高维统计分析及其在NGC 253的ALMA图中的应用
High Dimensional Statistical Analysis and its Application to ALMA Map of NGC 253
AI总结：
本研究将高维统计分析方法（NRPCA和RPCA）引入天文学，成功应用于NGC 253的ALMA光谱图，精确描述了星系旋转并提取了中心外流信息，为处理高维小样本天文数据提供了新途径。
摘要：
在天文学中，如果我们将数据的维度记为$d$，样本数量记为$n$，我们经常遇到$n \ll d$的情况。传统上，这种情况被认为是非适定的，除了丢弃数据维度中的大部分信息以使$d < n$之外，别无选择。$n \ll d$的数据被称为高维小样本量（HDLSS）。为了处理HDLSS问题，一种称为高维统计的方法在过去十年中得到了迅速发展。在这项工作中，我们首次将高维统计分析引入天文学界。我们将高维统计分析中的两种代表性方法——降噪主成分分析（NRPCA）和正则化主成分分析（RPCA），应用于由阿塔卡马大型毫米波/亚毫米波阵列（ALMA）观测的邻近典型星暴星系NGC 253的光谱图。该ALMA图是一个典型的HDLSS数据集。我们首先分析了包含由系统旋转引起的多普勒频移的原始数据。高维PCA能够精确描述旋转的空间结构。然后，我们将其应用于多普勒频移校正后的数据，以分析更细微的光谱特征。NRPCA和RPCA能够量化ALMA光谱非常复杂的特征。特别是，我们能够提取出NGC 253中心全球外流的信息。这种方法不仅可以应用于光谱巡天数据，还可以应用于任何小样本量和大维度的数据类型。
英文摘要：
In astronomy, if we denote the dimension of data as $d$ and the number of samples as $n$, we often meet a case with $n \ll d$. Traditionally, such a situation is regarded as ill-posed, and there was no choice but to throw away most of the information in data dimension to let $d < n$. The data with $n \ll d$ is referred to as high-dimensional low sample size (HDLSS). {}To deal with HDLSS problems, a method called high-dimensional statistics has been developed rapidly in the last decade. In this work, we first introduce the high-dimensional statistical analysis to the astronomical community. We apply two representative methods in the high-dimensional statistical analysis methods, the noise-reduction principal component analysis (NRPCA) and regularized principal component analysis (RPCA), to a spectroscopic map of a nearby archetype starburst galaxy NGC 253 taken by the Atacama Large Millimeter/Submillimeter Array (ALMA). The ALMA map is a typical HDLSS dataset. First we analyzed the original data including the Doppler shift due to the systemic rotation. The high-dimensional PCA could describe the spatial structure of the rotation precisely. We then applied to the Doppler-shift corrected data to analyze more subtle spectral features. The NRPCA and RPCA could quantify the very complicated characteristics of the ALMA spectra. Particularly, we could extract the information of the global outflow from the center of NGC 253. This method can also be applied not only to spectroscopic survey data, but also any type of data with small sample size and large dimension.
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