Svd Pc Importance

svd-pc-importance

Earth as a Proxy Exoplanet: Deconstructing and Reconstructing Spectrophotometric Light Curves — Gu et al. (2020) (arXiv:2012.10556, 2020)

What this evaluates

This protocol evaluates the ability of singular value decomposition (SVD) and gradient boosting regression trees (GBRT) to decompose unresolved planetary light curves into principal components that physically correspond to specific surface and atmospheric features. It quantifies feature attribution through variance explained, model importance scores, and linear correlations.

Datasets

• DSCOVR/EPIC Earth light curves — total ?; splits: test (-1)

Metrics

• SVD eigenvalue variance ratio (primary) — range: [0, 1]
  • The proportion of total temporal variance in the light curve matrix captured by each principal component, calculated as the squared singular value divided by the sum of all squared singular values.
• GBRT relative importance — range: [0, 1]
  • The normalized contribution of each spatial feature fraction to predicting a specific PC time series, derived from a gradient boosting regression tree model.
• Pearson correlation coefficient — range: other
  • Linear correlation between the time series of a spatial feature fraction and its corresponding PC, measuring monotonic relationship strength.
• Synthetic-observed light curve agreement — range: other
  • Visual and spectral comparison between disk-integrated synthetic light curves (reconstructed from altered spatial features) and actual observations to validate PC interpretations.

Input / output format

Input: Time-series of disk-integrated multi-wavelength reflectance spectra (light curves) for a planetary body, alongside time-varying fractional coverage of spatial features (ocean, desert, snow/ice, vegetation, low/high clouds).

Output: Principal component time series and spectra, along with feature importance scores and correlation coefficients linking PCs to spatial surface/atmosphere fractions.

Scoring recipe

# 1. SVD decomposition of light curve matrix X (time x wavelength)
U, S, Vt = np.linalg.svd(X, full_matrices=False)
variance_ratio = S**2 / np.sum(S**2)

# 2. GBRT regression to predict PC time series from spatial feature fractions
model = GradientBoostingRegressor()
model.fit(feature_fractions, pc_time_series)
importance = model.feature_importances_ / np.sum(model.feature_importances_)

# 3. Correlation analysis
corr = np.corrcoef(feature_fractions, pc_time_series)[0, 1]

Common pitfalls

• PC ordering can switch between observed and synthetic data when eigenvalues are similar (~10% difference), requiring careful spectral matching rather than relying on index order.
• Averaging spatial features in synthetic reconstruction loses fine-grained temporal variation, artificially lowering eigenvalues and obscuring minor features.
• UV channels are dominated by atmospheric scattering/ozone not captured by surface features, complicating feature attribution and requiring exclusion or separate modeling.

Evidence (verbatim from paper)

We use SVD to separate the contributions of different spatial features to the light curves. ... evaluate their relative importance using the GBRT model (Figure 4). Linear correlations between the fraction of three spatial features and their corresponding PCs suggested by the GBRT model result are shown in Figure 5.

Citation

@misc{gu2020earthproxy,
  title={Earth as a Proxy Exoplanet: Deconstructing and Reconstructing Spectrophotometric Light Curves},
  author={Gu et al. (2020)},
  year={2020},
  note={arXiv:2012.10556}
}

• arXiv: 2012.10556