利用天文光谱中的低维结构
Exploiting Low-Dimensional Structure in Astronomical Spectra
摘要：
简化技术可以大大改善天文学中的统计推断。一个标准的方法是使用主成分分析（PCA）。在这项工作中，我们应用最近开发的技术，扩散图，天文光谱数据参数化和降维，并开发一个强大的，基于本征模的框架回归。我们展示了我们的框架如何提供一种计算效率高的方法来预测星系的红移，从而可以告知更昂贵的红移估计，如模板互相关。它还提供了一种自然的方法来识别离群值（例如，错误分类的光谱、具有异常特征的光谱）。我们分析了3835 SDSS光谱，并展示了我们的框架如何产生超过95%的降维。最后，我们表明，基于扩散图的回归方法的预测误差明显小于基于PCA的类似方法，清楚地表明了扩散图优于PCA的回归任务。
英文摘要：
Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical spectra for data parameterization and dimensionality reduction, and develop a robust, eigenmode-based framework for regression. We show how our framework provides a computationally efficient means by which to predict redshifts of galaxies, and thus could inform more expensive redshift estimators such as template cross-correlation. It also provides a natural means by which to identify outliers (e.g., misclassified spectra, spectra with anomalous features). We analyze 3835 SDSS spectra and show how our framework yields a more than 95% reduction in dimensionality. Finally, we show that the prediction error of the diffusion map-based regression approach is markedly smaller than that of a similar approach based on PCA, clearly demonstrating the superiority of diffusion maps over PCA for this regression task.
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