers of features from tiny image	Technical Report, University of Toronto	CIFAR-10	Images	Link	Dataset (or from torchvision)
2009	Alex Krizhevsky, Geoffrey Hinton, et al.	Learning multiple layers of features from tiny image	Technical Report, University of Toronto	CIFAR-100	Images	Link	Dataset (or from torchvision)
2009	Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei.	Imagenet: A large-scale hierarchical image database	IEEE Conference on Computer Vision and Pattern Recognition	ImageNet	Images	Link	Dataset
1998	Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner	Gradient-based learning applied to document recognition	Proc. IEEE	MNIST	Images	Link	Dataset
1996	Sameer A Nene, Shree K Nayar, Hiroshi Murase, et al.	Columbia object image library	Technical Report, Department of Computer Science, Columbia University	COIL-20	Images	Link	Dataset