  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, ESI and PHI, describe heuristic methods to score
similarity/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
probability that life in some form may exist on any given world, and is based
on the essential requirements of known life: 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 calculated planetary input parameters. The proposed
metric, with exponents accounting for metric elasticity, is endowed with
verifiable analytical properties that ensure global optima, and is scalable to
accommodate finitely many input parameters. The model is elastic, does not
suffer from curvature violations and, as we discovered, the standard PHI is a
special case of CDHS. Computed CDHS scores are fed to K-NN (K-Nearest
Neighbour) 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.
