Exploring Dimensionality Reduction of SDSS Spectral Abundances

High-resolution stellar spectra offer valuable insights into atmospheric parameters and chemical compositions. However, their inherent complexity and high-dimensionality present challenges in fully utilizing the information they contain. In this study, we utilize data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) within the Sloan Digital Sky Survey IV (SDSS-IV) to explore latent representations of chemical abundances by applying five dimensionality reduction techniques: PCA, t-SNE, UMAP, Autoencoder, and VAE. Through this exploration, we evaluate the preservation of information and compare reconstructed outputs with the original 19 chemical abundance data. Our findings reveal a performance ranking of PCA < UMAP < t-SNE < VAE < Autoencoder, through comparing their explained variance under optimized MSE. The performance of non-linear (Autoencoder and VAE) algorithms has approximately 10\% improvement compared to linear (PCA) algorithm. This difference can be referred to as the "non-linearity gap." Future work should focus on incorporating measurement errors into extension VAEs, thereby enhancing the reliability and interpretability of chemical abundance exploration in astronomical spectra.