High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253
In astronomy, if we denote the dimension of data as d and the number of samples as n , we often find a case with n ≪ d . Traditionally, such a situation is regarded as ill-posed, and there was no choice but to discard most of the information in data dimensions to let d < n . The data with n ≪ d i...
| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal Supplement Series |
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| Online Access: | https://doi.org/10.3847/1538-4365/ad2517 |
| _version_ | 1797244475823620096 |
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| author | Tsutomu T. Takeuchi Kazuyoshi Yata Kento Egashira Makoto Aoshima Aki Ishii Suchetha Cooray Kouichiro Nakanishi Kotaro Kohno Kai T. Kono |
| author_facet | Tsutomu T. Takeuchi Kazuyoshi Yata Kento Egashira Makoto Aoshima Aki Ishii Suchetha Cooray Kouichiro Nakanishi Kotaro Kohno Kai T. Kono |
| author_sort | Tsutomu T. Takeuchi |
| collection | DOAJ |
| description | In astronomy, if we denote the dimension of data as d and the number of samples as n , we often find a case with n ≪ d . Traditionally, such a situation is regarded as ill-posed, and there was no choice but to discard most of the information in data dimensions to let d < n . The data with n ≪ d is referred to as the high-dimensional low sample size (HDLSS). To deal with HDLSS problems, a method called high-dimensional statistics has rapidly developed in the last decade. In this work, we first introduce high-dimensional statistical analysis to the astronomical community. We apply two representative methods in the high-dimensional statistical analysis methods, noise-reduction principal component analysis (NRPCA) and automatic sparse principal component analysis (A-SPCA), 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 an example of a typical HDLSS data set. First, we analyzed the original data, including the Doppler shift due to the systemic rotation. High-dimensional PCA can precisely describe the spatial structure of the rotation. We then applied to the Doppler-shift corrected data to analyze more subtle spectral features. NRPCA and R-SPCA were able to quantify the very complicated characteristics of the ALMA spectra. Particularly, we were able to extract information on the global outflow from the center of NGC 253. This method can also be applied not only to spectroscopic survey data, but also to any type of data with a small sample size and large dimension. |
| first_indexed | 2024-04-24T19:11:36Z |
| format | Article |
| id | doaj.art-4c6dc03948c849bfb68a832fb2be502d |
| institution | Directory Open Access Journal |
| issn | 0067-0049 |
| language | English |
| last_indexed | 2024-04-24T19:11:36Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal Supplement Series |
| spelling | doaj.art-4c6dc03948c849bfb68a832fb2be502d2024-03-26T09:45:23ZengIOP PublishingThe Astrophysical Journal Supplement Series0067-00492024-01-0127124410.3847/1538-4365/ad2517High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253Tsutomu T. Takeuchi0https://orcid.org/0000-0001-8416-7673Kazuyoshi Yata1https://orcid.org/0000-0001-6814-4463Kento Egashira2Makoto Aoshima3Aki Ishii4Suchetha Cooray5https://orcid.org/0000-0002-9217-1696Kouichiro Nakanishi6https://orcid.org/0000-0002-6939-0372Kotaro Kohno7https://orcid.org/0000-0002-4052-2394Kai T. Kono8Division of Particle and Astrophysical Science, Nagoya University , Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan ; tsutomu.takeuchi.ttt@gmail.com; The Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics , 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, JapanInstitute of Mathematics, University of Tsukuba , 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, JapanDepartment of Information Sciences, Tokyo University of Science , 2641 Yamazaki, Noda, Chiba 278-8510, Japan; Graduate School of Science and Technology, University of Tsukuba , 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, JapanInstitute of Mathematics, University of Tsukuba , 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, JapanDepartment of Information Sciences, Tokyo University of Science , 2641 Yamazaki, Noda, Chiba 278-8510, JapanNational Astronomical Observatory of Japan, National Institutes of Natural Sciences (NINS) , 2-21-1 Osawa, Mitaka, Tokyo 181-8588, JapanNational Astronomical Observatory of Japan, National Institutes of Natural Sciences (NINS) , 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan; Department of Astronomy, School of Science, Graduate University for Advanced Studies (SOKENDAI) , 2-21-1 Osawa, Mitaka, Tokyo 181-8588, JapanInstitute of Astronomy, Graduate School of Science, The University of Tokyo , 2-21-1 Osawa, Mitaka, Tokyo, 181-0015, JapanDivision of Particle and Astrophysical Science, Nagoya University , Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan ; tsutomu.takeuchi.ttt@gmail.comIn astronomy, if we denote the dimension of data as d and the number of samples as n , we often find a case with n ≪ d . Traditionally, such a situation is regarded as ill-posed, and there was no choice but to discard most of the information in data dimensions to let d < n . The data with n ≪ d is referred to as the high-dimensional low sample size (HDLSS). To deal with HDLSS problems, a method called high-dimensional statistics has rapidly developed in the last decade. In this work, we first introduce high-dimensional statistical analysis to the astronomical community. We apply two representative methods in the high-dimensional statistical analysis methods, noise-reduction principal component analysis (NRPCA) and automatic sparse principal component analysis (A-SPCA), 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 an example of a typical HDLSS data set. First, we analyzed the original data, including the Doppler shift due to the systemic rotation. High-dimensional PCA can precisely describe the spatial structure of the rotation. We then applied to the Doppler-shift corrected data to analyze more subtle spectral features. NRPCA and R-SPCA were able to quantify the very complicated characteristics of the ALMA spectra. Particularly, we were able to extract information on the global outflow from the center of NGC 253. This method can also be applied not only to spectroscopic survey data, but also to any type of data with a small sample size and large dimension.https://doi.org/10.3847/1538-4365/ad2517Astrostatistics techniquesStarburst galaxiesMolecular spectroscopyMolecular gasMillimeter astronomySubmillimeter astronomy |
| spellingShingle | Tsutomu T. Takeuchi Kazuyoshi Yata Kento Egashira Makoto Aoshima Aki Ishii Suchetha Cooray Kouichiro Nakanishi Kotaro Kohno Kai T. Kono High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 The Astrophysical Journal Supplement Series Astrostatistics techniques Starburst galaxies Molecular spectroscopy Molecular gas Millimeter astronomy Submillimeter astronomy |
| title | High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 |
| title_full | High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 |
| title_fullStr | High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 |
| title_full_unstemmed | High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 |
| title_short | High-dimensional Statistical Analysis and Its Application to an ALMA Map of NGC 253 |
| title_sort | high dimensional statistical analysis and its application to an alma map of ngc 253 |
| topic | Astrostatistics techniques Starburst galaxies Molecular spectroscopy Molecular gas Millimeter astronomy Submillimeter astronomy |
| url | https://doi.org/10.3847/1538-4365/ad2517 |
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