From Tutte institute for mathematics and computing
Problem: dimension reduction
Theoretical foundations:
Methodology:
Two phases.
In the first phase, a particular weighted k-neighbour graph is constructed. In the second phase, a low dimensional layout of this graph is computed
Supplementary knowledge:
1. simplicial sets. 单纯集
In mathematics, a simplicial set is an object made up of “simplices单纯形” in a specific way. Simplicial sets are higher-dimensional generalizations of directed graphs, partially ordered sets and categories.
simplex: 单纯形,
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron四边形 to arbitrary dimensions.
For example,
- a 0-simplex is a point,
- a 1-simplex is a line segment,
- a 2-simplex is a triangle,
- a 3-simplex is a tetrahedron,
- a 4-simplex is a 5-cell.
2. Hadamard product/ pointwise product
3.