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- W4286984920 abstract "The shape of a planar curve and/or landmark configuration is considered its equivalence class under translation, rotation and scaling, its form its equivalence class under translation and rotation while scale is preserved. We extend generalized additive regression to models for such shapes/forms as responses respecting the resulting quotient geometry by employing the squared geodesic distance as loss function and a geodesic response function to map the additive predictor to the shape/form space. For fitting the model, we propose a Riemannian $L_2$-Boosting algorithm well suited for a potentially large number of possibly parameter-intensive model terms, which also yields automated model selection. We provide novel intuitively interpretable visualizations for (even non-linear) covariate effects in the shape/form space via suitable tensor-product factorization. The usefulness of the proposed framework is illustrated in an analysis of 1) astragalus shapes of wild and domesticated sheep and 2) cell forms generated in a biophysical model, as well as 3) in a realistic simulation study with response shapes and forms motivated from a dataset on bottle outlines." @default.
- W4286984920 created "2022-07-25" @default.
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- W4286984920 date "2021-09-06" @default.
- W4286984920 modified "2023-09-28" @default.
- W4286984920 title "Functional additive models on manifolds of planar shapes and forms" @default.
- W4286984920 doi "https://doi.org/10.48550/arxiv.2109.02624" @default.
- W4286984920 hasPublicationYear "2021" @default.
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