By Kardi Teknomo, PhD .

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Aggregation Function of Neural Network

Inside a computational neuron, the weights and the inputs to the neurons are interacted and aggregated into a single value. The way we gather the input from the other previous neurons are called aggregation function. There are many aggregation functions but we will focus on the few important ones.

The most important aggregation function is called sum of product. Internally, this neuron will accumulate the sum product of the synapses weights and the input neurons, which includes the bias and the dummy input. This neuron will compute:

Aggregation Function

(1)

If we have more than one computational neurons, the synapses weights are denoted by two subscriptsAggregation Function. Subscript Aggregation Function represents the previous neuron and subscript Aggregation Function represent the current neuron under consideration. The sum of product for current neuron Aggregation Function is computed as

Aggregation Function

(2)

 

Example

When there are more than one arrows going out of a cell, all of these arrows provide the same value. For example, in the diagram below a sensory cell Aggregation Function has two arrows out of the cell. Suppose the valueAggregation Function. This value would be used as the input to both neuron Aggregation Function andAggregation Function. Notice we use two subscripts for the synapses weights.

Aggregation Function

Example

We have a simple neural network with three sensory cells and one neuron. The synapses weight values are given in the diagram below. Suppose the values of the sensory cells areAggregation Function. What is the value of the sum product?

Aggregation Function

Answer:

Aggregation Function

Aggregation Function

Note in the diagram above, the two operations inside the neuron are not shown to make the diagram simpler. The number inside neuron represents the bias input value. You have to remember that the operation of sum product and the activation function are always there inside a neuron cell.

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See Also :
K means clustering , Similarity Measurement , Reinforcement Learning (Q-Learning) , Discriminant Analysis , Kernel Regression , Clustering , Decision Tree

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Preferable reference for this tutorial is

Teknomo, Kardi (2017). Neural NetworkTutorial. http:\\people.revoledu.com\kardi\tutorial\NeuralNetwork\