CD-HPF: new habitability score via data analytic modeling

Abstract

The search for life on the planets outside the Solar System can be broadly classified into the following: looking for Earth-like conditions or the planets similar to the Earth (Earth similarity), and looking for the possibility of life in a form known or unknown to us (habitability). The two frequently used indices, Earth Similarity Index (ESI) and Planetary Habitability Index (PHI), describe heuristic methods to score habitability in the efforts to categorize different exoplanets (or exomoons). ESI, in particular, considers Earth as the reference frame for habitability, and is a quick screening tool to categorize and measure physical similarity of any planetary body with the Earth. The PHI assesses the potential habitability of any given planet, and is based on the essential requirements of known life: presence of a stable and protected substrate, energy, appropriate chemistry and a liquid medium. We propose here a different metric, a Cobb–Douglas Habitability Score (CDHS), based on Cobb–Douglas habitability production function (CD-HPF), which computes the habitability score by using measured and estimated planetary input parameters. As an initial set, we used radius, density, escape velocity and surface temperature of a planet. The values of the input parameters are normalized to the Earth Units (EU). The proposed metric, with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima, and scales up to accommodate finitely many input parameters. The model is elastic, and, as we discovered, the standard PHI turns out to be a special case of the CDHS. Computed CDHS scores are fed to K-NN (K-Nearest Neighbor) classification algorithm with probabilistic herding that facilitates the assignment of exoplanets to appropriate classes via supervised feature learning methods, producing granular clusters of habitability. The proposed work describes a decision-theoretical model using the power of convex optimization and algorithmic machine learning.