mlsanityData to 7 Oct 2026

From Principal Subspaces to Principal Components with Linear Autoencoders

arXiv 1804.10253 ↗First posted 26 Apr 2018stat.ML cs.LGcited by 38

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Abstract (arXiv)

The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principal component loading vectors, but that they are not identical to the loading vectors. In this paper, we show how to recover the loading vectors from the autoencoder weights.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Apr 2018.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 9; 2024: 4; 2025: 8; 2026: 6.

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  1. 2022Self-supervised Learning in Remote Sensing: A Reviewcited by 137
  2. 2021The Power of Contrast for Feature Learning: A Theoretical Analysiscited by 53
  3. 2022The dynamics of representation learning in shallow, non-linear autoencoderscited by 27
  4. 2023Geometric Autoencoders -- What You See is What You Decodecited by 23
  5. 2021Symmetry-Aware Autoencoders: s-PCA and s-nlPCAcited by 8
  6. 2021Probabilistic Robust Autoencoders for Outlier Detectioncited by 7
  7. 2022Predicting waves in fluids with deep neural networkcited by 7
  8. 2021A Mechanism for Producing Aligned Latent Spaces with Autoencoderscited by 5
  9. 2022InDiReCT: Language-Guided Zero-Shot Deep Metric Learning for Imagescited by 5
  10. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  11. 2023Neural Image Compression: Generalization, Robustness, and Spectral Biasescited by 4
  12. 2023Latent Noise Segmentation: How Neural Noise Leads to the Emergence of Segmentation and Groupingcited by 4
26 more
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  2. 2025DREAMS: Preserving both Local and Global Structure in Dimensionality Reductioncited by 4
  3. 2022Predicting Wind-Driven Spatial Deposition through Simulated Color Images using Deep Autoencoderscited by 3
  4. 2024The Persian Rug: solving toy models of superposition using large-scale symmetriescited by 3
  5. 2021Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEscited by 2
  6. 2023The Effect of SGD Batch Size on Autoencoder Learning: Sparsity, Sharpness, and Feature Learningcited by 2
  7. 2023Are We Using Autoencoders in a Wrong Way?cited by 2
  8. 2025Autoencoder-based non-intrusive model order reduction in continuum mechanicscited by 2
  9. 2026PCAE: Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencodercited by 2
  10. 2023An autoencoder compression approach for accelerating large-scale inverse problemscited by 1
  11. 2023Targeted collapse regularized autoencoder for anomaly detection: black hole at the centercited by 1
  12. 2023Quantifying Credit Portfolio sensitivity to asset correlations with interpretable generative neural networkscited by 1
  13. 2024Principal Orthogonal Latent Components Analysis (POLCA Net)cited by 1
  14. 2025Optimal Stopping in Latent Diffusion Modelscited by 1
  15. 2025Enforcing Orderedness to Improve Feature Consistencycited by 1
  16. 2022Realization of Causal Representation Learning to Adjust Confounding Bias in Latent Spacecited by 0
  17. 2023Autocodificadores Variacionales (VAE) Fundamentos Te'oricos y Aplicacionescited by 0
  18. 2024Probabilistic transfer learning methodology to expedite high fidelity simulation of reactive flowscited by 0
  19. 2025Optimal Linear Baseline Models for Scientific Machine Learningcited by 0
  20. 2025RAE: A Neural Network Dimensionality Reduction Method for Nearest Neighbors Preservation in Vector Searchcited by 0
  21. 2025Rethinking PCA Through Dualitycited by 0
  22. 2026Fault Detection in Electrical Distribution System using Autoencoderscited by 0
  23. 2026A convolutional autoencoder and neural ODE surrogate modeling framework applied to transient counterflow flamescited by 0
  24. 2026Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probingcited by 0
  25. 2026Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spacescited by 0
  26. 2026Partially Linear Autoencoders for Manifold Learning and Dimensionality Reductioncited by 0