Generalizable Spectral Embedding with an Application to UMAP

Fuente: arXiv
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Main Authors: Ben-Ari, Nir, Yacobi, Amitai, Shaham, Uri
Format: Preprint
Published: 2025
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author Ben-Ari, Nir
Yacobi, Amitai
Shaham, Uri
author_facet Ben-Ari, Nir
Yacobi, Amitai
Shaham, Uri
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_11305
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generalizable Spectral Embedding with an Application to UMAP
Ben-Ari, Nir
Yacobi, Amitai
Shaham, Uri
Machine Learning
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.
title Generalizable Spectral Embedding with an Application to UMAP
topic Machine Learning
url https://arxiv.org/abs/2501.11305