Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data
Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation. A scale-invariant contamination model built from multiplicative perturbation combines with a propagation theorem showing that corruption of a single raw part induces a rank-one shift of the log-ratio vector, with direction determined by...
| Authors | Matthias Templ |
|---|---|
| Primary category | stat.ML |
| Published | 29 May 2026 |
| Last updated at source | 29 May 2026 |
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