**Understanding Voronoi Diagrams**

In this diagram the yellow dot is closer to point A than point B. In fact, any point in the dark blue region is closer to point A than to point B. Closer in this case means distance and distance is measured as "Euclidean distance" using the Pythagorean theorem.

Another way to think about this is any point in the darker blue region is more similar to A than to B. Similarity is the basis of clustering. What makes two points similar is proximity. Proximity is nearness in place, time, order, occurrence or relation. In this case, proximity is measured in distance.

Is a flight attendant more like a pilot than a nurse? Is apple pie more like cherry pie than cake? The problem with clustering is there has to be some quantitative method to distinguish similarity and measure proximity. You have to be able to put some number to it so proximity can be calculated. The numerical value assigned can be simply yes or no (binary). Does this item have a crust, yes or no (1 or 0)? If it has a crust it is more likely to be a pie than a cake? Similarity can be measured by income, age, gender, geography or some other variable