mlsanityData to 14 Oct 2026

Generalizable Spectral Embedding with an Application to UMAP

arXiv 2501.11305 ↗First posted 20 Jan 2025cs.LG stat.MLcited by 1

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Abstract (arXiv)

Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. Existing SE implementations often address two of these drawbacks; however, they fall short in addressing the remaining one. In this paper, we introduce Sep-SpectralNet (eigenvector-separated SpectralNet), a SE implementation designed to address all three limitations. Sep-SpectralNet extends SpectralNet with an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate Sep-SpectralNet's ability to consistently approximate and generalize SE, while maintaining SpectralNet's scalability. Additionally, we show how Sep-SpectralNet can be leveraged to enable generalizable UMAP visualization. Our codes are publicly available.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 18 of its 68 references that are in the map. First posted on arXiv 20 Jan 2025.

Builds on

18 of 68 references.

References · 18

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  2. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  3. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  4. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
  5. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 179
  6. 2020Parametric UMAP embeddings for representation and semi-supervised learningcited by 104
  7. 2018SpectralNet: Spectral Clustering using Deep Neural Networkscited by 94
  8. 2020EigenGame: PCA as a Nash Equilibriumcited by 39
  9. 2018Spectral Inference Networks: Unifying Deep and Spectral Learningcited by 35
  10. 2022From t-SNE to UMAP with contrastive learningcited by 28
  11. 2022NeuralEF: Deconstructing Kernels by Deep Neural Networkscited by 27
  12. 2023Laplacian Canonization: A Minimalist Approach to Sign and Basis Invariant Spectral Embeddingcited by 21
6 more
  1. 2015Diffusion Netscited by 19
  2. 2020Eigen-GNN: A Graph Structure Preserving Plug-in for GNNscited by 14
  3. 2020Fiedler Regularization: Learning Neural Networks with Graph Sparsitycited by 8
  4. 2022SpecNet2: Orthogonalization-free spectral embedding by neural networkscited by 5
  5. 2022BASiS: Batch Aligned Spectral Embedding Spacecited by 4
  6. 2022Parametric t-Stochastic Neighbor Embedding With Quantum Neural Networkcited by 1

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Citing papers per year: 2025: 1.

1 paper.

  1. 2025Learning Shared Representations from Unpaired Datacited by 4