  The growing number of exoplanet discoveries and advances in machine learning
techniques have opened new avenues for exploring and understanding the
characteristics of worlds beyond our Solar System. In this study, we employ
efficient machine learning approaches to analyze a dataset comprising 762
confirmed exoplanets and eight Solar System planets, aiming to characterize
their fundamental quantities. By applying different unsupervised clustering
algorithms, we classify the data into two main classes: 'small' and 'giant'
planets, with cut-off values at $R_{p}=8.13R_{\oplus}$ and
$M_{p}=52.48M_{\oplus}$. This classification reveals an intriguing distinction:
giant planets have lower densities, suggesting higher H-He mass fractions,
while small planets are denser, composed mainly of heavier elements. We apply
various regression models to uncover correlations between physical parameters
and their predictive power for exoplanet radius. Our analysis highlights that
planetary mass, orbital period, and stellar mass play crucial roles in
predicting exoplanet radius. Among the models evaluated, the Support Vector
Regression consistently outperforms others, demonstrating its promise for
obtaining accurate planetary radius estimates. Furthermore, we derive
parametric equations using the M5P and Markov Chain Monte Carlo methods.
Notably, our study reveals a noteworthy result: small planets exhibit a
positive linear mass-radius relation, aligning with previous findings.
Conversely, for giant planets, we observe a strong correlation between
planetary radius and the mass of their host stars, which might provide
intriguing insights into the relationship between giant planet formation and
stellar characteristics.
