Location, Localization, and Localizability by Yunhao Liu & Zheng Yang

Author:Yunhao Liu & Zheng Yang
Language: eng
Format: epub
ISBN: 9789819731763
Publisher: Springer Nature Singapore

This result is intuitive: If G contains no outlier, then the ground truth is an embedding, and G cannot be unembeddable. Nevertheless, this is the best we can do for detecting outliers only based on ranging information. Formally, if G is embeddable, even if G actually contains some outliers, we have no way to detect them.

Theorem 6.1 only provides a fine granularity way to detect outliers but cannot tell which are outliers and which are not. To address this issue, a concept of outlier disprovable is proposed:

Definition 6.1

Given a weighted graph G = <V, E, W>, G is outlier disprovable if and only if the embeddability of G implies that it contains no outlier edge.

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