The Voronoy (or Voronoi) Tessellation (Voronoy 1908) is a technique that enables the division of a such multi-dimensional spaces into subspaces. Its application defines geometric areas equivalent to subspaces by defining several vectors as centres of subspaces. Any other vector in space can then be attributed to the closest centre vector effectively dividing the whole space in subspaces. Thus an excellent choice to divide semantic vector spaces.

Voronoi diagrams and Delaunay tessellations are one of a few truly interdisciplinary concepts with relevant material to be found in, but not limited to, anthropology, archaeology, astronomy, biology, cartography, chemistry, computational geometry, crystallography, ecology, forestry, geography, geology, linguistics, marketing, metallography, meteorology, operations research, physics, physiology, remote sensing, statistics, and urban and regional planning. (Okabe, Boots, Sugihara and Chiu, 2000)

2D Voronoy Tessellation

Aurenhammer (1991) describes Voronoy Tessellation as “one of the most fundamental data structures in computational geometry” which are used in modelling natural phenomena, to investigate “their mathematical, in particular, geometrical, combinatorial, and stochastic properties” and their computational representation. It also offers various methods for clustering of multi-dimensional data.

Georgy Feodosevich Voronoy/Вороной Георгий Феодосьевич