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 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. 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 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.

Seven Earth-sized planets, known as the TRAPPIST-1 system was discovered with great fanfare in the last week of February 2017. Three of these planets are in the habitable zone of their star, making them potentially habitable planets a mere 40 light years away. Discovery of the closest potentially habitable planet to us just a year before -Proxima b and a realization that Earth-type planets in circumstellar habitable zones are a common occurrence provides the impetus to the existing pursuit for life outside the Solar System. The search for life has two goals essentially: Earth similarity and habitability. An index was recently proposed, Cobb-Douglas Habitability Score (CDHS), based on Cobb-Douglas habitability production function, which computes the habitability score by using measured and estimated planetary parameters like radius, density, escape velocity and surface temperature of a planet. The proposed metric, with exponents accounting for metric elasticity, is endowed with analytical properties that ensure global optima and can be scaled to accommodate a finite number of input parameters. We show here that the model is elastic, and the conditions on elasticity to ensure global maxima can scale as the number of predictor parameters increase. K-Nearest Neighbor classification algorithm, embellished with probabilistic herding and thresholding restriction, utilizes CDHS scores and labels exoplanets to appropriate classes via feature-learning methods. The algorithm works on top of a decision-theoretical model using the power of convex optimization and machine learning. The goal is to classify the recently discovered exoplanets into the "Earth League" and other classes. A second approach, based on a novel feature-learning and tree-building method classifies the same planets without computing the CDHS of the planets and produces a similar outcome. The convergence of the two different approaches indicates the strength of the proposed scheme and the likelihood of the potential habitability of the recent discoveries. 2016). This planet generated a lot of stir in the news (Witze, 2016) because it is located in the habitable zone and its mass is in the Earth's mass range: 1.27 − 3 M ⊕ , making it a potentially habitable planet (PHP) and an immediate destination for the Breakthrough Starshot initiative (Starshot, 2016). A few months after the announcement of Proxima b, another family of terrestrial-size exoplanets -the TRAPPIST-1 systemwas discovered (Gillon, 2016).This work is motivated by testing the efficacy of the suggested model, CDHS, in determining the habitability score, the proximity to the "Earth-League", of the recently discovered Proxima b. The habitability score model has been found to work well in classifying previously known exoplanets in terms of potential habitability. Therefore it was natural to test whether the model can also classify it as potentially habitable by computing its habitability score. This could indicate whether the model may be extended for a quick check of the potential habitability of n...

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We explore the efficacy of machine learning (ML) in characterizing exoplanets into different classes. The source of the data used in this work is University of Puerto Rico's Planetary Habitability Laboratory's Exoplanets Catalog (PHL-EC). We perform a detailed analysis of the structure of the data and propose methods that can be used to effectively categorize new exoplanet samples. Our contributions are two fold. We elaborate on the results obtained by using ML algorithms by stating the accuracy of each method used and propose the best paradigm to automate the task of exoplanet classification. The exploration led to the development of new methods fundamental and relevant to the context of the problem and beyond. Data exploration and experimentation methods also result in the development of a general data methodology and a set of best practices which can be used for exploratory data analysis experiments.