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# Competitive Process Assignment Help

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Neural Networks - Competitive Process
**Competitive Process**

Assume m indicates the dimension of input space. Suppose an input pattern selected at random from the input space be denoted by as:

** X = [ x**_{1} , x_{2} , ... , x_{m} ]^{T}.............................Eqn(12)

The synaptic weight vector of all neuron in the network has the similar dimension as the input space. Suppose the synaptic weight vector of neuron j be denoted by as:

**W**_{j} = [w_{j1}, w_{j2} , ... , w_{jm} ]^{T} ,............................Eqn(13)

** **

** j = 1, 2, ... , l**

Whereas l is the total number of neurons in the network

To find the best match of the input vector X along with the synaptic weight vector, compare the inner products w_{j}^{T} x for j = 1, 2, . . . , l and choose the largest. This supposes that the same threshold is applied to all the neurons; the threshold is negative of bias. Hence, by selecting the neuron along with the largest inner product w_{j}^{T} x, the location whereas the topological neighborhood of excited neurons is to be centered is calculated.

It is discovered that the best matching criterion, based upon maximizing the inner product w_{j}^{T} x, is mathematically equivalent to minimizing the Euclidean distance in between the vectors X and W_{j}. If the index i(X) is utilized to identify the neuron that best matches the input vector X, then find i(X) by applying the condition which sums up the essence of the competition process in between the neurons.

** i(x) = arg min|| x - w j ||; j = 1, 2, . . . , l....................Eqn(14)**

According to the above equation i(X) is the subject of attention like the requirement is to calculate the neuron i. The particular neuron i which satisfy this situation is named as the best-matching or winning neuron for the input vector X. Depending on the application of interest, the response of the network can be either the index of the winning neuron, or the synaptic weight vector, which is closest to the input vector in a Euclidean sense.

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**Competitive Process**

**X = [ x**

_{1}, x_{2}, ... , x_{m}]^{T}.............................Eqn(12)**W**

_{j}= [w_{j1}, w_{j2}, ... , w_{jm}]^{T},............................Eqn(13)

**j = 1, 2, ... , l**

_{j}

^{T}x for j = 1, 2, . . . , l and choose the largest. This supposes that the same threshold is applied to all the neurons; the threshold is negative of bias. Hence, by selecting the neuron along with the largest inner product w

_{j}

^{T}x, the location whereas the topological neighborhood of excited neurons is to be centered is calculated.

_{j}

^{T}x, is mathematically equivalent to minimizing the Euclidean distance in between the vectors X and W

_{j}. If the index i(X) is utilized to identify the neuron that best matches the input vector X, then find i(X) by applying the condition which sums up the essence of the competition process in between the neurons.

**i(x) = arg min|| x - w j ||; j = 1, 2, . . . , l....................Eqn(14)**