算法在2D装修抽象的距离 [英] Algorithm for fitting abstract distances in 2D

问题描述

假设我们有一个小数目在它们之间的对象和距离的 - 存在什么算法在二维空间中近似于这些距离的方式嵌合这些对象来分？

Suppose we are given a small number of objects and "distances" between them -- what algorithm exists for fitting these objects to points in two-dimensional space in a way that approximates these distances?

这里的困难是，距离是不是距离，欧氏空间 - 这就是为什么我们只能容纳/近似

The difficulty here is that the "distance" is not distance in Euclidean space -- this is why we can only fit/approximate.

（对于那些有兴趣在什么距离的概念是precisely，它是一个（有限）集合的幂集对称的距离度量）。

(for those interested in what the notion of distance is precisely, it is the symmetric distance metric on the power set of a (finite) set).

推荐答案

鉴于对象的数目是小的，则可以创建一个无向加权图，其中，这些对象将是节点和任意两个节点之间的边缘已重对应于这两个对象之间的距离。你最终与N *（N-1）/ 2的边缘。

Given that the number of objects is small, you can create an undirected weighted graph, where these objects would be nodes and the edge between any two nodes has the weight that corresponds to the distance between these two objects. You end up with n*(n-1)/2 edges.

在该图被创建，有很多可视化软件和算法的对应图形。

Once the graph is created, there are a lot of visualization software and algorithms that correspond to graphs.

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