Line Index of A-Type Stellar Astronomical Spectrum Predict Effective Temperature by Ridge Regression Model
XUE Ren-zheng1, CHEN Shu-xin1*, HUANG Hong-ben2
1. School of Computer and Control Engineering, Qiqihar University, Qiqihar 161006, China
2. School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, China
Abstract：Line index is widely used in describing the features of spectral lines for astronomical objects because it retains the main physical characteristic information of these objects. Based on line index, a multi-parameter model for regression analysis could be used to uncover co-variation relationship of data and the inherent laws of spectral lines. The observed spectra released by LAMOST, which has the highest spectra acquisition capability, provide us with real data for establishing a robust regression model. The multivariate linear regression was applied to get the co-linearity of the dependent variables, however, it resulted in large variance. It is unstable to obtain the least squares regression coefficient sometimes. Especially, it’s difficult for the multivariate linear regression to obtain the evaluation coefficient of independent predictor from the regression equation. In this paper, we use the A-type stellar Lick line index in the LAMOST survey data as the data source. Selecting the spectra with effective temperature (Teff) from 7 000 to 8 500 K, and the signal-to-noise ratio higher than 50 to realize the regression analysis. After a set of linear biased estimation experiment for A-type stars, the method of ridge regression training was employed. In the catalogue of LAMOST data release 5 (DR5), 86 097 A-type spectra have provided the Teff value. After statistical analysis of the eigenvalues of 26 line indices, the kp12, halpha12 and hgamma12 with similar distribution and bandwidth of 12 Å were selected to reduce the data redundance. The number of variety was optimized for the redundant variable variance expansion factor (VIF) coefficient. Two regression experiments selected the same observation dataset to locally fit the regression scatter, using the overall contour of the scatter plot to generate a high-density scatter plot, highlighting the data-intensive region with the color difference transparency. The results show that both the multiple linear regression and the ridge regression algorithm can determine the effective temperature (Teff) of the A-type star through the low-resolution spectrum, but the co-linearity data analysis has some biased estimation. The ridge regression model can more accurately predict the effective temperature of A type stars from the low resolution spectra.
Key words：Stellar spectra; LAMOST (Large sky area multi-object fiber spectroscopy telescope); Ridge regression; Linear model; Lick line index
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