# A supra-hexagonal map is a a giant hexagon formed seamlessly by smaller hexagons. This architecture is prevalent in many natural and man-made objects, such as a honeycomb or at Giant's Causeway. It has symmetric beauty around the center, from which individual hexagons radiate outwards.

# generate data with an iid matrix of 1000 x 3
data <- matrix(rnorm(1000*3,mean=0,sd=1), nrow=1000, ncol=3)
# train a supra-hexagonal map by data
sMap <- sPipeline(data, xdim=15)

Start at 2017-03-27 18:59:32

First, define topology of a map grid (2017-03-27 18:59:32)...
Second, initialise the codebook matrix (169 X 3) using 'linear' initialisation, given a topology and input data (2017-03-27 18:59:32)...
Third, get training at the rough stage (2017-03-27 18:59:32)...
	1 out of 2 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	2 out of 2 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
Fourth, get training at the finetune stage (2017-03-27 18:59:32)...
	1 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	2 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	3 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	4 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	5 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	6 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
	7 out of 7 (2017-03-27 18:59:32)
	updated (2017-03-27 18:59:32)
Next, identify the best-matching hexagon/rectangle for the input data (2017-03-27 18:59:32)...
Finally, append the response data (hits and mqe) into the sMap object (2017-03-27 18:59:32)...

Below are the summaries of the training results:
   dimension of input data: 1000x3
   xy-dimension of map grid: xdim=15, ydim=15, r=8
   grid lattice: hexa
   grid shape: suprahex
   dimension of grid coord: 169x2
   initialisation method: linear
   dimension of codebook matrix: 169x3
   mean quantization error: 0.342702855593103

Below are the details of trainology:
   training algorithm: batch
   alpha type: invert
   training neighborhood kernel: gaussian
   trainlength (x input data length): 2 at rough stage; 7 at finetune stage
   radius (at rough stage): from 4 to 1
   radius (at finetune stage): from 1 to 1

End at 2017-03-27 18:59:32
Runtime in total is: 0 secs

# visualise the supra-hexagonal map with node numbering
visHexMapping(sMap, mappingType="indexes")

# As you have seen, this architecture has a total of 169 smaller hexagons (ie map nodes) that are indexed as follows: start from the center, and then expand circularly outwards, and for each circle increase in an anti-clockwise order. It is uniquely determined by the x- or y-dimension of the map grid (or its radius r).

# There is an inherent relationship between x-dimension (or y-dimension), the radius r and the total number of hexagons nHex:
xdim <- sMap$xdim


r <- (xdim + 1)/2
nHex <- 1 + 6 * r * (r - 1)/2
      

Source faq

Functions used in this FAQ

• sPipeline
• visHexMapping