V2EX frechet

Frechet

定义 Definition

Fréchet(常作 Frechet)多用于数学与计算机科学中,最常见指Fréchet 距离:一种衡量两条曲线(或轨迹)相似度的度量,直观上常被解释为“人牵着狗分别沿两条路径走,所需的最短牵绳长度”。

(该词也可出现在 Fréchet 导数、Fréchet 空间、Fréchet 分布 等术语中,均源自同一位数学家姓氏。)

发音 Pronunciation

/free/

例句 Examples

We used the Frechet distance to compare two GPS tracks.
我们用 Fréchet 距离来比较两条 GPS 轨迹。

Although the curves look similar, their Frechet distance is large because one path has a sharp detour.
尽管两条曲线看起来相似,但由于其中一条路径有一个急转弯绕路,它们的 Fréchet 距离仍然很大。

词源 Etymology

Fréchet 来自法国数学家 Maurice Fréchet(莫里斯弗雷歇) 的姓氏。许多以他命名的概念出现在泛函分析、拓扑学与概率论中,后来也被广泛应用于计算几何、轨迹匹配与形状分析等领域。

相关词 Related Words

文学作品 Literary Works

  • Computational Geometry: Algorithms and Applications(计算几何经典教材,涉及曲线相似度与相关距离概念)
  • Pattern Recognition and Machine Learning by Christopher M. Bishop(机器学习教材中常在度量/距离与相似度语境下出现相关术语)
  • Maurice Fréchet 的论文与著作(如其在度量空间与泛函分析方向的早期工作,奠定“Fréchet-”相关术语的命名基础)
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