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- W4287250908 abstract "Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a differentiable function that maps arbitrary inputs of a Euclidean space onto the manifold. In this paper, we establish a set of desirable properties for such mapping, and in particular highlight the importance of pre-images connectivity/convexity. We illustrate these properties with a case study regarding 3D rotations. Through theoretical considerations and methodological experiments on a variety of tasks, we review various differentiable mappings on the 3D rotation space, and conjecture about the importance of their local linearity. We show that a mapping based on Procrustes orthonormalization generally performs best among the mappings considered, but that a rotation vector representation might also be suitable when restricted to small angles." @default.
- W4287250908 created "2022-07-25" @default.
- W4287250908 creator A5022956258 @default.
- W4287250908 date "2021-03-30" @default.
- W4287250908 modified "2023-09-27" @default.
- W4287250908 title "Deep Regression on Manifolds: A 3D Rotation Case Study" @default.
- W4287250908 doi "https://doi.org/10.48550/arxiv.2103.16317" @default.
- W4287250908 hasPublicationYear "2021" @default.
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