GrEASE: Generalizable Spectral Embedding with an Application to UMAP
Keywords: Spectral Embedding, Eigenvectors separation, Visualization, Laplacian, UMAP
TL;DR: We introduce GrEASE, a novel generalizable Spectral Embedding technique, along with an application for generalizable UMAP.
Abstract: 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. In this paper, we introduce $\textit{GrEASE}$: Generalizable and Efficient Approximate Spectral Embedding, a novel deep-learning approach designed to address these limitations. GrEASE incorporates an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability, allowing for the computation of the Laplacian’s eigenvectors on unseen data. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate GrEASE's ability to consistently approximate and generalize SE, while ensuring scalability. Additionally, we show how GrEASE can be leveraged to enhance existing methods. Specifically, we focus on UMAP, a leading visualization technique, and introduce $\textit{NUMAP}$, a generalizable version of UMAP powered by GrEASE. Our code will be publicly available upon acceptance.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 4556
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