Python Programming for Biology: Bioinformatics and Beyond

Figure 24.3.  A schematic of the learning process of a self-organising map. A regular

array of initially random feature vectors is constructed. The feature vector for each real

data item is compared to the array and the most similar point in the map is found. This

closest matching vector in the map and its neighbours are adjusted to better match the data

item. The matching and adjustment is then repeated for all the other data items before a

new cycle considers all the data points again. The process continues for a large number of

cycles or to convergence.

The organisation process of the self-organising map occurs by repeatedly exposing the

input  data  to  the  map  of  nodes,  which  initially  have  random  similarities  to  the  data.  For

each input data point the single node on the grid that best matches is determined: how well

the  input  features  (e.g.  colour  vector)  match  the  features  stored  for  the  node.  This  best

node  is  then  pulled  closer  to  the  input  point  along  with  a  few  of  the  surrounding  grid

nodes,  so  that  the  feature  vectors  of  that  region  of  the  grid  more  closely  resemble  that

input. Different input points will pull different parts of the grid, in terms of feature vectors,

towards themselves and away from dissimilar points. After many rounds of adjustment to

the nodes, similar feature vectors will cluster together on the grid; similar input points will

map to nodes that are close on the grid. After sufficient iterations for the features of the

grid  nodes  to  stabilise  the  ‘learning’  process  stops.  To  help  with  this  stabilisation  the

strength  of  the  pull  from  the  inputs  on  the  grid  features  is  gradually  diminished,  so  that

towards the end of the process only minor adjustments are made. Any data point, even if

not seen before, may then be mapped onto the grid by finding the closest node. Naturally

for any given input there need not be an exact match on the grid, even for the values used

in  the  training  data;  the  grid  is  of  a  finite  size  and  nodes  may  represent  compromises

between competing data. Nevertheless, by finding a matching node, data may be mapped,

reducing dimensionality and allowing categorisation if the map is divided into regions.

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