# 3 Dimensional Perceptron Computer

This is a perceptron simulator. A perceptron takes a set of inputs usually {-1,1} and uses them to evaluate an activation function:
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This activation value is then used in the threshold function:
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This output is compared against the desired output for that input pair and if it is not correct an error function adjusts the weights according to this equation:
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This is then repeated with the new weight values until an acceptable error level is reached:
.

This examples uses two inputs and a set of 10 data triples (the third value is the bias, β). The graphs section shows the error and the linear seperation of the two classes. In this example I use the terms vector and list interchangably. This is because where the algorithm calls for vectors I use Mathematica list data types. I also use the list data type to store data for error computation and other uses.

## Compute Perceptron

### Compute

The perceptron algorithm.
Line 1 - Go through the input vector loop times.
Line 2 - Reset the output vector to an empty list for another pass through.
Line 3 - Reset the activation vector to an empty list for another pass through.
Line 4 - Loop through each of the input values. --TODO-- Change the hard coded value to a length function of the input vector.
Line 5 - The net activation level, net, is calculated using the activation function . For this algorithm I substituted a dot product for the summation for computational convenience.
Line 6 - The activation level is added to a storage list.
Line 7 - The activation value is used to produce and output value using the bipolar threshold function .
Line 8 - The output value is added to a storage list.
Line 9 - Calculate the weight adjustment if necessary and store it to the weight vector, else store the same weight to the weight vector since the out put was correct.
Line 13 - Calculate the error for this loop through the data set and store it to the error list.
Line 14 - Store this loops weight vector to a list of weight vectors for later use.
Line 15 - Reset the weight vector to the last set of weight values for use in the next loop.

## Results

### Results

##### Show tables

Table (Activation values Weights}

Table (Activation values Weights}

##### Show graphs

Error Graph

Region Graph

The Seperation

The progression of the seperation

Converted by Mathematica      December 8, 2003