In the networks with
competitive and corporative learning, it can be said that the neurons compete
and cooperate ones with the others to give a specific task. Differing from the
net of Hebbian learning basis, where many output nodes can be activated
simultaneously, in the case of competitive learning only one can be activated
at a time. In this method , the neurons of the output layer compete among themselves to become
active. This feature is highly suited to discover the statistical features of a
set of input patterns.
Three elements of competitive
learning
A
set of neurons are same except for the randomly distributed weights. There fore
each neuron responds differently to a given input.
A
limit is imposed on the strength of each neuron.
A
mechanism that permits the neuron to compete so that only one is active at a
time. The neuron that wins is called winnertakeallneuron.
In its simplest
form the network has a single layer of output neurons each of which is fully
connected to the input (source) nodes. The network may include feedback
connections among the neurons. The feedback connections perform lateral
inhibition. Each neuron tends to inhibit the other neuron to which it is
laterally connected.
For an output
neuron k to be the winning neuron, its activation input X_{k } for a specified input pattern S must be the
largest among all the neurons in the output layer. The output layer is
therefore set to 1; and the output of all other neurons that lose the
competition are set to zero.
1
if X_{k}> X_{l} for all l ≠
k
Y_{k}
=
0 otherwise
Where
the induced local field X_{k } represents the combined action for all the feed forward and feedback
inputs to neuron k. The weights W_{kj
}for all input nodes j connected to output node k are +ve and distributed
such that
å
W_{kj }=1 for all k
The
neuron then learns by shifting its weights from its inactive inputs to active
inputs. According the standard competitive learning rule, the change in weight DW_{kj }is
defined by
h
(S_{j}  W_{jk } if neuron k wins the competition
DW_{kj }= 0 if neuron k
loses the competition
Where h
is the learning parameter. This rule has the overall effect of moving the
weight vector W_{k }of the winning neuron k of the toward the input
pattern S.
Instar and Outstar
The instar and outstar can be connected together to form complex
networks.
Instar
Learning : An star configuration consists of a
neuron fed by a set of inputs through synaptic weights. It can be trained to
respond to a specific input vector S. Training is accomplished by adjusting its
weights so that the weight vector becomes similar to the input
vector.
The output is
calculated as the weighted sum of its inputs or the dot product of the weight
vector with the input vector. The dot
product of normalized vectors is a measure of similarity between the vectors.
Once the training is over the output from the is maximum(the neuron fires)
when the input vector is similar to the weight vector.
W_{ji}(m+1)=
W_{ji}(m)+h[S_{i}(m)W_{ji}(m)] The value of h
starts with 0.1 and is generally reduced during the training process.
Outstar
Learning
In outstar
configuration, the neuron drives a set of synapses through its synaptic weights. The outstar produces a
desired excitation pattern to other neurons whenever it fires. The weight update equation is
W_{kj}(m+1)=
W_{kj}(m)+b[Y_{k}(m)W_{kj}(m)]
b
is learning parameter . The value of b is close to 1
at the beginning and is gradually reduced during training.
