A note on the triangle inequality for the Jaccard distance

By Sven Kosub. 2016

246 citations recorded by the source corpus.

Abstract Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.

Subfields: Applied Mathematics, Geometry and Topology, Algorithms & Complexity

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Bernardino Romera-Paredes
2. Tien-Ping Tan
3. Danilo Jimenez Rezende

In Geometry and Topology

1. Tien-Ping Tan

In Algorithms & Complexity

1. S. M. Ali Eslami
2. Ian David Reid
3. Silvio Savarese
4. Danilo Jimenez Rezende

Citations in the corpus

• Generalized Intersection Over Union: A Metric and a Loss for Bounding Box Regression (2019, background): “LIoU = 1−IoU , is a metric (by mathematical definition) [9].”
• Focal and Efficient IOU Loss for Accurate Bounding Box Regression (2021, background): “It has been proved to be a metric (by the mathematical definition [12]).”
• A Probabilistic U-Net for Segmentation of Ambiguous Images (2018, background): “In our case we choose d(x, y) = 1− IoU(x, y), which as proved in [30, 31], is a metric.”