# What is the main differences between choosing hexagonal grid and rectangular grid for SOM?

While I'd expect people to answer this question by saying 'depends on the distribution of data', but what are the thumb rules for deciding which grid to use (either hexagonal or rectangular) for generating a SOM?

For rectangular grid there are a few heuristic rules to choose the grid dimensions and number of neurons, but I couldn't find anything on a hexagonal grid. So how do I begin with and what preliminary observations to take in consideration to choose the size?

Also, when using kohonen package in R to build a SOM, the default settings of the som() function are to use a circular neighbourhood for hexagonal grid, and square neighbourhood for rectangular grid.

Is there a reason for such default values? In many examples available online, a rectangular grid has been used with a circular neighbourhood.

• For your last question about the default settings of the kohonen package, you should ask the main author (Ron Wehrens) directly. I don't think he looks at CV/SE. He's very helpful. – a different ben Dec 3 '15 at 22:46
• @adifferentben I'll do that but I thought he might have done that because of some thumb rules regarding SOM – Gaurav Dec 4 '15 at 5:14
• A hexagon has 6 adjacent neighbors while a square has only 4, if you don't count the corners. Since SOMs return the topological structure in the data, I presume hexagonal grids result in smoother maps. Another thing to consider is the larger picture: what is the advantage of picking hexagons over squares? – shuriken x blue Dec 16 '15 at 3:34