Pattern Recognition Techniques - Biomedical Signal Analysis: Contemporary Methods and Applications - page 172

λ = 3

i

λ = 2

i

λ = 1

i

λ = 0

i

Two-dimensional
array of neurons

Input

(a) (b)

Figure 6.6
(a) Kohonen neural network and (b) neighborhood Λ i , of varying size, around the
“winning” neuron i , (the black circle).

3. A learning paradigm that chooses the winner and its neighbors simulta-
neously. A neighborhood Λ i( x ) ( n ) is centered on the winning neuron and
is adapted in its size over time n . Figure 6.6b illustrates such a neigh-
borhood, which first includes the whole neural lattice and then shrinks
gradually to only one “winning neuron” (the black circle).
4. An adaptive learning process that updates positively (reinforces) all
neurons in the close neighborhood of the winning neuron, and updates
negatively (inhibits) all those that are farther from the winner.

The learning algorithm of the self-organized map is simple and is
described below.

1. Initialization : Choose random values for the initial weight vectors
w j (0) to be different for j =1 , 2 ,...,N, where N is the number of
neurons in the lattice. The magnitude of the weights should be small.
2. Sampling :Drawasample x from the input data; the vector x represents
the new pattern that is presented to the lattice.
3. Similarity Matching : Find the “winner neuron” i ( x )attime n based
on the minimum distance Euclidean criterion:

i ( x )=argmin
j

|| x ( n ) − w j ( n ) || , j =1 , 2 ,...,N (6.12)