Tree-Structured Orthonormal Decomposition of the Aitchison Simplex
Compositional data -- vectors encoding relative proportions -- arise across scientific domains, including ecology, geochemistry, and genomics. The features in these data often come with known hierarchical structure (e.g., taxonomies, phylogenies, ontologies), yet existing methods either ignore this structure, discard the intrinsic Aitchison geometry, are designed for binary trees, or yield incomplete coordinate systems. We describe PolyILR, a canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology. Our construction defines a weighted local geometry at each internal node capturing full branching structure, then lifts these to a global orthonormal b...
| Authors | Daisuke Yamada, Qijun Zhang, Travis Pence et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 June 2026 |
| Last updated at source | 10 June 2026 |
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