A Voronoi diagram is a group of geometric regions that express classifying points in such a way that any point within the region is the nearest to the classifier than any other neighbor classifiers based on their spatial distance from one another.

Let's assume that there is a city whose shape is perfectly square (figure above). The location of People in this city is generally classified by their "income" into 6 large groups. For example, if their income is within the specific limit, they have to settle down in a specific region. Here, spatial constraints can be sensed! Therefore, the whole city is classified into 6 different regions.

Now, assume that inside each of 6 regions, people are forced to shop from their nearest mall. There are a total of 30 malls shown by black nodes in the figure.

Question: If a new person is coming into the city and his "income" is between 0 and 5. how many malls are there that he can shop? Answer: the limit of 0 and 5 is indicated by the blue region at the west of the city. We can see there are 3 black nodes (3 malls) that people can shop there. To predict which exact mall he can shop at, we need his exact address.

This hierarchical classification can be used in different applications as well. For example, check out my research paper that shows nested Voronoi partitioning in geoscience applications.