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Parametric UMAP embeddings for representation and semi-supervised learning

T0 review · 3 major / 6 minor · reviewed 2026-08-27 · deepseek-v4-flash

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Pith's one-line read Parametric UMAP trains a neural network to minimize UMAP's structure-preserving loss, matching the original's embedding quality while adding instant inference, tunable global structure, and semi-supervised gains.

desk verdict A genuinely useful parametric extension of UMAP with broad experiments, but the comparability claim is only shown on training data, so the advertised online-embedding benefit is unverified. read the letter →

arxiv 2009.12981 v4 pith:XHBPQWHN submitted 2020-09-27 cs.LG cs.CGq-bio.QMstat.ML

Tim Sainburg , Leland McInnes , Timothy Q Gentner This is my paper · ORCID
classification cs.LGcs.CGq-bio.QMstat.ML
keywords dimensionalityreductionmanifoldlearningparametricembeddingrepresentationsemi-supervisedstructure-preservinglossautoencoderregularizationdatavisualization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

UMAP finds low-dimensional embeddings by first building a graph of local relationships in a dataset and then moving embedding coordinates until the graph is well preserved. This paper makes that second step parametric: a neural network is trained to map data points into the embedding by minimizing the same UMAP cost, with negative sampling making the loss cheap enough to estimate from small minibatches. The paper's central claim, tested on MNIST, Fashion-MNIST, CIFAR10, mouse retina transcriptomes, and birdsong, is that this trained mapping produces embeddings of quality comparable to the original non-parametric UMAP while letting new data be embedded in a single forward pass. That learned mapping is then reused as a building block: a regularizer for autoencoder latents, a dial for trading local against global structure, and a structure-preserving loss for semi-supervised classifiers.

What carries the argument

The central object is a parametric re-formulation of UMAP's cross-entropy cost, minimized over neural network weights instead of embedding coordinates. The cost compares the fuzzy-graph probabilities $p_{ij}$ with the unnormalized embedding probabilities $q_{ij} = (1 + a\|z_i - z_j\|^{2b})^{-1}$, and its key property is that negative sampling turns the repulsive half of the loss into a per-edge estimate, so backpropagation can train on minibatches without ever normalizing over the whole dataset. That single substitution carries the argument: it makes UMAP loss a drop-in regularizer for any neural network objective, which the paper then demonstrates through the autoencoder, global-structure, and semi-supervised variants.

What would settle it

Train Parametric UMAP and non-parametric UMAP on the same fuzzy graph for a dataset whose class structure is invisible to Euclidean distance (CIFAR10 at 64 embedding dimensions is the paper's own example), let both converge, and compare trustworthiness and RNX area-under-the-curve on a held-out set; if the parametric embeddings fall measurably below the non-parametric ones, or if the parametric training loss plateaus well above the non-parametric minimum, the comparable-quality claim fails in that regime. A complementary check of the learned mapping's generality: embed held-out data and compare the nearest-neighbor graph of those embeddings with the UMAP graph computed directly on the held-out points in data space.

Watch

Extended reading notes

Core claim

Parametric UMAP replaces UMAP's second step — stochastic gradient descent on embedding coordinates — with descent on the weights of an encoder network. The objective is the same cross-entropy between the graph probabilities $p_{ij}$ of UMAP's fuzzy simplicial complex, a probabilistically weighted neighborhood graph, and the embedding-space probabilities $q_{ij} = (1 + a \|z_i - z_j\|^{2b})^{-1}$, namely $C = \sum_{i \neq j} p_{ij}\log(p_{ij}/q_{ij}) + (1 - p_{ij})\log((1 - p_{ij})/(1 - q_{ij}))$; negative sampling supplies the repulsive term so the gradient can be formed from minibatches as small as a single edge. On trustworthiness, multi-scale neighbor preservation, silhouette score, and clustering agreement, the parametric embeddings are comparable to non-parametric UMAP, while embedding held-out data is orders of magnitude faster and reconstruction becomes available when a decoder is added. Because the training signal is the graph rather than a fixed target embedding, the authors argue, the network can be jointly constrained by additional losses — reconstruction for autoencoding, Pearson correlation of pairwise distances for global structure, classification for semi-supervised learning — and the UMAP loss in turn regularizes those objectives.

Load-bearing premise

Everything rests on one premise: UMAP's cross-entropy loss, minimized over neural network weights with minibatch negative sampling, reliably drives the network to embeddings as structure-preserving as those obtained by optimizing the same loss directly over coordinates — the paper gives empirical evidence on five datasets but no argument that this optimization succeeds for arbitrary data distributions or architectures.

Editorial extensions

If this is right

  • Fast online inference: once trained, the network embeds new or held-out data with a single forward pass, several orders of magnitude faster than non-parametric UMAP, making near-real-time embedding practical for brain-machine interfaces, bioacoustics, and behavioral tracking.
  • UMAP loss becomes a generic regularizer: any neural network trained with a supervised or reconstruction objective can be jointly trained on unlabeled data to give its latent space a graph-preserving structure.
  • Global and local structure can be traded off continuously by weighting a Pearson-correlation term on pairwise distances, capturing more global relationship than UMAP or t-SNE while retaining most local quality.
  • For datasets whose data-space distances carry category-relevant structure, semi-supervised classifiers trained with an auxiliary UMAP loss beat supervised baselines, with the largest gains when labeled examples are scarce.
  • Combining the UMAP loss with augmented data trains a classifier to be invariant to augmentation while preserving the UMAP graph, improving accuracy even on less-structured datasets like CIFAR10 when the graph is computed over learned latent activations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same substitution should transfer to other graph-embedding objectives that already rely on negative sampling (for example LargeVis-style losses), turning each into a trainable regularizer with the same minibatch-friendly behavior; the paper only demonstrates the trick for UMAP's cross-entropy.
  • The paper diagnoses CIFAR10's poor semi-supervised results as a distance-metric problem rather than a flaw in the parametric loss, so the recipe should extend to visually unstructured domains once a category-relevant metric (a supervised or Fisher-style distance) replaces Euclidean distance in the UMAP graph; the discussion points at this direction but does not test it.
  • Because the embedding is a continuous function of the input, Parametric UMAP should support smooth latent-space interpolation and manipulation on time-series and behavioral data, not just the facial-feature algebra demonstrated on CelebAMask-HQ.
  • After training, embedding time no longer grows with dataset size, so applications with tight latency budgets can accept a slower training phase for instant deployment; the paper's timing measurements show the trained network embeds new data only slightly slower than PCA.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes Parametric UMAP, a variant of UMAP in which the second optimization step is replaced by training a neural network encoder that maps data points to embeddings by minimizing the UMAP cross-entropy loss with minibatch training and negative sampling. The authors claim that Parametric UMAP produces embeddings of comparable quality to non-parametric UMAP while providing a learned parametric mapping that enables fast online embedding of new data. They further explore applications of the UMAP loss as a regularizer: combining it with autoencoders, adding a global structure preservation term, and using it for semi-supervised learning. The empirical evaluation spans five datasets (MNIST, FMNIST, CIFAR10, mouse retina transcriptomes, Cassin's vireo song) and compares against a wide range of non-parametric and parametric baselines on trustworthiness, AUC of RNX, KNN classification, silhouette score, and clustering NMI, plus reconstruction quality, speed, and SSL accuracy.

Significance. If the central claim holds, Parametric UMAP is a practically valuable contribution to parametric dimensionality reduction: it brings the favorable properties of UMAP's negative-sampling-based optimization into the deep-learning paradigm, enabling fast inference, minibatch training, and integration with auxiliary losses. The paper is unusually thorough in its breadth of comparisons and datasets, and it ships open-source code and a Colab walkthrough, which are clear strengths. The SSL experiments also include an honest negative control: training on the network's own learned latent graph provides little or no improvement without augmentation, an informative result that the authors report straightforwardly. The main unaddressed gap is the lack of any evaluation of embedding quality on held-out data, which is the load-bearing point for the paper's central practical claim.

major comments (3)
  1. [Section 5.1 and Appendix 8.3 (Fig. 16 caption)] The central claim that Parametric UMAP produces embeddings of similar quality to non-parametric UMAP is only established on training-set projections. The caption for Fig. 16 explicitly states that trustworthiness is computed over 10,000 samples of the training dataset, and the other metrics (AUC RNX, silhouette, NMI) are not described as held-out. Since the paper's stated benefit of the parametric form is a learned mapping for fast online embeddings of new data (abstract; Section 5.2), the paper should evaluate embedding quality on a held-out test set, for example by embedding the test data and computing trustworthiness or KNN accuracy with respect to the training data or against the test labels. Without such an experiment, the practical claim that new data can be embedded at comparable quality is unverified.
  2. [Section 5.2 (Fig. 7)] The speed comparison on the held-out testing dataset measures only wall-clock time (median over 10 runs) and does not report any quality metric for those test-set embeddings. Time alone is insufficient to support the 'fast online embeddings' benefit because a network that simply memorized training projections could be fast but produce poor embeddings for new data. Please add at least one embedding-quality metric (e.g., trustworthiness or KNN accuracy) computed on the same held-out embeddings used in Fig. 7.
  3. [Tables 2-7] All embedding-quality metrics are reported as single numbers without variance, confidence intervals, or significance tests. For the 'comparable quality' claim, where differences between UMAP variants are often small (e.g., Table 2 trustworthiness differs by ~0.01 between UMAP-learn, UMAP-TF, and Parametric UMAP on MNIST 2D), the absence of any uncertainty measure makes it difficult to assess whether the observed differences are meaningful. Please report mean and standard deviation over multiple runs (or a paired significance test) for the key comparisons that underpin the central claim.
minor comments (6)
  1. [Section 2.1] In the sentence 'such that one standard deviation of the Gaussian kernel fits a a set number of nearest-neighbors in X', there is a duplicated article 'a a' and a stray hyphen; please correct to 'fits a set number of nearest neighbors'.
  2. [Figure 2 caption] The caption reads 'Varients of UMAP used in this paper'; 'Varients' is misspelled and should be 'Variants'.
  3. [Table 3 header] The header 'AUCRM X' appears to be a typo for 'AUC RNX'; please fix.
  4. [Appendix 8.3] The subsections are numbered 8.1 (Trustworthiness), 8.2 (KNN Classifier), 8.3 (Silhouette score), and 8.4 (Clustering), but these appear inside Section 8.3 of the appendix; renumber them as 8.3.1, 8.3.2, 8.3.3, and 8.3.4 for consistency.
  5. [Figure 5] The x-axis label shows 'CIFAR100' but the dataset used throughout is CIFAR10; please correct.
  6. [Section 2.4] The sentence 'making it suitable for minibatch training needed for memory-expensive neural networks trained on the full graph over large datasets as well as online learning' is unclear; please rephrase to separate the minibatch-training benefit for large graphs from the online-learning benefit.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; Parametric UMAP is an empirical extension benchmarked against external metrics, and the SSL section includes honest negative controls.

full rationale

Parametric UMAP reuses the UMAP graph construction and cross-entropy loss (Eq. 8) but optimizes over neural network weights instead of embedding coordinates directly. The central claim of comparable embedding quality (Section 5.1) is tested against external, non-loss metrics: trustworthiness, AUC RNX, KNN accuracy, silhouette score, and NMI. These metrics are not part of the UMAP loss, so the comparison is not forced by construction. The only parameters fitted are the network weights, optimized for the same objective that non-parametric UMAP optimizes; no fitted parameter is renamed as a prediction. The self-citation of UMAP (McInnes, Healy, & Melville, 2018, coauthored by L. McInnes) defines the baseline algorithm being extended and is not used to justify a controversial or unverified premise; it is normal foundational citation. The semi-supervised learning section provides genuine negative controls, explicitly reporting that UMAP loss over Euclidean distances impairs CIFAR10 accuracy and that the learned-metric UMAP without augmentation 'confers little to no improvement'. These null results undermine any selective-reporting or forced-conclusion concern. The skeptic's point about generalization of the learned encoder to held-out data is an evidentiary gap, not a circular derivation: the paper measures held-out reconstruction error (Table 8) and SSL accuracy (Table 9), but not held-out embedding-quality metrics like trustworthiness. That is a limitation in experimental coverage, not a circularity in the derivation chain. Overall, the paper's claims are empirical and self-contained against external benchmarks; no step reduces by definition to its own inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method inherits UMAP's graph construction and loss, with no new theoretical entities. Main free parameters are UMAP hyperparameters plus additional loss weights; the central new assumption is that the graph loss optimizes well over network weights.

free parameters (4)
  • n_neighbors (k) = 15 (default)
    Sets local neighborhood size in UMAP graph construction; inherited from UMAP and not tuned in this paper.
  • min_dist (and a,b embedding kernel parameters) = UMAP defaults
    Controls the density of embedding points via Eq. 6; chosen by hand in UMAP and adopted as-is.
  • Global structure loss weight (CPearson) = Varied across 0, small, medium, large in Fig 8
    Hand-selected to demonstrate the local-global tradeoff; no automatic selection criterion is given.
  • UMAP/SSL loss weight in semi-supervised training = Not stated in main text
    Weight balancing classifier and UMAP losses in Fig 2D; presumably specified in code, not enumerated in the paper.
assumptions (4)
  • domain assumption Data lie on a manifold on which UMAP's uniform distribution assumption and local metric scaling hold.
    UMAP graph construction (Eqs. 2, 3) inherited from McInnes et al.; if this fails, the graph itself misrepresents structure.
  • domain assumption Negative sampling over non-edges approximates the full cross-entropy repulsive term.
    Section 2.3 relies on this word2vec-style shortcut to make minibatch training valid; inherited from UMAP.
  • ad hoc to paper Minimizing the UMAP cross-entropy by SGD over neural network weights reaches embeddings comparable to direct coordinate optimization.
    Central training assumption of Parametric UMAP (Section 2.4); only empirically demonstrated, no convergence proof.
  • domain assumption The UMAP graph computed over input distances captures task-relevant category structure for semi-supervised learning.
    Load-bearing for the SSL experiments (Section 5.5); the paper itself shows it fails for CIFAR10 with Euclidean distances.

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Cite this review

Pith. "Pith review of Parametric UMAP embeddings for representation and semi-supervised learning." pith.science (2026). https://pith.science/paper/XHBPQWHN

@misc{pith2026200912981,
  author       = {Pith},
  title        = {Pith review of: Parametric UMAP embeddings for representation and semi-supervised learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHBPQWHN}},
  note         = {Machine review of arXiv:2009.12981}
}
read the original abstract

UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a graphical representation of a dataset (fuzzy simplicial complex), and (2) Through stochastic gradient descent, optimize a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that Parametric UMAP performs comparably to its non-parametric counterpart while conferring the benefit of a learned parametric mapping (e.g. fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semi-supervised learning by capturing structure in unlabeled data. Google Colab walkthrough: https://colab.research.google.com/drive/1WkXVZ5pnMrm17m0YgmtoNjM_XHdnE5Vp?usp=sharing

Figures

Figures reproduced from arXiv: 2009.12981 by the authors.

Figure 1
Figure 1. Overview of UMAP (A → B) and Parametric UMAP (A → C). 2 Parametric and non-parametric UMAP UMAP and t-SNE have the same goal: Given a D-dimensional data set X ∈ R D, produce a d dimensional embedding Z ∈ R d such that points that are close together in X (e.g. xi and xj ) are also close together in Z (zi and zj ). Both algorithms are comprised of the same two broad steps: first construct a graph of local relationship… view at source ↗
Figure 2
Figure 2. Varients of UMAP used in this paper. Solid lines represent neural networks. [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. An example of semi-supervised learning with UMAP on the moons dataset. [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (19 more)
Figure 4
Figure 4. Figure 4: Comparison of projections from multiple datasets using UMAP, UMAP in [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Embedding metrics for 2D projections. Full results are given in the Appendix. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Training times comparison between UMAP and Parametric UMAP. All results [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: Comparison of embedding speeds using parametric UMAP and other embed [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: Global loss applied to Parametric UMAP embeddings with different weights. [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]
Figure 9
Figure 9. Figure 9: Comparison of pairwise global and local relationship preservation across [PITH_FULL_IMAGE:figures/full_fig_p025_9.png]
Figure 10
Figure 10. Figure 10: Reconstruction accuracy measured as mean squared error (MSE). MSE is [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]
Figure 11
Figure 11. Figure 11: Reconstruction and interpolation. (A) Parametric UMAP reconstructions [PITH_FULL_IMAGE:figures/full_fig_p028_11.png]
Figure 12
Figure 12. Figure 12: Baseline classifier with an additional UMAP loss with different numbers [PITH_FULL_IMAGE:figures/full_fig_p030_12.png]
Figure 13
Figure 13. Figure 13: Comparison of baseline classifier, augmentation, and augmentation with an [PITH_FULL_IMAGE:figures/full_fig_p031_13.png]
Figure 14
Figure 14. Figure 14: Non-parametric UMAP projections of activations in the last layer of a trained [PITH_FULL_IMAGE:figures/full_fig_p032_14.png]
Figure 15
Figure 15. Figure 15: (top) Cross entropy loss for one-hidden-layer instance of Parametric UMAP [PITH_FULL_IMAGE:figures/full_fig_p035_15.png]
Figure 16
Figure 16. Figure 16: Trustworthiness scores for five datasets using 2- and 64-dimensional pro [PITH_FULL_IMAGE:figures/full_fig_p050_16.png]
Figure 17
Figure 17. Figure 17: AUC RNX results on latent projections. MNIST FMNIST Retina Cassin's CIFAR10 0 20 40 60 80 100 Accuracy 2 Dimensions MNIST FMNIST Retina Cassin's CIFAR10 64 Dimensions TSNE P. TSNE UMAP (UMAP-learn) P. UMAP UMAP AE SCVIS IVIS PHATE VAE AE PCA [PITH_FULL_IMAGE:figures/…
Figure 18
Figure 18. Figure 18: Generalization errors of KNN classifiers (k=1) on latent projections. [PITH_FULL_IMAGE:figures/full_fig_p050_18.png]
Figure 19
Figure 19. Figure 19: Generalization errors of KNN classifiers (k=5) on latent projections. [PITH_FULL_IMAGE:figures/full_fig_p050_19.png]
Figure 20
Figure 20. Figure 20: Silhouette scores for five datasets using 2- and 64-dimensional projections [PITH_FULL_IMAGE:figures/full_fig_p051_20.png]
Figure 21
Figure 21. Figure 21: Clustering results. Comparisons are based upon the Normalized Mutual [PITH_FULL_IMAGE:figures/full_fig_p051_21.png]
Figure 22
Figure 22. Figure 22: Reconstruction speed. Reconstructions are performed on the same machine [PITH_FULL_IMAGE:figures/full_fig_p051_22.png]

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Reference graph

Works this paper leans on

61 extracted references · 60 canonical work pages · cited by 3 Pith papers

  1. [1]

    TriMap: Large-scale Dimensionality Reduction Using Triplets

    amid2019trimap APACrefauthors Amid, E. \ Warmuth, M K. APACrefauthors \ 2019 . TriMap: Large-scale dimensionality reduction using triplets Trimap: Large-scale dimensionality reduction using triplets . arXiv preprint arXiv:1910.00204

    work page Pith review arXiv 2019

  2. [2]

    , McInnes, L

    becht2019dimensionality APACrefauthors Becht, E. , McInnes, L. , Healy, J. , Dutertre, C A. , Kwok, I W. , Ng, L G. Newell, E W. APACrefauthors \ 2019 . Dimensionality reduction for visualizing single-cell data using UMAP Dimensionality reduction for visualizing single-cell data using umap . Nature biotechnology 37 1 38--44

    work page 2019

  3. [3]

    , Carlini, N

    berthelot2019remixmatch APACrefauthors Berthelot, D. , Carlini, N. , Cubuk, E D. , Kurakin, A. , Sohn, K. , Zhang, H. \ Raffel, C. APACrefauthors \ 2020 . ReMixMatch: Semi-Supervised Learning with Distribution Matching and Augmentation Anchoring Remixmatch: Semi-supervised learning with distribution matching and augmentation anchoring . International Conf...

    work page 2020

  4. [4]

    \ De Bivort, B

    brown2018ethology APACrefauthors Brown, A E. \ De Bivort, B. APACrefauthors \ 2018 . Ethology as a physical science Ethology as a physical science . Nature Physics 14 7 653--657

    work page 2018

  5. [5]

    , Biehl, M

    bunte2012general APACrefauthors Bunte, K. , Biehl, M. \ Hammer, B. APACrefauthors \ 2012 . A general framework for dimensionality-reducing data visualization mapping A general framework for dimensionality-reducing data visualization mapping . Neural Computation 24 3 771--804

    work page 2012

  6. [6]

    , Armstrong, Z

    carter2019activation APACrefauthors Carter, S. , Armstrong, Z. , Schubert, L. , Johnson, I. \ Olah, C. APACrefauthors \ 2019 . Activation atlas Activation atlas . Distill 4 3 e15

    work page 2019

  7. [7]

    \ Tenenbaum, J B

    de2003global APACrefauthors De Silva, V. \ Tenenbaum, J B. APACrefauthors \ 2003 . Global versus local methods in nonlinear dimensionality reduction Global versus local methods in nonlinear dimensionality reduction . Advances in neural information processing systems 721--728

    work page 2003

  8. [8]

    , Condon, A

    ding2018interpretable APACrefauthors Ding, J. , Condon, A. \ Shah, S P. APACrefauthors \ 2018 . Interpretable dimensionality reduction of single cell transcriptome data with deep generative models Interpretable dimensionality reduction of single cell transcriptome data with deep generative models . Nature communications 9 1 1--13

    work page 2018

Show all 61 references
  1. [9]

    \ Regev, A

    ding2019deep APACrefauthors Ding, J. \ Regev, A. APACrefauthors \ 2019 . Deep generative model embedding of single-cell RNA-Seq profiles on hyperspheres and hyperbolic spaces Deep generative model embedding of single-cell rna-seq profiles on hyperspheres and hyperbolic spaces ...

    2019

  2. [10]

    , Moses, C

    dong2011efficient APACrefauthors Dong, W. , Moses, C. \ Li, K. APACrefauthors \ 2011 . Efficient k-nearest neighbor graph construction for generic similarity measures Efficient k-nearest neighbor graph construction for generic similarity measures . Proceedings of the 20th inte...

    2011

  3. [11]

    APACrefauthors \ 2019

    umapzoo APACrefauthors Duhaime, D. APACrefauthors \ 2019 . UMAP Zoo. Umap zoo. https://github.com/duhaime/umap-zoo . GitHub

    2019

  4. [12]

    , Morin, S

    duque2020extendable APACrefauthors Duque, A F. , Morin, S. , Wolf, G. \ Moon, K R. APACrefauthors \ 2020 . Extendable and invertible manifold learning with geometry regularized autoencoders Extendable and invertible manifold learning with geometry regularized autoencoders . ar...

    2020 arXiv

  5. [13]

    , Lueks, W

    gisbrecht2012out APACrefauthors Gisbrecht, A. , Lueks, W. , Mokbel, B. \ Hammer, B. APACrefauthors \ 2012 . Out-of-sample kernel extensions for nonparametric dimensionality reduction. Out-of-sample kernel extensions for nonparametric dimensionality reduction. ESANN. Esann

    2012

  6. [14]

    , Schulz, A

    gisbrecht2015parametric APACrefauthors Gisbrecht, A. , Schulz, A. \ Hammer, B. APACrefauthors \ 2015 . Parametric nonlinear dimensionality reduction using kernel t-SNE Parametric nonlinear dimensionality reduction using kernel t-sne . Neurocomputing 147 71--82

    2015

  7. [15]

    \ Couzin, I D

    graving2020vae APACrefauthors Graving, J M. \ Couzin, I D. APACrefauthors \ 2020 . VAE-SNE: a deep generative model for simultaneous dimensionality reduction and clustering Vae-sne: a deep generative model for simultaneous dimensionality reduction and clustering . BioRxiv

    2020

  8. [16]

    APACrefauthors \ 2016 1

    hedley2016complexity APACrefauthors Hedley, R W. APACrefauthors \ 2016 1 . Complexity, predictability and time homogeneity of syntax in the songs of Cassin’s vireo (Vireo cassinii) Complexity, predictability and time homogeneity of syntax in the songs of cassin’s vireo (vireo ...

    2016

  9. [17]

    APACrefauthors \ 2016 2

    hedley2016composition APACrefauthors Hedley, R W. APACrefauthors \ 2016 2 . Composition and sequential organization of song repertoires in Cassin’s Vireo (Vireo cassinii) Composition and sequential organization of song repertoires in cassin’s vireo (vireo cassinii) . Journal o...

    2016

  10. [18]

    \ Salakhutdinov, R R

    hinton2006reducing APACrefauthors Hinton, G E. \ Salakhutdinov, R R. APACrefauthors \ 2006 . Reducing the dimensionality of data with neural networks Reducing the dimensionality of data with neural networks . science 313 5786 504--507

    2006

  11. [19]

    , Kwitt, R

    hofer2019connectivity APACrefauthors Hofer, C. , Kwitt, R. , Niethammer, M. \ Dixit, M. APACrefauthors \ 2019 . Connectivity-optimized representation learning via persistent homology Connectivity-optimized representation learning via persistent homology . International Confere...

    2019

  12. [20]

    , Liu, M Y

    huang2018multimodal APACrefauthors Huang, X. , Liu, M Y. , Belongie, S. \ Kautz, J. APACrefauthors \ 2018 . Multimodal unsupervised image-to-image translation Multimodal unsupervised image-to-image translation . Proceedings of the European Conference on Computer Vision (ECCV) ...

    2018

  13. [21]

    , Sun, L

    jia2015laplacian APACrefauthors Jia, K. , Sun, L. , Gao, S. , Song, Z. \ Shi, B E. APACrefauthors \ 2015 . Laplacian auto-encoders: An explicit learning of nonlinear data manifold Laplacian auto-encoders: An explicit learning of nonlinear data manifold . Neurocomputing 160 250--260

    2015

  14. [22]

    \ Welling, M

    kingma2013auto APACrefauthors Kingma, D P. \ Welling, M. APACrefauthors \ 2013 . Auto-encoding variational bayes Auto-encoding variational bayes . arXiv preprint arXiv:1312.6114

    2013 arXiv

  15. [23]

    APACrefauthors \ 2020

    fitsne APACrefauthors KlugerLab. APACrefauthors \ 2020 . Open Source Survey. Open source survey. https://github.com/KlugerLab/FIt-SNE, commit = 4f57d6a0e4c030202a07a60bc1bb1ed1544bf679 . GitHub

    2020

  16. [24]

    \ Linderman, G C

    kobak2021initialization APACrefauthors Kobak, D. \ Linderman, G C. APACrefauthors \ 2021 . Initialization is critical for preserving global data structure in both t-SNE and UMAP Initialization is critical for preserving global data structure in both t-sne and umap . Nature Bio...

    2021

  17. [25]

    APACrefauthors \ 2009

    Krizhevsky09learningmultiple APACrefauthors Krizhevsky, A. APACrefauthors \ 2009 . Learning Multiple Layers of Features from Tiny Images Learning multiple layers of features from tiny images . Master's thesis, University of Toronto

    2009

  18. [26]

    APACrefauthors \ 1998

    lecun1998mnist APACrefauthors LeCun, Y. APACrefauthors \ 1998 . The MNIST database of handwritten digits The mnist database of handwritten digits . http://yann. lecun. com/exdb/mnist/

    1998

  19. [27]

    , Liu, Z

    CelebAMask-HQ APACrefauthors Lee, C H. , Liu, Z. , Wu, L. \ Luo, P. APACrefauthors \ 2020 . MaskGAN: Towards Diverse and Interactive Facial Image Manipulation Maskgan: Towards diverse and interactive facial image manipulation . IEEE Conference on Computer Vision and Pattern Re...

    2020

  20. [28]

    , Peluffo-Ord \'o \ n ez, D H

    lee2015multi APACrefauthors Lee, J A. , Peluffo-Ord \'o \ n ez, D H. \ Verleysen, M. APACrefauthors \ 2015 . Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure Multi-scale similarities in stochas...

    2015

  21. [29]

    , Renard, E

    lee2013type APACrefauthors Lee, J A. , Renard, E. , Bernard, G. , Dupont, P. \ Verleysen, M. APACrefauthors \ 2013 . Type 1 and 2 mixtures of Kullback--Leibler divergences as cost functions in dimensionality reduction based on similarity preservation Type 1 and 2 mixtures of k...

    2013

  22. [30]

    \ Verleysen, M

    lee2009quality APACrefauthors Lee, J A. \ Verleysen, M. APACrefauthors \ 2009 . Quality assessment of dimensionality reduction: Rank-based criteria Quality assessment of dimensionality reduction: Rank-based criteria . Neurocomputing 72 7-9 1431--1443

    2009

  23. [31]

    , Rachh, M

    linderman2017efficient APACrefauthors Linderman, G C. , Rachh, M. , Hoskins, J G. , Steinerberger, S. \ Kluger, Y. APACrefauthors \ 2017 . Efficient algorithms for t-distributed stochastic neighborhood embedding Efficient algorithms for t-distributed stochastic neighborhood em...

    2017 arXiv

  24. [32]

    , Rachh, M

    linderman2019fast APACrefauthors Linderman, G C. , Rachh, M. , Hoskins, J G. , Steinerberger, S. \ Kluger, Y. APACrefauthors \ 2019 . Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data Fast interpolation-based t-sne for improved visualization...

    2019

  25. [33]

    , Luo, P

    liu2015faceattributes APACrefauthors Liu, Z. , Luo, P. , Wang, X. \ Tang, X. APACrefauthors \ 2015 December . Deep Learning Face Attributes in the Wild Deep learning face attributes in the wild . Proceedings of International Conference on Computer Vision (ICCV). Proceedings of...

    2015

  26. [34]

    , Basu, A

    macosko2015highly APACrefauthors Macosko, E Z. , Basu, A. , Satija, R. , Nemesh, J. , Shekhar, K. , Goldman, M. others APACrefauthors \ 2015 . Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets Highly parallel genome-wide expression p...

    2015

  27. [35]

    , Healy, J

    mcinnes2018umap APACrefauthors McInnes, L. , Healy, J. \ Melville, J. APACrefauthors \ 2018 . Umap: Uniform manifold approximation and projection for dimension reduction Umap: Uniform manifold approximation and projection for dimension reduction . arXiv preprint arXiv:1802.03426

    2018 arXiv

  28. [36]

    , Sutskever, I

    mikolov2013distributed APACrefauthors Mikolov, T. , Sutskever, I. , Chen, K. , Corrado, G S. \ Dean, J. APACrefauthors \ 2013 . Distributed representations of words and phrases and their compositionality Distributed representations of words and phrases and their compositionali...

    2013

  29. [37]

    , Shaham, U

    mishne2019diffusion APACrefauthors Mishne, G. , Shaham, U. , Cloninger, A. \ Cohen, I. APACrefauthors \ 2019 . Diffusion nets Diffusion nets . Applied and Computational Harmonic Analysis 47 2 259--285

    2019

  30. [38]

    , van Dijk, D

    moon2017phate APACrefauthors Moon, K R. , van Dijk, D. , Wang, Z. , Gigante, S. , Burkhardt, D B. , Chen, W S. others APACrefauthors \ 2019 . Visualizing structure and transitions in high-dimensional biological data Visualizing structure and transitions in high-dimensional bio...

    2019

  31. [39]

    , Horn, M

    moor2019topological APACrefauthors Moor, M. , Horn, M. , Rieck, B. \ Borgwardt, K. APACrefauthors \ 2020 . Topological autoencoders Topological autoencoders . ICML

    2020

  32. [40]

    , Odena, A

    oliver2018realistic APACrefauthors Oliver, A. , Odena, A. , Raffel, C A. , Cubuk, E D. \ Goodfellow, I. APACrefauthors \ 2018 . Realistic evaluation of deep semi-supervised learning algorithms Realistic evaluation of deep semi-supervised learning algorithms . Advances in neura...

    2018

  33. [41]

    , Talmon, R

    pai2019dimal APACrefauthors Pai, G. , Talmon, R. , Bronstein, A. \ Kimmel, R. APACrefauthors \ 2019 . Dimal: Deep isometric manifold learning using sparse geodesic sampling Dimal: Deep isometric manifold learning using sparse geodesic sampling . 2019 IEEE Winter Conference on ...

    2019

  34. [42]

    , O’Shea, D J

    pandarinath2018inferring APACrefauthors Pandarinath, C. , O’Shea, D J. , Collins, J. , Jozefowicz, R. , Stavisky, S D. , Kao, J C. others APACrefauthors \ 2018 . Inferring single-trial neural population dynamics using sequential auto-encoders Inferring single-trial neural popu...

    2018

  35. [43]

    , Varoquaux, G

    pedregosa2011scikit APACrefauthors Pedregosa, F. , Varoquaux, G. , Gramfort, A. , Michel, V. , Thirion, B. , Grisel, O. others APACrefauthors \ 2011 . Scikit-learn: Machine learning in Python Scikit-learn: Machine learning in python . the Journal of machine Learning research 1...

    2011

  36. [44]

    , Lee, J A

    peluffo2014recent APACrefauthors Peluffo, D H. , Lee, J A. \ Verleysen, M. APACrefauthors \ 2014 . Recent methods for dimensionality reduction: A brief comparative analysis Recent methods for dimensionality reduction: A brief comparative analysis

    2014

  37. [45]

    , Stra z ar, M

    Poliar731877 APACrefauthors Poli c ar, P G. , Stra z ar, M. \ Zupan, B. APACrefauthors \ 2019 . openTSNE: a modular Python library for t-SNE dimensionality reduction and embedding opentsne: a modular python library for t-sne dimensionality reduction and embedding . bioRxiv . A...

    2019 doi

  38. [46]

    , Metz, L

    radford2015unsupervised APACrefauthors Radford, A. , Metz, L. \ Chintala, S. APACrefauthors \ 2015 . Unsupervised representation learning with deep convolutional generative adversarial networks Unsupervised representation learning with deep convolutional generative adversarial...

    2015 arXiv

  39. [47]

    APACrefauthors \ 2020

    robinson2020interpretable APACrefauthors Robinson, I. APACrefauthors \ 2020 . Interpretable Visualizations with Differentiating Embedding Networks Interpretable visualizations with differentiating embedding networks . arXiv preprint arXiv:2006.06640

    2020 arXiv

  40. [48]

    APACrefauthors \ 1987

    rousseeuw1987silhouettes APACrefauthors Rousseeuw, P J. APACrefauthors \ 1987 . Silhouettes: a graphical aid to the interpretation and validation of cluster analysis Silhouettes: a graphical aid to the interpretation and validation of cluster analysis . Journal of computationa...

    1987

  41. [49]

    , Thielk, M

    Sainburg870311 APACrefauthors Sainburg, T. , Thielk, M. \ Gentner, T Q. APACrefauthors \ 2019 . Latent space visualization, characterization, and generation of diverse vocal communication signals Latent space visualization, characterization, and generation of diverse vocal com...

    2019 doi

  42. [50]

    , Thielk, M

    sainburg2018generative APACrefauthors Sainburg, T. , Thielk, M. , Theilman, B. , Migliori, B. \ Gentner, T. APACrefauthors \ 2018 . Generative adversarial interpolative autoencoding: adversarial training on latent space interpolations encourage convex latent distributions Gene...

    2018 arXiv

  43. [51]

    , Javanmardi, M

    sajjadi2016regularization APACrefauthors Sajjadi, M. , Javanmardi, M. \ Tasdizen, T. APACrefauthors \ 2016 . Regularization with stochastic transformations and perturbations for deep semi-supervised learning Regularization with stochastic transformations and perturbations for ...

    2016

  44. [52]

    , Hinder, F

    schulz2019deepview APACrefauthors Schulz, A. , Hinder, F. \ Hammer, B. APACrefauthors \ 2019 . Deepview: Visualizing classification boundaries of deep neural networks as scatter plots using discriminative dimensionality reduction Deepview: Visualizing classification boundaries...

    2019 arXiv

  45. [53]

    , Berthelot, D

    sohn2020fixmatch APACrefauthors Sohn, K. , Berthelot, D. , Li, C L. , Zhang, Z. , Carlini, N. , Cubuk, E D. Raffel, C. APACrefauthors \ 2020 . Fixmatch: Simplifying semi-supervised learning with consistency and confidence Fixmatch: Simplifying semi-supervised learning with con...

    2020 arXiv

  46. [54]

    , Cole, J E

    szubert2019structure APACrefauthors Szubert, B. , Cole, J E. , Monaco, C. \ Drozdov, I. APACrefauthors \ 2019 . Structure-preserving visualisation of high dimensional single-cell datasets Structure-preserving visualisation of high dimensional single-cell datasets . Scientific ...

    2019

  47. [55]

    , Liu, J

    tang2016visualizing APACrefauthors Tang, J. , Liu, J. , Zhang, M. \ Mei, Q. APACrefauthors \ 2016 . Visualizing large-scale and high-dimensional data Visualizing large-scale and high-dimensional data . Proceedings of the 25th international conference on world wide web Proceedi...

    2016

  48. [56]

    APACrefauthors \ 2009

    van2009learning APACrefauthors Van Der Maaten, L. APACrefauthors \ 2009 . Learning a parametric embedding by preserving local structure Learning a parametric embedding by preserving local structure . Artificial Intelligence and Statistics Artificial intelligence and statistics...

    2009

  49. [57]

    APACrefauthors \ 2014

    van2014accelerating APACrefauthors Van Der Maaten, L. APACrefauthors \ 2014 . Accelerating t-SNE using tree-based algorithms Accelerating t-sne using tree-based algorithms . The Journal of Machine Learning Research 15 1 3221--3245

    2014

  50. [58]

    \ Hinton, G

    van2008visualizing APACrefauthors van der Maaten, L. \ Hinton, G. APACrefauthors \ 2008 . Visualizing Data using t-SNE Visualizing data using t-sne . Journal of Machine Learning Research 9 2579--2605

    2008

  51. [59]

    \ Kaski, S

    venna2006local APACrefauthors Venna, J. \ Kaski, S. APACrefauthors \ 2006 . Local multidimensional scaling Local multidimensional scaling . Neural Networks 19 6-7 889--899

    2006

  52. [60]

    APACrefauthors \ 2016

    white2016sampling APACrefauthors White, T. APACrefauthors \ 2016 . Sampling generative networks Sampling generative networks . arXiv preprint arXiv:1609.04468

    2016 arXiv

  53. [61]

    , Rasul, K

    xiao2017fashion APACrefauthors Xiao, H. , Rasul, K. \ Vollgraf, R. APACrefauthors \ 2017 . Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms . arXiv preprint arXiv...

    2017 arXiv

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