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arXiv 1201.3370astro-ph.COastro-ph.IM
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光谱的数据驱动模型：在斯隆数字巡天中发现双红移

A data-driven model for spectra: Finding double redshifts in the Sloan Digital Sky Survey

P. Tsalmantza, David W. Hogg

备注：
Accepted for publication in ApJ
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摘要：

我们提出了一种数据驱动的方法-异方差矩阵分解，一种概率因子分析-用于对观测光谱或其他具有已知但不均匀观测不确定性的高维数据进行建模或降维。该方法使用迭代逆方差加权最小二乘最小化过程来生成最佳基函数集。该方法类似于主成分分析，但具有实质性的优势，即它以负责任的方式使用测量不确定性，并自然地解释测量不佳和缺失的数据;它对噪声去卷积数据空间中的方差进行建模。正则化可以以平滑先验（受高斯过程启发）或非负约束的形式应用，而不会使该方法过于缓慢。由于该方法优化了合理的标量（与可能性相关），因此该基础在概率意义上比任何PCA基础提供了更好的数据拟合。我们在SDSS光谱上测试了该方法，重点关注已知包含两个红移分量的光谱：这些是引力透镜候选者和大质量黑洞双星的光谱。我们应用假设检验来比较这些光谱的一个红移和两个红移模型，利用所有SDSS光谱的随机子集上训练的数据驱动模型。该测试确认了我们样本中131个镜头候选者中的129个以及所有已知的二元候选者，并且几乎没有误报。

英文摘要：

We present a data-driven method - heteroscedastic matrix factorization, a kind of probabilistic factor analysis - for modeling or performing dimensionality reduction on observed spectra or other high-dimensional data with known but non-uniform observational uncertainties. The method uses an iterative inverse-variance-weighted least-squares minimization procedure to generate a best set of basis functions. The method is similar to principal components analysis, but with the substantial advantage that it uses measurement uncertainties in a responsible way and accounts naturally for poorly measured and missing data; it models the variance in the noise-deconvolved data space. A regularization can be applied, in the form of a smoothness prior (inspired by Gaussian processes) or a non-negative constraint, without making the method prohibitively slow. Because the method optimizes a justified scalar (related to the likelihood), the basis provides a better fit to the data in a probabilistic sense than any PCA basis. We test the method on SDSS spectra, concentrating on spectra known to contain two redshift components: These are spectra of gravitational lens candidates and massive black-hole binaries. We apply a hypothesis test to compare one-redshift and two-redshift models for these spectra, utilizing the data-driven model trained on a random subset of all SDSS spectra. This test confirms 129 of the 131 lens candidates in our sample and all of the known binary candidates, and turns up very few false positives.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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