  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.
