Canonical Correlation and Regression Analyses of Globular Clusters in Milky Way Galaxy

摘要

Study about complex relationships between different characteristics of an astronomical object is a momentous research topic in Astronomy as well as Astrostatistics. Correlation and regression analyses are the techniques which can quantify such relationships. A study on the relationships between different parameters of globular clusters in the Milky Way is used to uncover the formation and evolution of the Milky Way galaxy. We consider a sample of 134 globular clusters in the Milky Way galaxy from the current catalog of globular clusters (2010 edition) compiled by William E. Harris. We have divided the globular clusters under study into three subpopulations (metal-rich disk, metal-poor disk, and metal-poor halo) according to the mixing proportion values of the fitted mixture model on metallicity values of clusters and distance from the galactic center. We investigate relationships between different parameter sets in different subpopulations using Canonical Correlation Analysis via Projection Pursuit (CCAPP) and Kernel Canonical Correlation Analysis (KCCA) using Radial Basis kernel function. According to the findings of CCAPP and KCCA, photometric and structural parameter sets are highly associated. For the more elaborate study about these relationships, we have considered Multiple Regression Analysis with structure parameters as explanatory variables and cluster luminosity as response variables. We face multicollinearity problems (using variance inflation factor) among structure parameters and fit regression models specially designed for tackling multicollinearity problem (Ridge, LASSO or Elastic net). It has been found that some structure parameters have nonlinear relationships with cluster luminosity and we have explained such nonlinear relationships using polynomial regression models.