提出可泛化的谱嵌入方法，解决扩展性与特征分离难题
Generalizable Spectral Embedding with an Application to UMAP
- 通过后处理实现特征向量分离，保持高效计算
- 支持新样本外推，提升模型泛化能力
- 适用于Umap等可视化任务，代码开源
谱嵌入（Spectral Embedding, SE）是一种广泛用于降维的方法，但现有实现存在三个主要缺陷：泛化能力（即外推能力）、可扩展性以及特征向量分离。现有方法通常只解决其中两项问题，而忽略剩余一项。本文提出Sep-SpectralNet（特征向量分离的SpectralNet），通过高效的后处理步骤，在保证泛化性和可扩展性的前提下实现特征向量分离。该方法拓展了谱嵌入在更广泛任务中的应用范围，并可提升其在已有场景下的性能。实验表明，Sep-SpectralNet能稳定逼近并泛化谱嵌入，同时维持SpectralNet的计算效率。此外，我们展示了如何利用Sep-SpectralNet实现可泛化的UMAP可视化。代码已公开。
原文摘要 · Abstract (English)
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.
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