Self-Organizing Maps and Their Applications in Image Processing, Information Organization, and Retrieval - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 423

A two-layer SOM architecture is also described that exploits the aforemen-
tioned homogeneity tests in its training phase and allows parallelism by split-
ting the training set into disjoint subsets. The training vectors of the first-layer
SOMs are the input patterns. The training patterns of the second-layer SOM
are the weight vectors of the first-layer SOMs after their convergence. The sec-
ond layer SOM clusters the weight vectors provided by the first-layer SOMs.
Some of them have been trained by patterns extracted from the same pop-
ulation; therefore they should be merged. Some others are reference vectors
associated with distinct populations; consequently they should be preserved.
A similar approach is adopted in Reference 68. Moreover, simplified versions
of the homogeneity tests are also proposed to be used in a parallel implemen-
tation of the two-layer SOM. Applications of the split-merge SOMs to color
image quantization and image segmentation are presented as well.
The proposed split-merge SOM algorithm embodies in its training phase
criteria for:

1. Merging the current input pattern x ( n ) into the cluster of patterns

( )

associated with the winner neuron w c n ,orequivalently, criteria

( )

for detecting if x is outlier to the cluster of patterns represented

by the winner neuron w c

n

)
2. Testing if cluster splitting is statistically significant

( n

In general, when the whole training set is presented in the input of SOM
for the first time, many wrong decisions are expected, because the winner
vectors fail to adequately approximate the true cluster means. Therefore, a
need for further testing the correctness of the classification of the input train-
ing patterns to the cluster represented by the winner is recognized. Similarly,
when a training pattern moves from one cluster to another, an additional test
is needed to approve the correctness of such a decision. In the latter case,
the cluster where the input training pattern was formerly classified may be
considered unstable, because it has been affected by outliers. Consequently,
during the session when a pattern removal has occurred, we have decided
to check further whether the classification of input training patterns to this
unstable cluster on the basis of the Euclidean distance metric is still correct.
The outline of the split-merge SOM learning algorithm is as follows.

ALGORITHM 2

1. For each pattern presentation x ( n ) :

a. Find the winner w c ( n ) .

b. Test if x ( n ) is outlier to the patterns that are represented by w c ( n )

for
(i) Pattern presentations during the first session
(ii) Patterns that are moved from one cluster to another