Improving Channel Charting with Representation-Constrained Autoencoders

Christoph Studer; Emre G\"on\"ulta\c{s}; Olav Tirkkonen; Oscar Casta\~neda; Pengzhi Huang; Sa\"id Medjkouh; Tom Goldstein

REVIEW 4 major objections 4 minor 26 references

Improving Channel Charting with Representation-Constrained Autoencoders

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Representation-constrained autoencoders recover the global geometry of channel charts, enabling approximate positioning from CSI alone.

desk verdict A clean formulation of pairwise distance constraints for AE-based channel charting, but the global-geometry claim rests on an unreported temporal threshold and a small gain over anchors alone. read the letter →

arxiv 1908.02878 v1 pith:RXV3TBD3 submitted 2019-08-07 eess.SP cs.ITmath.ITstat.ML

Pengzhi Huang , Oscar Castañeda , Emre Gönültaş , Saïd Medjkouh , Olav Tirkkonen , Tom Goldstein , Christoph Studer This is my paper · ORCID

classification eess.SPcs.ITmath.ITstat.ML

keywords channelchartingautoencoderrepresentationconstraintswirelesspositioningstateinformationdimensionalityreductionsemi-supervisedlearningKruskalstress

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

This paper argues that the relative-position maps learned from cellular channel state information, called channel charts, can be upgraded from local layouts into globally accurate maps by adding two kinds of side information to autoencoder training: a few known anchor locations and the fact that a moving user's consecutive CSI measurements must be close together. The proposed pairwise constraints, fixed absolute distance (FAD) for anchors and maximum relative distance (MRD) for temporally adjacent measurements, are regularizers added to the reconstruction loss. In simulated 1000 m by 500 m scenarios, the constrained charts reproduce the true scene geometry, improving Kruskal stress from about 0.35 to 0.26 in line-of-sight conditions and from about 0.41 to 0.27 without a line of sight. If true, this means approximate absolute positioning can be obtained from passively collected CSI plus a small fraction of labeled locations, without GNSS or dense fingerprint surveys.

What carries the argument

The mechanism is a set of four pairwise regularizers on the autoencoder's latent space, summarized as fixed/maximum and absolute/relative distance constraints. FAD enforces $\|\mathbf{y}_i-\bar{\mathbf{y}}_j\|=d_{i,j}$ with a known representation $\bar{\mathbf{y}}_j$, so setting $d_{i,j}=0$ pins selected chart points to anchors; MRD enforces $\|\mathbf{y}_i-\mathbf{y}_j\|\le d_{i,j}$ between two learned representations, so consecutive CSI samples from a moving user stay within a bounded chart distance. The regularizers have generalized gradients, so they plug into standard stochastic training of the autoencoder; the encoder then becomes the charting function that maps new CSI to position. The claim that global geometry is recovered rests on these constraints being strong enough to unwrap the chart without destroying local neighborhoods.

What would settle it

Run the same simulation with the temporal MRD threshold set at half and at ten times the maximum travel distance implied by the CSI sampling rate; if the chart's Kruskal stress and anchor-to-ground-truth alignment stay within a few percent, the threshold is not load-bearing, but if they degrade sharply, the global-geometry claim is contingent on that unreported quantity.

Watch

Extended reading notes

Core claim

Channel charting normally preserves only local neighborhoods: nearby users map to nearby points, but the whole chart is free to bend, rotate, and scale. The paper's discovery is that adding representation constraints recovers the global geometry of the chart. Concretely, randomly choosing 10% of the users as anchors and using FAD constraints with $d_{i,j}=0$ pins those chart points to their true locations, unwrapping the embedding; adding MRD constraints between consecutive samples on a user's trajectory enforces that the chart moves no faster than the physical motion. In the QuaDRiGa-based Q-LoS and Q-NLoS simulations, FAD and MRD together make the learned chart visually match the original 1000 m by 500 m scenario and reduce Kruskal stress substantially, while trustworthiness improves slightly at the cost of a small reduction in continuity. The authors read this as approximate absolute positioning from CSI with only a fraction of labeled anchor locations plus temporal side information.

Load-bearing premise

The claim stands on being able to set an upper bound on how far adjacent channel-chart representations may lie from the CSI sampling rate; the paper never reports the velocity model, the threshold value, or the constraint weight.

Editorial extensions

If this is right

With 10% anchors plus temporal MRD, the chart's global geometry is recovered well enough that channel charting can provide approximate absolute positions, not just relative ones.
Kruskal stress drops from 0.3548 to 0.2598 in Q-LoS and from 0.4096 to 0.2693 in Q-NLoS, indicating substantially better global structure preservation.
Both trustworthiness and continuity remain high, so the local neighborhood structure is not sacrificed; trustworthiness rises slightly and continuity falls slightly.
The gain holds across LoS and NLoS propagation, so the method does not depend on a direct path from user to base station.
The authors expect this is not yet GNSS-grade accuracy; further geometry constraints or better CSI features are needed for that.
The same regularizer framework can absorb other pairwise side information, such as known distances between fixed access points, without changing the training procedure.
Because the temporal MRD constraint only assumes a bound on physical displacement between acquisitions, it can be applied to any time-ordered sensor stream with a known sampling rate, such as multiple users' trajectories or UAV flights, without requiring anchors.
The anchor fraction and the MRD threshold are separate knobs; a testable extension is to map the trade-off curve between anchor fraction and global-geometry error, which would tell operators how few labeled points suffice for a target positioning accuracy.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the paper's actual contribution is modest but real: it takes the pairwise distance-constraint idea that is standard in metric learning and applies it to autoencoder-based channel charting, using a small number of anchored locations and temporal continuity as side information. The four regularizers in Table I are clearly defined and the gradients in Eqs. (2)-(3) are correct. Second, the headline claim that these constraints 'recover the global geometry' is only partially supported. In the one simulated scenario, FAD constraints (10% anchor labels) improve Kruskal's stress substantially, but adding the MRD temporal constraint on top of FAD gives a small additional KS gain (e.g., Q-LoS 0.2652 to 0.2598). The abstract's 'without supervised learning' is an overstatement—10% anchor positions are supervised labels. And the key MRD threshold—the only place temporal information enters—is never reported, so the reader cannot tell whether the temporal constraint is doing meaningful work or is nearly inactive.

What the paper does well: the problem framing is honest about the tradeoff—TW improves, CT worsens—and the metrics are standard. The simulation uses QuaDRiGa, a reasonable channel model. The idea of using the CSI acquisition rate to set a maximum-distance bound is plausible, as long as the threshold is grounded in a physical velocity model.

The soft spots are real but proportionate to a conference-style paper. The evaluation is a single scenario with no error bars or multiple seeds, which makes the KS numbers hard to interpret. No ablation isolates the effect of MRD independently of FAD. The missing calibration details (velocity, acquisition rate, d_ij, weights) are not just a reporting lapse; they are load-bearing for the temporal constraint's contribution. The CT decrease is acknowledged but not discussed in terms of whether the positioning gains are worth the neighborhood-quality loss.

Who is this for? Researchers working on channel charting or semi-supervised dimensionality reduction for positioning. The constraint framework is a reasonable starting point, and the paper gives a clean formulation. I'd cite it if I were working on CC side information.

Recommendation: this deserves a serious referee. It is not a desk reject. The reviewer should ask for the missing hyperparameters, multiple seeds, and a clear decomposition of FAD vs MRD gains. If the authors supply those, the claim will either stand or be usefully qualified.

Referee Report

4 major / 4 minor

Summary. The paper proposes augmenting autoencoder-based channel charting with pairwise representation constraints derived from side information available during CSI acquisition. Two families of constraints are introduced: fixed-distance constraints (FAD, FRD) and maximum-distance constraints (MAD, MRD), implemented as nonconvex regularizers with generalized gradients. The authors evaluate plain AEs, AEs with 10% FAD anchors, and AEs with FAD plus temporal MRD constraints on a simulated 1000 m x 500 m scenario with Quadriga LoS and NLoS channels. They report trustworthiness (TW), continuity (CT), and Kruskal stress (KS) metrics, and conclude that representation-constrained AEs recover global geometry and enable approximate positioning without GNSS or dense supervised measurement campaigns.

Significance. If the result holds, the paper offers a practical way to turn channel charting from a purely relative-localization method into one capable of approximate absolute positioning using a modest number of anchor points plus temporal side information. The regularizer gradients in Eqs. (2) and (3) are correctly derived, and TW, CT, and KS are standard dimensionality-reduction quality metrics. The idea of deriving pairwise constraints from the CSI acquisition process is timely and well motivated. However, the empirical evidence is limited to one simulated scenario with no reported hyperparameters, no multiple trials or error bars, and no ablations that separate the contribution of the temporal MRD constraint from the anchor-based FAD constraint. The paper also reports a consistent degradation in CT when constraints are added, so the general claim of 'improving the quality' of channel charts overstates what the data show.

major comments (4)

[§III-B, §III-C, Table II] The MRD temporal constraint is the only mechanism by which temporal side information enters the model, but the paper never reports the velocity model, the CSI acquisition rate, the chosen maximum-distance threshold d_ij, or the regularization penalty weight used for the MRD term. Since MRD is an upper-bound regularizer, an overly loose threshold makes it inactive and an overly tight threshold can deform the chart; without these values, the reported KS reductions from FAD to FAD&MRD (0.2652 to 0.2598 for Q-LoS and 0.2749 to 0.2693 for Q-NLoS) cannot be interpreted or reproduced.
[§III-C2, Table II, Fig. 2] Because the FAD constraints fix 10% of the representations to their true coordinates, the large KS improvement from plain AE to FAD (Q-LoS 0.3548 to 0.2652; Q-NLoS 0.4096 to 0.2749) is substantially built into the objective: anchor-to-anchor distances in the chart are exact by construction, and anchor-to-other distances are strongly constrained. The additional MRD improvement is small, so the claim that 'FAD and MRD combined are able to reproduce the original scenario' needs an ablation that quantifies the contribution of MRD without anchors and reports KS restricted to non-anchor points.
[Table II, §III-C2] The paper's general wording that representation constraints 'improve the quality' of channel charts is contradicted by the CT results in Table II: CT decreases in every configuration relative to plain AE, e.g., Q-LoS at K=1 from 0.9700 to 0.9195 (FAD) and 0.9321 (FAD&MRD). The conclusion should explicitly present this as a tradeoff between improved global geometry and worsened local continuity, rather than an unqualified improvement.
[§III-C, Table II] All numerical results come from a single simulated scenario with no information about the optimizer, learning rate, epoch count, batch size, regularization weights, anchor selection procedure, or random seeds. The reported differences, some as small as 0.003, are therefore not distinguishable from run-to-run variation. At minimum, the authors should provide multiple random initializations/seeds with standard deviations and report the exact hyperparameters used for each constraint.

minor comments (4)

[§III-C2] In the description of the 'vip' curve, the text says 'maximum absolute distance constraints among pairs of representations pertaining to this curve,' but since both representations are learned, this should be 'maximum relative distance' (MRD).
[Abstract] The abstract's phrase 'without global navigation satellite systems or supervised learning methods that rely on extensive and expensive measurement campaigns' is potentially misleading, because the FAD anchors are supervised labels, albeit for only 10% of the data; the method is semi-supervised, not label-free.
[§III-C1] The paper states that 2048 CSI vectors are extracted and that the input dimension is D=32 real dimensions, but the angular-domain feature extraction and scaling steps from [9] are only summarized; a brief description of the exact feature vector would improve reproducibility.
[Fig. 2] The visual comparison in Figure 2 would be strengthened by adding the same axis limits and a scale bar across all panels, since KS improvement is about global geometry and the current color gradients make the 'vip' curve discrepancies hard to assess quantitatively.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's improvements are empirical demonstrations on an external QuaDRiGa benchmark, with anchor labels and temporal constraints applied as declared side information rather than as predictions derived from the reported metrics.

full rationale

The central claim, that FAD and MRD constraints improve channel-chart global geometry, is supported by simulated QuaDRiGa scenarios and by the standard TW, CT, and KS metrics, not by a derivation that reimports the conclusion. The FAD anchors are labeled inputs: 10% of user positions are known and used to unwrap the chart, which is legitimate semi-supervised side information. The KS metric compares representation distances to CSI-feature distances rather than to the anchor coordinates themselves, so the reported KS improvement is not an identity forced by construction. The MRD constraint enforces an upper bound motivated by the CSI acquisition rate; the paper does not report the threshold or velocity model, which is a real reproducibility and transparency limitation, but no equation in the paper reduces the claimed geometry recovery to that threshold. Self-citations to the authors' prior channel charting work supply the baseline scenario, features, and network architecture, and the paper reproduces that baseline; these citations are contextual rather than load-bearing proofs of the new constraint mechanism. No uniqueness theorem, embedded ansatz, or renamed quantity is invoked to force the conclusion, so there is no circular step to flag.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central demonstration rests on a small number of domain assumptions inherited from channel charting and on several unreported hyperparameters (MRD threshold, regularization weights, anchor fraction). No new physical entities are postulated. The paper's main support comes from one QuaDRiGa simulation, so the ledger is short but the validation is thin.

free parameters (4)

MRD temporal distance threshold d_i,j = Not reported; stated to be estimable from acquisition rate
Used for maximum relative distance constraints on the 'vip' trajectory in §III-B. The threshold controls how strongly consecutive representations are pulled together; no value or velocity assumption is given, so results depend on an unreported input.
Anchor fraction = 0.10
10% of the 2048 UEs are randomly chosen as FAD anchors with known true positions (§III-C2). Results likely depend on this fraction and no ablation is shown.
Regularization penalty weight for constraint losses = Not reported
The total loss combines reconstruction MSE (Eq. 1) with the regularizers in Table I; the balance weight is not specified and no tuning procedure is described (§II-B3).
Autoencoder architecture hyperparameters = Layer sizes 500, 100, 50, 20; latent 2; activations mostly unstated
Architecture is copied from [9] and reported in §III-C1, but activations, initialization, and training iterations are not given; these design choices affect the learned charts.

assumptions (5)

domain assumption Large-scale fading CSI features are a (noisy) function of UE position, so similar features imply nearby positions.
Stated as 'The main assumption of CC...' in §III-A; this premise underlies the whole channel charting approach.
domain assumption UE velocity is bounded, so consecutive CSI measurements of a moving user map to representations within a known maximum distance.
Used to justify MRD constraints in §III-B; requires a velocity prior that the paper does not specify.
domain assumption QuaDRiGa Berlin UMa channel simulations are representative of real channels.
All numerical results use simulated CSI from [26]; no real measurements validate the method (§III-C1).
domain assumption Gradient-based training of the nonconvex regularized AE reaches a useful local optimum.
The method relies on stochastic optimization of a nonconvex objective with no convergence guarantee (§II-B3).
standard math Subgradients of the max-based regularizers are valid generalized gradients for training.
Eqs. (2)-(3) use subgradient calculus, which is standard, but the non-smooth points at the constraint boundary are not discussed.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Improving Channel Charting with Representation-Constrained Autoencoders." pith.science (2026). https://pith.science/paper/RXV3TBD3

@misc{pith2026190802878,
  author       = {Pith},
  title        = {Pith review of: Improving Channel Charting with Representation-Constrained Autoencoders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RXV3TBD3}},
  note         = {Machine review of arXiv:1908.02878}
}

read the original abstract

Channel charting (CC) has been proposed recently to enable logical positioning of user equipments (UEs) in the neighborhood of a multi-antenna base-station solely from channel-state information (CSI). CC relies on dimensionality reduction of high-dimensional CSI features in order to construct a channel chart that captures spatial and radio geometries so that UEs close in space are close in the channel chart. In this paper, we demonstrate that autoencoder (AE)-based CC can be augmented with side information that is obtained during the CSI acquisition process. More specifically, we propose to include pairwise representation constraints into AEs with the goal of improving the quality of the learned channel charts. We show that such representation-constrained AEs recover the global geometry of the learned channel charts, which enables CC to perform approximate positioning without global navigation satellite systems or supervised learning methods that rely on extensive and expensive measurement campaigns.

Figures

Figures reproduced from arXiv: 1908.02878 by the authors.

**Figure 2.** Channel charts learned from the scenario in Figure 1. The channel [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 22 canonical work pages

[1]

Reducing the dimensionality of data with neural networks,

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science, vol. 313, no. 5786, pp. 504–507, Jul. 2006

2006
[2]

Dimensionality reduction: A comparative review,

L. van der Maaten, E. Postma, and J. Van den Herik, “Dimensionality reduction: A comparative review,” in J. Mach. Learn. Res. , vol. 10, Oct. 2009, pp. 66–71

work page 2009
[3]

Goodfellow, Y

I. Goodfellow, Y . Bengio, and A. Courville, Deep Learning . MIT Press, 2016

2016
[4]

Autoencoders, unsupervised learning, and deep architectures,

P. Baldi, “Autoencoders, unsupervised learning, and deep architectures,” in Proc. ICML Workshop Unsupervised Transfer Learn. , vol. 27, Jul. 2012, pp. 37–49

work page 2012
[5]

High-resolution SAR image classiﬁcation via deep convolutional autoencoders,

J. Geng, J. Fan, H. Wang, X. Ma, B. Li, and F. Chen, “High-resolution SAR image classiﬁcation via deep convolutional autoencoders,” IEEE Geosci. Remote Sens. Lett. , vol. 12, no. 11, pp. 2351–2355, Nov. 2015

work page 2015
[6]

Distributed representations of words and phrases and their compositionality,

T. Mikolov, I. Sutskever, K. Chen, G. Corrado, and J. Dean, “Distributed representations of words and phrases and their compositionality,” in Adv. Neural Inf. Process. Syst. , Dec. 2013, pp. 3111–3119

work page 2013
[7]

Lossy Image Compression with Compressive Autoencoders,

L. Theis, W. Shi, A. Cunningham, and F. Huszár, “Lossy Image Compression with Compressive Autoencoders,” ArXiv, Mar. 2017

work page 2017
[8]

Generalized denoising auto-encoders as generative models,

Y . Bengio, L. Yao, G. Alain, and P. Vincent, “Generalized denoising auto-encoders as generative models,” in Adv. Neural Inf. Process. Syst. , Dec. 2013, pp. 899–907

work page 2013

Show all 26 references

[9]

Channel charting: Locating users within the radio environment using channel state information,

C. Studer, S. Medjkouh, E. Gönülta¸ s, T. Goldstein, and O. Tirkkonen, “Channel charting: Locating users within the radio environment using channel state information,” IEEE Access, vol. 6, pp. 47 682–47 698, Aug. 2018

2018
[10]

Unsupervised charting of wireless channels

S. Medjkouh, C. Studer, E. Gönülta¸ s, T. Goldstein, and O. Tirkkonen, “Unsupervised charting of wireless channels.” submitted to GLOBE- COM 2018, 2018

2018
[11]

A fast learning algorithm for deep belief nets,

G. E. Hinton, S. Osindero, and Y .-W. Teh, “A fast learning algorithm for deep belief nets,” Neural Comput., vol. 18, no. 7, pp. 1527–1554, Jul. 2006

2006
[12]

Tutorial on variational autoencoders,

C. Doersch, “Tutorial on variational autoencoders,” ArXiv, Jun. 2016

2016
[13]

Auto-encoding variational Bayes,

D. P. Kingma and M. Welling, “Auto-encoding variational Bayes,”ArXiv, Dec. 2013

2013
[14]

Deep convolutional inverse graphics network,

T. D. Kulkarni, W. F. Whitney, P. Kohli, and J. Tenenbaum, “Deep convolutional inverse graphics network,” in Adv. Neural Inf. Process. Syst., Dec. 2015, pp. 2539–2547

2015
[15]

Survey of wireless indoor positioning techniques and systems,

H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor positioning techniques and systems,” IEEE Trans. Syst., Man, Cybern. C, vol. 37, no. 6, pp. 1067–1080, Nov. 2007

2007
[16]

Device ﬁngerprinting in wireless networks: Challenges and opportunities,

Q. Xu, R. Zheng, W. Saad, and Z. Han, “Device ﬁngerprinting in wireless networks: Challenges and opportunities,” IEEE Commun. Surveys Tuts. , vol. 18, no. 1, pp. 94–104, 1st Quarter 2016

2016
[17]

A nonlinear mapping for data structure analysis,

J. W. Sammon, “A nonlinear mapping for data structure analysis,” IEEE Trans. Computers, vol. C-18, no. 5, pp. 401–409, May 1969

1969
[18]

M. L. Davison, Multidimensional scaling. Krieger Publishing, 1991

1991
[19]

ConFi: Convolutional neural networks based indoor wi-ﬁ localization using channel state information,

H. Chen, Y . Zhang, W. Li, X. Tao, and P. Zhang, “ConFi: Convolutional neural networks based indoor wi-ﬁ localization using channel state information,” IEEE Access, vol. 5, pp. 18 066–18 074, 2017

2017
[20]

Deep convolutional neural networks for massive MIMO ﬁngerprint-based positioning,

J. Vieira, E. Leitinger, M. Sarajlic, X. Li, and F. Tufvesson, “Deep convolutional neural networks for massive MIMO ﬁngerprint-based positioning,” in Proc. IEEE Intl. Symp. Personal, Indoor, Mobile Radio Commun., Oct. 2017, pp. 1–6

2017
[21]

On deep learning-based massive MIMO indoor user localization,

M. Arnold, S. Dörner, S. Cammerer, and S. ten Brink, “On deep learning-based massive MIMO indoor user localization,” ArXiv, Apr. 2018

2018
[22]

TensorFlow: Large-scale machine learning on heterogeneous systems,

M. Abadi et al. , “TensorFlow: Large-scale machine learning on heterogeneous systems,” 2015, software available from tensorﬂow.org

2015
[23]

Chollet et al., “Keras,” https://keras.io, 2015

F. Chollet et al., “Keras,” https://keras.io, 2015

2015
[24]

Quality assessment of dimensionality reduction: Rank-based criteria,

J. A. Lee and M. Verleysen, “Quality assessment of dimensionality reduction: Rank-based criteria,” in Neurocomputing, vol. 72, no. 7, Mar. 2009, pp. 1431–1443

2009
[25]

The analysis of proximities: Multidimensional scaling with an unknown distance function. I

R. N. Shepard, “The analysis of proximities: Multidimensional scaling with an unknown distance function. I.” Psychometrika, vol. 27, no. 2, pp. 125–140, Jun. 1962

1962
[26]

QuaDRiGa: A 3- D multi-cell channel model with time evolution for enabling virtual ﬁeld trials,

S. Jaeckel, L. Raschkowski, K. Börner, and L. Thiele, “QuaDRiGa: A 3- D multi-cell channel model with time evolution for enabling virtual ﬁeld trials,” IEEE Trans. Antennas Propag. , vol. 62, no. 6, pp. 3242–3256, Jun. 2014

2014

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Reducing the dimensionality of data with neural networks,

G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimensionality of data with neural networks,” Science, vol. 313, no. 5786, pp. 504–507, Jul. 2006

2006

[2] [2]

Dimensionality reduction: A comparative review,

L. van der Maaten, E. Postma, and J. Van den Herik, “Dimensionality reduction: A comparative review,” in J. Mach. Learn. Res. , vol. 10, Oct. 2009, pp. 66–71

work page 2009

[3] [3]

Goodfellow, Y

I. Goodfellow, Y . Bengio, and A. Courville, Deep Learning . MIT Press, 2016

2016

[4] [4]

Autoencoders, unsupervised learning, and deep architectures,

P. Baldi, “Autoencoders, unsupervised learning, and deep architectures,” in Proc. ICML Workshop Unsupervised Transfer Learn. , vol. 27, Jul. 2012, pp. 37–49

work page 2012

[5] [5]

High-resolution SAR image classiﬁcation via deep convolutional autoencoders,

J. Geng, J. Fan, H. Wang, X. Ma, B. Li, and F. Chen, “High-resolution SAR image classiﬁcation via deep convolutional autoencoders,” IEEE Geosci. Remote Sens. Lett. , vol. 12, no. 11, pp. 2351–2355, Nov. 2015

work page 2015

[6] [6]

Distributed representations of words and phrases and their compositionality,

T. Mikolov, I. Sutskever, K. Chen, G. Corrado, and J. Dean, “Distributed representations of words and phrases and their compositionality,” in Adv. Neural Inf. Process. Syst. , Dec. 2013, pp. 3111–3119

work page 2013

[7] [7]

Lossy Image Compression with Compressive Autoencoders,

L. Theis, W. Shi, A. Cunningham, and F. Huszár, “Lossy Image Compression with Compressive Autoencoders,” ArXiv, Mar. 2017

work page 2017

[8] [8]

Generalized denoising auto-encoders as generative models,

Y . Bengio, L. Yao, G. Alain, and P. Vincent, “Generalized denoising auto-encoders as generative models,” in Adv. Neural Inf. Process. Syst. , Dec. 2013, pp. 899–907

work page 2013