2 Dimensional Perceptron Computer

by Chad Rempp
This is a perceptron simulator. A perceptron takes a set of inputs usually {-1,1} and uses them to evaluate an activation function:
    .
This activation value is then used in the threshold function:
    .
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:
    .
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

Initialize Variables

Reset Variables

Set the input vector values

Set the initial weight vector

Set the weight record vector to an empty list

Set the output vector to an empty list

Set the net activation vector to an empty list

Set the region 1 vector to an empty list

Set the region 2 vector to an empty list

Set the desired output vector

Set the error vector to an empty list

Set the learning constant

Set the number of times to loop throught the network during training.
      Note that the total training iterations = loops * sets of input values

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

Preprocessing

Create Tables

Create equation for linear seperation

Create data regions for graphing

Create error graph

Create seperation line graph

Create region 1 graph

Create region 2 graph

Create a list of graphs that represent the linear seperation at the end of each loop

Results

Show tables

Table (Activation values Weights}

Table (Activation values Weights}

Show graphs

Error Graph

Region Graph

The Seperation

The progression of the seperation