Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910001908416512 |
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| author | Zhan, Qipeng Zhou, Zhuoping Wang, Zexuan Shen, Li |
| author_facet | Zhan, Qipeng Zhou, Zhuoping Wang, Zexuan Shen, Li |
| contents | Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by incorporating non-uniform $\ell_2$ regularization or by adjusting the loss function. However, these approaches become insufficient in the nonlinear setting, as the remaining variance cannot be properly captured independently of the nonlinear mapping. In this work, we propose a novel autoencoder framework that integrates non-uniform variance regularization with an isometric constraint. This design serves as a natural generalization of PCA, enabling the model to preserve key advantages, such as ordered representations and variance retention, while remaining effective for nonlinear dimensionality reduction tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder Zhan, Qipeng Zhou, Zhuoping Wang, Zexuan Shen, Li Machine Learning Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by incorporating non-uniform $\ell_2$ regularization or by adjusting the loss function. However, these approaches become insufficient in the nonlinear setting, as the remaining variance cannot be properly captured independently of the nonlinear mapping. In this work, we propose a novel autoencoder framework that integrates non-uniform variance regularization with an isometric constraint. This design serves as a natural generalization of PCA, enabling the model to preserve key advantages, such as ordered representations and variance retention, while remaining effective for nonlinear dimensionality reduction tasks. |
| title | Learning Ordered Representations in Latent Space for Intrinsic Dimension Estimation via Principal Component Autoencoder |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.19179 |