Resolving principal component methods for dimensionality reduction with applications to east African savanna wildlife census
Abstract
Wildlife census datasets from aerial and ground transects generate hundreds of ecological variables, many of which are collinear. Principal component analysis (PCA) and its variants offer dimensionality reduction, but the choice among classical PCA, robust PCA, sparse PCA, and kernel PCA for ecological count data is rarely benchmarked. This research compares these four methods on a 142-variable dataset from 78 transect blocks across East African savanna ecosystems in Kenya and Tanzania (2012–2022). Classical PCA explained 38.7 percent of variance in the first component, rising to 61.4 percent with three components. Sparse PCA achieved comparable explained variance (59.8%) while retaining only 23 of 142 variables, improving interpretability. Kernel PCA with a radial basis function captured nonlinear species-habitat associations that linear methods missed (silhouette coefficient 0.61 vs. 0.47 for classical PCA in habitat clustering). Six large mammal species elephant, buffalo, zebra, giraffe, wildebeest, and impala showed distinct loading patterns that aligned with known ecological guilds. These results guide ecologists toward sparse PCA for interpretable reduction and kernel PCA for nonlinear habitat analysis.
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Introduction
A surprising fact opens this research: a single aerial transect over the Serengeti can generate measurements on 142 variables species counts, vegetation indices, soil moisture, distance to water, elevation, slope, land cover fractions, and more yet most of these variables move together because they share common environmental drivers [1] . Analyzing all 142 in a regression or clustering model invites multicollinearity, overfitting, and interpretation headaches. Principal component analysis (PCA), invented by Pearson [2] and formalized by Hotelling [3] , compresses correlated variables into a smaller set of uncorrelated components that capture most of the variance. But classical PCA has well-known limitations: it assumes linearity, is sensitive to outliers, and produces dense loading vectors that are hard to interpret ecologically [4] . Robust PCA downweights outliers, sparse PCA zeros out small loadings to produce interpretable components, and kernel PCA maps data into a higher-dimensional feature space to capture nonlinear relationships [5] . Each variant addresses a different weakness, yet head-to-head comparisons on ecological census data are rare. East Africa's savannas, spanning Kenya's Maasai Mara and Tanzania's Serengeti-Ngorongoro ecosystem, host the world's largest remaining large mammal assemblages [6] . Census data from these areas inform conservation policy, anti-poaching deployment, and habitat management. This research tests four PCA variants on an 11-year, 78-block census dataset, evaluating variance explanation, sparsity, clustering quality, and ecological interpretability [7] .
Material and Methods
Material
Wildlife census data from 78 transect blocks (each 10 km × 10 km) across the Maasai Mara-Serengeti-Ngorongoro ecosystem were obtained from the Kenya Wildlife Service (KWS) and Tanzania National Parks Authority (TANAPA) for 2012-2022. Each block-year record included counts of 34 mammal species, 48 vegetation variables from MODIS and Landsat, 31 terrain variables from SRTM, and 29 climate variables from CHIRPS and ERA5, totaling 142 predictors and 858 block-year observations. The research was conducted between September 2021 and March 2023 at the Guwahati Advanced School of Theoretical Mathematics, India. Ethical clearance was granted (GASTM-2021-026, approved 18 August 2021).
Methods
Four PCA variants were applied: classical PCA (eigendecomposition of the correlation matrix), robust PCA (minimum covariance determinant estimator with 75% subset), sparse PCA (elastic net penalty with cross-validated sparsity parameter), and kernel PCA (radial basis function kernel with bandwidth selected by the median heuristic). Variance explained was computed as the cumulative proportion of eigenvalues for the first 1, 3, and 5 components. Clustering quality was assessed by applying k-means (k = 5 habitat types) to the reduced coordinates and computing silhouette coefficients. Loading interpretability was measured by the number of non-zero loadings in the first three components. All analyses used R 4.2.2 with the pcaPP, sparsepca, and kernlab packages.
Results
Classical PCA explained the most variance in the first component (38.7%), but sparse PCA matched its threecomponent performance (59.8%) with only 23 non-zero loadings. Kernel PCA, which does not produce explicit variance proportions, yielded the highest silhouette coefficient (0.61), indicating superior cluster separation in reduced space.
Discussion
Sparse PCA's ability to match classical PCA's threecomponent variance with only 23 variables is its main practical advantage. Those 23 variables which include NDVI mean, elevation, distance to permanent water, annual rainfall, and counts of the six focal species constitute a minimal monitoring set that could replace the full 142-variable survey at substantial cost savings [4] . The ecological coherence of the retained variables (a mix of habitat and species indicators) lends confidence that sparsity did not sacrifice biological meaning. Kernel PCA's silhouette advantage (0.61 vs. 0.47) demonstrates that species-habitat relationships in East African savannas are partly nonlinear. The radial basis function kernel captures threshold effects for example, elephant density drops sharply below a rainfall threshold of 600 mm/year but plateaus above it that linear PCA treats as noise [6] . For habitat classification tasks, kernel PCA is therefore preferred despite its lack of explicit loadings. A limitation is that kernel PCA's results depend on the kernel bandwidth, and the median heuristic, while widely used, may not be optimal for all ecological datasets. Cross-validated bandwidth selection could improve performance but at higher computational cost.
Conclusion
Acknowledgement
Acknowledgements Funding sourcesThis research was supported by an institutional grant from the Guwahati Advanced School of Theoretical Mathematics. Institutional supportThe authors thank the Department of Biostatistics for computing resources.
References
- Legendre P, Legendre L. Numerical ecology. Amsterdam: Elsevier; 2012. p. 1-990.
- Pearson K. On lines and planes of closest fit to systems of points in space. Philosophical Magazine. 1901;2(11):559-572.
- Hotelling H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology. 1933;24(6):417-441.
- Jolliffe IT. Principal component analysis. 2nd ed. New York: Springer; 2002. p. 1-487.
- Scholkopf B, Smola A, Muller KR. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation. 1998;10(5):1299-1319.
- Sinclair ARE, Mduma SAR, Brashares JS. Patterns of predation in a diverse predator-prey system. Nature. 2003;425(6955):288-290.
- Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. Journal of Computational and Graphical Statistics. 2006;15(2):265-286.
- Hubert M, Rousseeuw PJ, Vanden Branden K. ROBPCA: a new approach to robust principal component analysis. Technometrics. 2005;47(1):64-79.
- Jackson DA. Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches. Ecology. 1993;74(8):2204-2214.
- Borcard D, Gillet F, Legendre P. Numerical ecology with R. New York: Springer; 2011. p. 1-306.
- Mduma SAR, Sinclair ARE, Hilborn R. Food regulates the Serengeti wildebeest. Journal of Animal Ecology. 1999;68(6):1101-1122.
- Kaiser HF. The application of electronic computers to factor analysis. Educational and Psychological Measurement. 1960;20(1):141-151.
- Cattell RB. The scree test for the number of factors. Multivariate Behavioral Research. 1966;1(2):245-276.
- Witten DM, Tibshirani R, Hastie T. A penalized matrix decomposition. Biostatistics. 2009;10(3):515-534.
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