论文标题
定性欧几里得嵌入分离点
Qualitative Euclidean embedding of Disjoint Sets of Points
论文作者
论文摘要
我们考虑两点不相交的积分。如果至少可以将其中一组嵌入到欧几里得空间中，那么我们提供了足够的条件，使两组共同嵌入一个欧几里得空间中。在这个关节欧几里得的嵌入中，点之间的距离是由特定关系的函数产生的。因此，同一组的两个点之间的相互距离是其原始空间中相互距离的特定定性变换。可以从任意接近函数构建不同集合点之间的成对距离。
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function.
