用最优传输距离分析蛋白光谱，揭示二级结构差异的深层模式。
Metric Similarity and Manifold Learning of Circular Dichroism Spectra of Proteins
- 以1-Wasserstein距离衡量光谱相似性，抗噪性强且与传统度量一致。
- t-SNE降维后聚类清晰：β-丰富蛋白与α/β混合蛋白分属不同簇。
- 适合蛋白质结构分析、生物物理研究者关注光谱数据的深层特征。
我们对SP175数据库中球状蛋白的圆二色性光谱进行了机器学习分析，采用基于最优传输的1-Wasserstein距离（p=1）和t-SNE流形学习算法。结果表明，该距离在噪声干扰下具有鲁棒性，且与欧氏距离和曼哈顿距离保持一致。同时，t-SNE能有效揭示高维数据中的有意义结构，其嵌入空间中的聚类主要由蛋白质的二级结构组成决定：一个簇以富含β结构的蛋白为主，另一个则以α/β混合及α-螺旋含量高的蛋白为主。
原文摘要 · Abstract (English)
We present a machine learning analysis of circular dichroism spectra of globular proteins from the SP175 database, using the optimal transport-based $1$-Wasserstein distance $\mathcal{W}_1$ (with order $p=1$) and the manifold learning algorithm $t$-SNE. Our results demonstrate that $\mathcal{W}_1$ is consistent with both Euclidean and Manhattan metrics while exhibiting robustness to noise. On the other hand, $t$-SNE uncovers meaningful structure in the high-dimensional data. The clustering in the $t$-SNE embedding is primarily determined by proteins with distinct secondary structure compositions: one cluster predominantly contains $β$-rich proteins, while the other consists mainly of proteins with mixed $α/β$ and $α$-helical content.
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