论文标题
用固定的方向学习多面体
Learning polytopes with fixed facet directions
论文作者
论文摘要
我们考虑通过有限的许多支持功能评估来重建固定方向的多型的任务。我们表明，对于固定的简单普通风扇，最小二乘估计值是由凸二次程序给出的。我们研究溶液集的几何形状，并给出组合表征，以使重建的独特性。我们提供了一种算法，在轻度假设下，随着噪声支持函数评估的数量增加，输入形状会收敛到未知的输入形状。如果删除对正常风扇的限制，我们还讨论了结果的局限性。
We consider the task of reconstructing polytopes with fixed facet directions from finitely many support function evaluations. We show that for a fixed simplicial normal fan the least-squares estimate is given by a convex quadratic program. We study the geometry of the solution set and give a combinatorial characterization for the uniqueness of the reconstruction in this case. We provide an algorithm that, under mild assumptions, converges to the unknown input shape as the number of noisy support function evaluations increases. We also discuss limitations of our results if the restriction on the normal fan is removed.
