High Dimensional Statistical Analysis of ALMA Map of NGC 253
speaker: Tsutomu Takeuchi
Abstract:
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 talk, we 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.