Euclidean Distance Matrix Completion and Point Configurations from the Minimal Spanning Tree
研究在统计数据分析中，仅给定最小生成树距离时如何补全欧几里得距离矩阵并保持最小生成树不变，提出一种基于引导随机搜索的新方法，实验表明其优于现有标准方法。
The paper introduces a special case of the Euclidean distance matrix completion problem of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the minimal spanning tree. Two solutions are proposed: one an adaptation of a more general method based on a dissimilarity parameterized formulation and the other an entirely novel method which constructs the point configuration directly through a guided random search. These methods as well as three standard edcmp methods are described and compared experimentally on real and synthetic data. It is found that the constructive method given by the guided random search algorithm clearly outperforms all others considered here. Notably, standard methods including the adaptation force peculiar and generally unwanted geometric structure on the point configurations their completions produce.