カテゴリー: paper

M. Uemura, K. S. Kawabata, S. Ikeda, K. Maeda, H. Y. Wu, K. Watanabe, S. Takahashi, and I. Fujishiro, “Data-driven approach to Type Ia supernovae: variable selection on the peak luminosity and clustering in visual analytics”, Journal of Physics: Conference Series, 699, id. 012009, 2016

 

Type Ia supernovae (SNIa) have an almost uniform peak luminosity, so that they are used as “standard candle” to estimate distances to galaxies in cosmology. In this article, we introduce our two recent works on SNIa based on data-driven approach. The diversity in the peak luminosity of SNIa can be reduced by corrections in several variables. The color and decay rate have been used as the explanatory variables of the peak luminosity in past studies. However, it is proposed that their spectral data could give a better model of the peak luminosity. We use cross-validation in order to control the generalization error and a LASSO-type estimator in order to choose the set of variables. Using 78 samples and 276 candidates of variables, we confirm that the peak luminosity depends on the color and decay rate. Our analysis does not support adding any other variables in order to have a better generalization error. On the other hand, this analysis is based on the assumption that SNIa originate in a single population, while it is not trivial. Indeed, several sub-types possibly having different nature have been proposed. We used a visual analytics tool for the asymmetric biclustering method to find both a good set of variables and samples at the same time. Using 14 variables and 132 samples, we found that SNIa can be divided into two categories by the expansion velocity of ejecta. Those examples demonstrate that the data-driven approach is useful for high-dimensional large-volume data which becomes common in modern astronomy.

M. Uemura, K. S. Kawabata, S. Ikeda, and K. Maeda, “Variable selection for modeling the absolute magnitude at maximum of Type Ia supernovae”, PASJ, vol. 67, 55, 2015

 

We discuss what is an appropriate set of explanatory variables in order to predict the absolute magnitude at the maximum of Type Ia supernovae. In order to have a good prediction, the error for future data, which is called the “generalization error,” should be small. We use cross-validation in order to control the generalization error and a LASSO-type estimator in order to choose the set of variables. This approach can be used even in the case that the number of samples is smaller than the number of candidate variables. We studied the Berkeley supernova database with our approach. Candidates for the explanatory variables include normalized spectral data, variables about lines, and previously proposed flux ratios, as well as the color and light-curve widths. As a result, we confirmed the past understanding about Type Ia supernovae: (i) The absolute magnitude at maximum depends on the color and light-curve width. (ii) The light-curve width depends on the strength of Si II. Recent studies have suggested adding more variables in order to explain the absolute magnitude. However, our analysis does not support adding any other variables in order to have a better generalization error.