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About this paper
Daisuke Yamada, Qijun Zhang, Travis Pence, Barbara B. Bendlin, Federico Rey, Vikas Singh
PolyILR offers a canonical orthonormal decomposition for compositional data on the Aitchison simplex, explicitly incorporating arbitrary tree topologies, including polytomies. This method provides stable, interpretable features for multiscale inference, generalizing existing approaches and demonstrating utility in microbiome and single-cell analyses.
Key insights
- A canonical orthonormal decomposition for compositional data on any tree topology can be constructed by combining local contrast subspaces at each internal node with a global weighting scheme.
- Weighted Helmert contrasts provide a deterministic and interpretable approach to define orthogonal features at each node, ensuring global orthonormality when projected onto the leaves.
- The mathematical equivalence between the centered logit space of a softmax classifier and the Aitchison tangent space allows PolyILR to analyze hierarchical predictions in machine learning models.
Summary by alphaXiv.
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