Dimensionality Reduction Techniques for Exoplanet Transit Spectroscopy

We investigate dimensionality reduction techniques for the analysis of spectral data from transiting exoplanets observed with the Hubble and James Webb space telescopes. The fundamental challenge is the inverse problem, where one tries to infer from the observed data the underlying parameters and properties of the targeted exoplanet. As a pre-processing step for any subsequent Machine Learning (ML) approach, we use dimensional analysis to identify the relevant dimensionless combinations of planet-specific variables and reduce the number of independent inputs, which improves the performance of the ML analysis. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters, which affect the characterization of an exoplanet atmosphere through transit spectroscopy.

We perform exploratory data analysis based on summary statistics and quantify the existing correlations in the high-dimensional spectral data. We linearly transform the observed spectra to more appropriate bases and utilize dimensionality reduction and manifold learning techniques to study and optimally extract the information content of the data. The new representation allows for informative visualization, which aids the scientific interpretability of the data.

We identify and visualize structures in the reduced-dimensionality bases, namely, well-defined spectral branches corresponding to different chemical regimes of the underlying atmospheres. The identified individual branches are also successfully being separated using a variety of clustering techniques. This method can be used to quickly determine and classify the atmospheric chemical composition of observed transiting planets complimenting already existing spectroscopic tools.