实线上与Gromov-Wasserstein距离有关的分配问题

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2023-06-23 DOI:10.1137/22m1497808
Robert Beinert, Cosmas Heiss, Gabriele Steidl
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引用次数: 2

摘要

设和为实数。我们通过一个例子证明了分配问题\begin{align*} \max_{\sigma \in S_n} F_\sigma (x,y) := \frac 12 \sum_{i,k=1}^n |x_i- x_k|^\alpha \, |y_{\sigma (i)}- y_{\sigma (k)}|^\alpha, \quad \alpha \gt 0, \end{align*}一般既不能用同置换解决,也不能用反同置换解决。实际上,根据点的数量,上述最大值可以是任意距离和的值。处理这种赋值问题的动机来自于它们与Gromov-Wasserstein距离的关系,后者最近在成像和形状分析中受到了很多关注。
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On Assignment Problems Related to Gromov–Wasserstein Distances on the Real Line
Let and , , be real numbers. We show by an example that the assignment problem \begin{align*} \max_{\sigma \in S_n} F_\sigma (x,y) := \frac 12 \sum_{i,k=1}^n |x_i- x_k|^\alpha \, |y_{\sigma (i)}- y_{\sigma (k)}|^\alpha, \quad \alpha \gt 0, \end{align*} is in general neither solved by the identical permutation nor the anti-identical permutation if . Indeed the above maximum can be, depending on the number of points, arbitrarily far away from and . The motivation to deal with such assignment problems came from their relation to Gromov–Wasserstein distances, which have recently received a lot of attention in imaging and shape analysis.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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