218
G.J. Bowden . G.C. Dandy . H.R. Maier
Selj-Organizing Map (SOM)
The Self-Organizing Map was developed by Kohonen (1982) and arose from
attempts to model the topographically organised maps found in the cortices of the
more developed animal brains. The underlying basis behind the development of
the SOM was that topologically correct maps can be formed in an n-dimensional
array of processing elements (PEs) that did not have this initial ordering to begin
with. In this way, input stimuli, which may have many dimensions, can come to
be represented by a one- or two-dimensional vector which preserves the order of
the higher dimensional data (NeuralWare 1998).
The SOM employs a type of leaming commonly referred to as competitive,
unsupervised or self-organizing, in which adjacent cells within the network are
able to interact and develop adaptively into detectors of a specific input pattern
(Kohonen 1990). The SOM can be considered to be as "neural" because results
have indicated that the adaptive processes utilized in the SOM may be similar to
the processes at work within the brain (Kohonen 1990).
The SOM has potential extending beyond its original purpose of modeling
biological phenomena. Sorting items into categories of similar objects is a
challenging, yet frequent task. The SOM achieves this task by nonlinearly
projecting the data onto a lower dimensional display and by clustering these data.
This attribute has been used in a wide number of applications ranging from
engineering (including image and signal processing and recognition,
telecommunications, process monitoring and control, and robotics) to natural
sciences, medicine, humanities, economics and mathematics (Kaski et al. 1998).
The Selj-Organizing Map Algorithm
In competitive leaming, neurons in the network adapt gradually to become
sensitive to different input categories. The SOM network generally consists of
two layers, an input layer and a Kohonen layer. The input layer is fully connected
to the Kohonen layer, which in most common applications is two-dimensional.
None of the PEs in the Kohonen layer are connected to each other. The PEs in the
Kohonen layer measure the distance of their weights to the input pattern. During
the recall phase, the Kohonen PE with the minimum distance is the winner and has
an output of 1.0, whilst the other Kohonen PEs have an output of 0.0.
The procedure for determining the winning PE is as follows:
The first step is to determine the extent to which the weights of each PE match
the corresponding input pattern. If the input data have N values and are denoted
by, X = (Xi; i = 1, ... , N) E 9t n , then each of the M PEs in the Kohonen layer
will also have N weight values and can be denoted by,
W ji = (w ji; j = 1, ... , M ; i = 1, ... , N) E 9\ n. For each of the M Kohonen
PEs, the distance, such as the Euclidean distance, is calculated using
I
D j = Il x -W j 11 = [t (Xi - W ji Y r, j = 1, ... , M .
( 11.2)
The PE with the lowest value of D j is the winner during recall. During training,
a conscience mechanism adjusts the distances to encourage PEs that are not
winning with an average frequency and to negatively adjust PEs that are winning
G.J. Bowden . G.C. Dandy . H.R. Maier
Selj-Organizing Map (SOM)
The Self-Organizing Map was developed by Kohonen (1982) and arose from
attempts to model the topographically organised maps found in the cortices of the
more developed animal brains. The underlying basis behind the development of
the SOM was that topologically correct maps can be formed in an n-dimensional
array of processing elements (PEs) that did not have this initial ordering to begin
with. In this way, input stimuli, which may have many dimensions, can come to
be represented by a one- or two-dimensional vector which preserves the order of
the higher dimensional data (NeuralWare 1998).
The SOM employs a type of leaming commonly referred to as competitive,
unsupervised or self-organizing, in which adjacent cells within the network are
able to interact and develop adaptively into detectors of a specific input pattern
(Kohonen 1990). The SOM can be considered to be as "neural" because results
have indicated that the adaptive processes utilized in the SOM may be similar to
the processes at work within the brain (Kohonen 1990).
The SOM has potential extending beyond its original purpose of modeling
biological phenomena. Sorting items into categories of similar objects is a
challenging, yet frequent task. The SOM achieves this task by nonlinearly
projecting the data onto a lower dimensional display and by clustering these data.
This attribute has been used in a wide number of applications ranging from
engineering (including image and signal processing and recognition,
telecommunications, process monitoring and control, and robotics) to natural
sciences, medicine, humanities, economics and mathematics (Kaski et al. 1998).
The Selj-Organizing Map Algorithm
In competitive leaming, neurons in the network adapt gradually to become
sensitive to different input categories. The SOM network generally consists of
two layers, an input layer and a Kohonen layer. The input layer is fully connected
to the Kohonen layer, which in most common applications is two-dimensional.
None of the PEs in the Kohonen layer are connected to each other. The PEs in the
Kohonen layer measure the distance of their weights to the input pattern. During
the recall phase, the Kohonen PE with the minimum distance is the winner and has
an output of 1.0, whilst the other Kohonen PEs have an output of 0.0.
The procedure for determining the winning PE is as follows:
The first step is to determine the extent to which the weights of each PE match
the corresponding input pattern. If the input data have N values and are denoted
by, X = (Xi; i = 1, ... , N) E 9t n , then each of the M PEs in the Kohonen layer
will also have N weight values and can be denoted by,
W ji = (w ji; j = 1, ... , M ; i = 1, ... , N) E 9\ n. For each of the M Kohonen
PEs, the distance, such as the Euclidean distance, is calculated using
I
D j = Il x -W j 11 = [t (Xi - W ji Y r, j = 1, ... , M .
( 11.2)
The PE with the lowest value of D j is the winner during recall. During training,
a conscience mechanism adjusts the distances to encourage PEs that are not
winning with an average frequency and to negatively adjust PEs that are winning