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Documentation Index

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ExoProfiler’s PCA step compresses 12 physical and orbital variables into 4 principal components that together retain 90.35% of the total variance. Each component captures a distinct physical dimension of the exoplanet population, making it possible to interpret the cluster structure in astrophysical terms.

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Variance Breakdown

ComponentIndividual VarianceCumulative VariancePhysical Dimension
PC144.65%44.65%Orbital scale
PC229.56%74.21%Stellar-thermal gradient
PC39.41%83.62%Orbital eccentricity
PC46.74%90.35%Metallicity & planet size
Three components alone do not meet the 85% variance threshold (83.62%). Four components are retained, reaching 90.35%.

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PC1 — Orbital Scale Dimension

PC1 is the single most informative axis, capturing 44.65% of total variance. Its dominant loadings reflect the geometry and timing of planetary orbits.
  • Largest contributor: pl_orbsmax (loading: 0.816)
  • Second contributor: pl_orbper (loading: 0.386)
  • Third contributor: pl_orbeccen (loading: 0.219)
Interpretation: PC1 primarily captures the size and period of the orbit. Planets with large positive PC1 scores have wide, long-period orbits; negative PC1 scores indicate compact, short-period orbits.

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PC2 — Stellar-Thermal Gradient

PC2 accounts for 29.56% of variance and contrasts the properties of the host star against the resulting thermal environment of the planet.
  • st_logg: +0.443 (higher surface gravity)
  • st_rad: -0.404 (smaller stellar radius)
  • pl_eqt: -0.371 (cooler equilibrium temperature)
  • st_mass: -0.365 (lower stellar mass)
Interpretation: PC2 contrasts high-gravity dwarf stars against large, massive stars with hotter planetary environments.

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PC3 — Eccentricity Dimension

PC3 captures 9.41% of variance and is almost entirely driven by a single physical quantity.
  • pl_orbeccen: +0.942 (dominant contributor)
  • pl_orbsmax: -0.239
  • pl_bmasse: +0.151
Interpretation: PC3 isolates orbital eccentricity. Most of the population clusters near circular orbits; the highly eccentric tail drives this component.

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PC4 — Metallicity and Planetary Size

PC4 contributes 6.74% of variance and preserves stellar chemistry information not captured by the first three components.
  • st_met: +0.829 (dominant contributor)
  • pl_bmasse: +0.293
  • pl_rade: +0.267
Interpretation: PC4 preserves stellar metallicity information that wasn’t captured in the first three components, along with planetary bulk properties.

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Sign Convention

The global sign of a PCA component is arbitrary. Inverting all loadings and scores within a component yields an equivalent solution. Do not interpret the sign of an individual loading in isolation — compare relative signs within the component.

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Loading Reference Table

The table below shows the contribution of each of the 12 input variables to each principal component. All values are rounded to three decimal places and sourced directly from data/processed/pca/pca_loadings.csv.
VariablePC1PC2PC3PC4
pl_orbsmax0.8160.230-0.2390.091
pl_orbper0.3860.156-0.036-0.068
pl_orbeccen0.2190.0170.942-0.166
st_met0.024-0.2000.0800.829
st_logg-0.1900.4430.0730.241
st_rad0.162-0.404-0.034-0.142
pl_eqt-0.069-0.371-0.059-0.073
st_mass0.160-0.365-0.040-0.083
pl_bmasse0.122-0.2100.1510.293
pl_rade0.096-0.2210.0890.267
st_teff0.130-0.269-0.054-0.146
pl_insol-0.060-0.295-0.052-0.061

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Loading the Loadings

import pandas as pd

loadings = pd.read_csv('data/processed/pca/pca_loadings.csv', index_col=0)
print(loadings)

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