Correlation dimension analysis and dimensionality reduction of OGLE data for stellar object characterization

The Optical Gravitational Lensing Experiment (OGLE) project provides a rich data set of stellar objects with multiple features such as their positions, magnitudes, temporal, and other photometric parameters. This paper attempts to utilize sophisticated computational and statistical techniques to investigate the OGLE data set, which discloses intrinsic dimensional structure in feature space and dimension reduction for better interpretability. Preprocessing of the data set was initially done to resolve inconsistencies and missing values to present a strong and firm basis for analysis. The data set is normalized, and Principal Component Analysis (PCA) is employed for dimension reduction to retain only the most significant features. Not only does the reduction make the data set interpretable and easy to handle, but it also highlights the principal components responsible for the largest variance in the data. In order to study the intrinsic structure of the data set in greater depth, we calculate the distance matrix of the principal components and employ it to estimate the correlation dimension D_2 , a measure of intrinsic dimensionality. This study examines the scaling behavior of the correlation function with different radii and, hence, we can understand the intrinsic structure of the observational parameter space. Our results indicate D_2 = 1.670 ± 0.18 for the normalized feature data, implying strong correlations among the observables.