Arduino Basics: Processing.org
Showing posts with label Processing.org. Show all posts
Showing posts with label Processing.org. Show all posts

3 June 2012

Jumper: Arduino controlled animation

In this project, I have connected an Arduino to my computer and used a photoresistor to control an animation on the screen. Other sensors could have been used, but I chose a photoresistor because it feels like magic!!

The photoresistor responds to changes in ambient light as my hand moves up and down. The Arduino sends the reading to a Processing sketch on the computer via a Serial command (through the USB cable). The processing sketch interprets the signal from the Arduino and selects the appropriate picture to display.

I took a series of screenshots from the following YouTube video: http://www.youtube.com/watch?v=h6nE8m74kDg  And after borrowing a bit of code from these sites (1,2), the project was born.
This idea is not new, nor my own. There are many people who have done this project before, but I thought to blog about how I have done it, just for fun.

The Project Movie




Components Required


  • Arduino Uno (and associated software), and USB cable
  • Photoresistor or Photocell
  • 10K resistor
  • Wires to put it all together
  • Processing IDE from http://processing.org
  • Computer/laptop


The Arduino Sketch






The Arduino Code:

You can download the Arduino IDE from this site.
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/* Jumper: Using an Arduino to animate:
   Written by ScottC on 02/06/2012 */

int photoRPin = 0; 
int minLight;
int maxLight;
int lightLevel;
int adjustedLightLevel;
int oldLightLevel;

void setup() {
  Serial.begin(9600);
  
  //Setup the starting light level limits
  lightLevel=analogRead(photoRPin);
  minLight=lightLevel-10;
  maxLight=lightLevel;
  oldLightLevel=lightLevel;
}

void loop(){
   lightLevel=analogRead(photoRPin);
   delay(10);
  
  //auto-adjust the minimum and maximum limits in real time   
   if(minLight>lightLevel){
     minLight=lightLevel;
   }
   if(maxLight<lightLevel){
     maxLight=lightLevel;
   }
   
   //Map the light level to produce a result between 1 and 28.
   adjustedLightLevel = map(lightLevel, (minLight+20), (maxLight-20), 1, 28); 
   adjustedLightLevel = constrain (adjustedLightLevel, 1,28);
   
   /*Only send a new value to the Serial Port if the 
     adjustedLightLevel value changes.*/
   if(oldLightLevel==adjustedLightLevel){
     //do nothing if the old value and the new value are the same.
   }else{
     //Update the oldLightLevel value for the next round
     oldLightLevel=adjustedLightLevel;
     
     /*Send the adjusted Light level result 
       to Serial port (processing)*/
     Serial.println(adjustedLightLevel);
   } 
}

The code above was formatted using this site.



The Processing Code:

You can download the Processing IDE from this site.

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/* Jumper: Using an Arduino to animate
   Written by ScottC on 02/06/2012

Source code derived from : 
  http://processing.org/learning/topics/sequential.html
  http://processing.org/discourse/beta/num_1267080062.html

Pictures captured from:
  http://www.youtube.com/watch?v=h6nE8m74kDg      
  
======================================================= */

import processing.serial.*;
Serial myPort;
String sensorReading="";

// Create the array that will hold the images
PImage[] movieImage = new PImage[29];

/* The frame variable is  used to control which 
   image is displayed */
int frame = 1;



/* Setup the size of the window. Initialise serial communication with Arduino
   and pre-load the images to be displayed later on. This is done only once.
   I am using COM6 on my computer, you may need replace this value with your
   active COM port being used by the Arduino.*/

void setup(){
  size(700,600);
  
  myPort = new Serial(this, "COM6", 9600);
  myPort.bufferUntil('\n');
  
  for(int i=0;i<28;i++){
    movieImage[i] = loadImage("Jumper" + (i+1) + ".jpg");
  }
}




// The draw function controls the animation sequence.

void draw(){
  
  //this draws the relevant image to the window  
  image(movieImage[frame-1],0,0,width,height);
}

void serialEvent (Serial myPort){
 sensorReading = myPort.readStringUntil('\n');
  if(sensorReading != null){
    sensorReading=trim(sensorReading);
    if (sensorReading.length()<2){
      frame = integerFromChar(sensorReading.charAt(0));
    }else{
      frame = integerFromChar(sensorReading.charAt(0))*10;
      frame += integerFromChar(sensorReading.charAt(1));
    }
  }
}



/* This function used to convert the character received from the
   serial port (Arduino), and converts it to a number */
   
int integerFromChar(char myChar) {
  if (myChar < '0' || myChar > '9') {
    return -1;
  }else{
  return myChar - '0';
  }
}

The code above was formatted using this site.


The pictures 

Captured from this YouTube Video: http://www.youtube.com/watch?v=h6nE8m74kDg






























15 August 2011

Neural Network (Part 7) : Cut and Paste Code

Ok - so you don't like tutorials, and would rather just cut and paste some code.
This is for you.
http://www.openprocessing.org/visuals/?visualID=33991

Make sure to select "Source code" when you get there, otherwise it will be quite boring.
Here is an animated gif which shows the program in action.



See BELOW for the WHOLE screenshot so that you don't have to speed read.



If you want to know how it works, then you will have to go back and read part 1 to 6.



  • Neural Network



  • But as you can see from the example above:
    Before the neural network is trained, the outputs are not even close to the expected outputs. After training, the neural network produces the desired results (or very close to it).

    Please note, this neural network also allows more than one output neuron, so you are not limited to single yes no decisions. You can use this neural network to make classifications. You will soon see this with my LED colour sensor.

    Feel free to use this Neural Network in your own projects, but please let me know if you do, just for curiosity sake.

    Update: See below for the Processing Sketch (much easier than going to the open processing site). It is a bit long - but saves you from having to navigate to another site.

    Processing sketch

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    /*Neural Network created by ScottC on 15th Aug 2011
     
    Please visit my blog for a detailed explanation of my Neural Network
    http://arduinobasics.blogspot.com/p/arduinoprojects.html
     
    */
       
       
     
    void setup(){
      ArrayList myTrainingInputs = new ArrayList();
      ArrayList myTrainingOutputs = new ArrayList();
       
      float[] myInputsA={0,0};
      float[] myInputsB={0,1};
      float[] myInputsC={1,0};
      float[] myInputsD={1,1};
      float[] myOutputsA={1};
      float[] myOutputsB={0};
       
       
      println("TRAINING DATA");
      println("--------------------------------------------");
      myTrainingInputs.add(myInputsA);
      myTrainingOutputs.add(myOutputsA);
      println("INPUTS= " + myInputsA[0] + ", " + myInputsA[1] + "; Expected output = " + myOutputsA[0]);
      myTrainingInputs.add(myInputsB);
      myTrainingOutputs.add(myOutputsB);
      println("INPUTS= " + myInputsB[0] + ", " + myInputsB[1] + "; Expected output = " + myOutputsB[0]);
      myTrainingInputs.add(myInputsC);
      myTrainingOutputs.add(myOutputsB);
      println("INPUTS= " + myInputsC[0] + ", " + myInputsC[1] + "; Expected output = " + myOutputsB[0]);
      myTrainingInputs.add(myInputsD);
      myTrainingOutputs.add(myOutputsA);
      println("INPUTS= " + myInputsD[0] + ", " + myInputsD[1] + "; Expected output = " + myOutputsA[0]);
      println("--------------------------------------------");
      
      NeuralNetwork NN = new NeuralNetwork();
      NN.addLayer(2,2);
      NN.addLayer(2,1);
      
      println("Before Training");
      float[] myInputDataA1={0,0};
      NN.processInputsToOutputs(myInputDataA1);
      float[] myOutputDataA1={};
      myOutputDataA1=NN.getOutputs();
      println("Feed Forward:  INPUT = 0,0; OUTPUT=" + myOutputDataA1[0]);
       
      float[] myInputDataB1={0,1};
      NN.processInputsToOutputs(myInputDataB1);
      float[] myOutputDataB1={};
      myOutputDataB1=NN.getOutputs();
      println("Feed Forward:  INPUT = 0,1; OUTPUT=" + myOutputDataB1[0]);
       
      float[] myInputDataC1={1,0};
      NN.processInputsToOutputs(myInputDataC1);
      float[] myOutputDataC1={};
      myOutputDataC1=NN.getOutputs();
      println("Feed Forward:  INPUT = 1,0; OUTPUT=" + myOutputDataC1[0]);
       
      float[] myInputDataD1={1,1};
      NN.processInputsToOutputs(myInputDataD1);
      float[] myOutputDataD1={};
      myOutputDataD1=NN.getOutputs();
      println("Feed Forward:  INPUT = 1,1; OUTPUT=" + myOutputDataD1[0]);
     
      println("");
      println("--------------------------------------------");
       
      println("Begin Training");
      NN.autoTrainNetwork(myTrainingInputs,myTrainingOutputs,0.0001,500000);
      println("");
      println("End Training");
      println("");
      println("--------------------------------------------");
      println("Test the neural network");
      float[] myInputDataA2={0,0};
      NN.processInputsToOutputs(myInputDataA2);
      float[] myOutputDataA2={};
      myOutputDataA2=NN.getOutputs();
      println("Feed Forward:  INPUT = 0,0; OUTPUT=" + myOutputDataA2[0]);
       
      float[] myInputDataB2={0,1};
      NN.processInputsToOutputs(myInputDataB2);
      float[] myOutputDataB2={};
      myOutputDataB2=NN.getOutputs();
      println("Feed Forward:  INPUT = 0,1; OUTPUT=" + myOutputDataB2[0]);
       
      float[] myInputDataC2={1,0};
      NN.processInputsToOutputs(myInputDataC2);
      float[] myOutputDataC2={};
      myOutputDataC2=NN.getOutputs();
      println("Feed Forward:  INPUT = 1,0; OUTPUT=" + myOutputDataC2[0]);
       
      float[] myInputDataD2={1,1};
      NN.processInputsToOutputs(myInputDataD2);
      float[] myOutputDataD2={};
      myOutputDataD2=NN.getOutputs();
      println("Feed Forward:  INPUT = 1,1; OUTPUT=" + myOutputDataD2[0]);
      
       
    }
     
     
    /* ---------------------------------------------------------------------
    A connection determines how much of a signal is passed through to the neuron.
    --------------------------------------------------------------------  */
     
    class Connection{
      float connEntry;
      float weight;
      float connExit;
       
      //This is the default constructor for an Connection
      Connection(){
        randomiseWeight();
      }
       
      //A custom weight for this Connection constructor
      Connection(float tempWeight){
        setWeight(tempWeight);
      }
       
      //Function to set the weight of this connection
      void setWeight(float tempWeight){
        weight=tempWeight;
      }
       
      //Function to randomise the weight of this connection
      void randomiseWeight(){
        setWeight(random(2)-1);
      }
       
      //Function to calculate and store the output of this Connection
      float calcConnExit(float tempInput){
        connEntry = tempInput;
        connExit = connEntry * weight;
        return connExit;
      }
    }
     
     
    /* -----------------------------------------------------------------
       A neuron does all the processing and calculation to convert an input into an output
    --------------------------------------------------------------------- */
     
    class Neuron{
      Connection[] connections={};
      float bias;
      float neuronInputValue;
      float neuronOutputValue;
      float deltaError;
       
      //The default constructor for a Neuron
      Neuron(){
      }
       
      /*The typical constructor of a Neuron - with random Bias and Connection weights */
      Neuron(int numOfConnections){
        randomiseBias();
        for(int i=0; i<numOfConnections; i++){
          Connection conn = new Connection();
          addConnection(conn);
        }
      }
       
      //Function to add a Connection to this neuron
      void addConnection(Connection conn){
          connections = (Connection[]) append(connections, conn);
      }
       
      /* Function to return the number of connections associated with this neuron.*/
      int getConnectionCount(){
          return connections.length;
      }
       
      //Function to set the bias of this Neron
      void setBias(float tempBias){
        bias = tempBias;
      }
       
      //Function to randomise the bias of this Neuron
      void randomiseBias(){
        setBias(random(1));
      }
       
      /*Function to convert the inputValue to an outputValue
      Make sure that the number of connEntryValues matches the number of connections */
       
      float getNeuronOutput(float[] connEntryValues){
        if(connEntryValues.length!=getConnectionCount()){
          println("Neuron Error: getNeuronOutput() : Wrong number of connEntryValues");
          exit();
        }
         
        neuronInputValue=0;
         
        /* First SUM all of the weighted connection values (connExit) attached to this neuron. This becomes the neuronInputValue. */
        for(int i=0; i<getConnectionCount(); i++){
          neuronInputValue+=connections[i].calcConnExit(connEntryValues[i]);
        }
         
        //Add the bias to the Neuron's inputValue
        neuronInputValue+=bias;
         
        /* Send the inputValue through the activation function to produce the Neuron's outputValue */
        neuronOutputValue=Activation(neuronInputValue);
         
        //Return the outputValue
        return neuronOutputValue;
      }
       
      //Activation function
      float Activation(float x){
        float activatedValue = 1 / (1 + exp(-1 * x));
        return activatedValue;
      }
       
    }
     
    class Layer{
      Neuron[] neurons = {};
      float[] layerINPUTs={};
      float[] actualOUTPUTs={};
      float[] expectedOUTPUTs={};
      float layerError;
      float learningRate;
       
       
      /* This is the default constructor for the Layer */
      Layer(int numberConnections, int numberNeurons){
        /* Add all the neurons and actualOUTPUTs to the layer */
        for(int i=0; i<numberNeurons; i++){
          Neuron tempNeuron = new Neuron(numberConnections);
          addNeuron(tempNeuron);
          addActualOUTPUT();
        }
      }
         
       
      /* Function to add an input or output Neuron to this Layer */
      void addNeuron(Neuron xNeuron){
            neurons = (Neuron[]) append(neurons, xNeuron);
      }
       
       
      /* Function to get the number of neurons in this layer */
      int getNeuronCount(){
        return neurons.length;
      }
       
       
      /* Function to increment the size of the actualOUTPUTs array by one. */
      void addActualOUTPUT(){
          actualOUTPUTs = (float[]) expand(actualOUTPUTs,(actualOUTPUTs.length+1));
      }
       
       
      /* Function to set the ENTIRE expectedOUTPUTs array in one go. */
      void setExpectedOUTPUTs(float[] tempExpectedOUTPUTs){
        expectedOUTPUTs=tempExpectedOUTPUTs;
      }
       
       
      /* Function to clear ALL values from the expectedOUTPUTs array */
      void clearExpectedOUTPUT(){
           expectedOUTPUTs = (float[]) expand(expectedOUTPUTs, 0);
      }
       
       
      /* Function to set the learning rate of the layer */
      void setLearningRate(float tempLearningRate){
        learningRate=tempLearningRate;
      }
       
       
      /* Function to set the inputs of this layer */
      void setInputs(float[] tempInputs){
        layerINPUTs=tempInputs;
      }
       
       
       
      /* Function to convert ALL the Neuron input values into Neuron output values in this layer, through a special activation function. */
      void processInputsToOutputs(){
         
        /* neuronCount is used a couple of times in this function. */
        int neuronCount = getNeuronCount();
         
        /* Check to make sure that there are neurons in this layer to process the inputs */
        if(neuronCount>0) {
          /* Check to make sure that the number of inputs matches the number of Neuron Connections. */
          if(layerINPUTs.length!=neurons[0].getConnectionCount()){
            println("Error in Layer: processInputsToOutputs: The number of inputs do NOT match the number of Neuron connections in this layer");
            exit();
          } else {
            /* The number of inputs are fine : continue
               Calculate the actualOUTPUT of each neuron in this layer,
               based on their layerINPUTs (which were previously calculated).
               Add the value to the layer's actualOUTPUTs array. */
            for(int i=0; i<neuronCount;i++){
              actualOUTPUTs[i]=neurons[i].getNeuronOutput(layerINPUTs);
            }
          }
        }else{
          println("Error in Layer: processInputsToOutputs: There are no Neurons in this layer");
          exit();
        }
      }
       
       
      /* Function to get the error of this layer */
      float getLayerError(){
        return layerError;
      }
       
       
      /* Function to set the error of this layer */
      void setLayerError(float tempLayerError){
        layerError=tempLayerError;
      }
       
       
      /* Function to increase the layerError by a certain amount */
      void increaseLayerErrorBy(float tempLayerError){
        layerError+=tempLayerError;
      }
       
       
      /* Function to calculate and set the deltaError of each neuron in the layer */
      void setDeltaError(float[] expectedOutputData){
        setExpectedOUTPUTs(expectedOutputData);
        int neuronCount = getNeuronCount();
        /* Reset the layer error to 0 before cycling through each neuron */
        setLayerError(0);
         for(int i=0; i<neuronCount;i++){
           neurons[i].deltaError = actualOUTPUTs[i]*(1-actualOUTPUTs[i])*(expectedOUTPUTs[i]-actualOUTPUTs[i]);
            
           /* Increase the layer Error by the absolute difference between the calculated value (actualOUTPUT) and the expected value (expectedOUTPUT). */
           increaseLayerErrorBy(abs(expectedOUTPUTs[i]-actualOUTPUTs[i]));
         }
      }
       
       
      /* Function to train the layer : which uses a training set to adjust the connection weights and biases of the neurons in this layer */
      void trainLayer(float tempLearningRate){
        setLearningRate(tempLearningRate);
         
        int neuronCount = getNeuronCount();
         
        for(int i=0; i<neuronCount;i++){
          /* update the bias for neuron[i] */
          neurons[i].bias += (learningRate * 1 * neurons[i].deltaError);
           
          /* update the weight of each connection for this neuron[i] */
          for(int j=0; j<neurons[i].getConnectionCount(); j++){
              neurons[i].connections[j].weight += (learningRate * neurons[i].connections[j].connEntry * neurons[i].deltaError);
          }  
        }
      }
    }
     
    /* -------------------------------------------------------------
       The Neural Network class is a container to hold and manage all the layers
       ---------------------------------------------------------------- */
     
    class NeuralNetwork{
      Layer[] layers = {};
      float[] arrayOfInputs={};
      float[] arrayOfOutputs={};
      float learningRate;
      float networkError;
      float trainingError;
      int retrainChances=0;
       
      NeuralNetwork(){
        /* the default learning rate of a neural network is set to 0.1, which can changed by the setLearningRate(lR) function. */
        learningRate=0.1;
      }
       
       
       
      /* Function to add a Layer to the Neural Network */
      void addLayer(int numConnections, int numNeurons){
        layers = (Layer[]) append(layers, new Layer(numConnections,numNeurons));
      }
     
     
     
      /* Function to return the number of layers in the neural network */
      int getLayerCount(){
          return layers.length;
      }
       
       
       
      /* Function to set the learningRate of the Neural Network */
      void setLearningRate(float tempLearningRate){
        learningRate=tempLearningRate;
      }
       
       
       
      /* Function to set the inputs of the neural network */
      void setInputs(float[] tempInputs){
        arrayOfInputs=tempInputs;
      }
       
       
       
      /* Function to set the inputs of a specified layer */
      void setLayerInputs(float[] tempInputs, int layerIndex){
        if(layerIndex>getLayerCount()-1){
          println("NN Error: setLayerInputs: layerIndex=" + layerIndex + " exceeded limits= " + (getLayerCount()-1));
        } else {
          layers[layerIndex].setInputs(tempInputs);
        }
      }
       
       
       
      /* Function to set the outputs of the neural network */
      void setOutputs(float[] tempOutputs){
        arrayOfOutputs=tempOutputs;
      }
       
       
       
      /* Function to return the outputs of the Neural Network */
      float[] getOutputs(){
        return arrayOfOutputs;
      }
       
       
       
      /* Function to process the Neural Network's input values and convert them to an output pattern using ALL layers in the network */
      void processInputsToOutputs(float[] tempInputs){
        setInputs(tempInputs);
         
        /* Check to make sure that the number of NeuralNetwork inputs matches the Neuron Connection Count in the first layer. */
        if(getLayerCount()>0){
          if(arrayOfInputs.length!=layers[0].neurons[0].getConnectionCount()){
            println("NN Error: processInputsToOutputs: The number of inputs do NOT match the NN");
            exit();
          } else {
            /* The number of inputs are fine : continue */
            for(int i=0; i<getLayerCount(); i++){
               
              /*Set the INPUTs for each layer: The first layer gets it's input data from the NN, whereas the 2nd and subsequent layers get their input data from the previous layer's actual output. */
              if(i==0){
                setLayerInputs(arrayOfInputs,i);
              } else {
                setLayerInputs(layers[i-1].actualOUTPUTs, i);
              }
               
              /* Now that the layer has had it's input values set, it can now process this data, and convert them into an output using the layer's neurons. The outputs will be used as inputs in the next layer (if available). */
              layers[i].processInputsToOutputs();
            }
            /* Once all the data has filtered through to the end of network, we can grab the actualOUTPUTs of the LAST layer
               These values become or will be set to the NN output values (arrayOfOutputs), through the setOutputs function call. */
            setOutputs(layers[getLayerCount()-1].actualOUTPUTs);
          }
        }else{
          println("Error: There are no layers in this Neural Network");
          exit();
        }
      }
       
       
       
       
      /* Function to train the entire network using an array. */
      void trainNetwork(float[] inputData, float[] expectedOutputData){
        /* Populate the ENTIRE network by processing the inputData. */
        processInputsToOutputs(inputData);
         
        /* train each layer - from back to front (back propagation) */
        for(int i=getLayerCount()-1; i>-1; i--){
          if(i==getLayerCount()-1){
            layers[i].setDeltaError(expectedOutputData);
            layers[i].trainLayer(learningRate);
            networkError=layers[i].getLayerError();
          } else {
            /* Calculate the expected value for each neuron in this layer (eg. HIDDEN LAYER) */
            for(int j=0; j<layers[i].getNeuronCount(); j++){
              /* Reset the delta error of this neuron to zero. */
              layers[i].neurons[j].deltaError=0;
              /* The delta error of a hidden layer neuron is equal to the SUM of [the PRODUCT of the connection.weight and error of the neurons in the next layer(eg OUTPUT Layer)]. */
              /* Connection#1 of each neuron in the output layer connect with Neuron#1 in the hidden layer */
              for(int k=0; k<layers[i+1].getNeuronCount(); k++){
                layers[i].neurons[j].deltaError += (layers[i+1].neurons[k].connections[j].weight * layers[i+1].neurons[k].deltaError);
              }
              /* Now that we have the sum of Errors x weights attached to this neuron. We must multiply it by the derivative of the activation function. */
              layers[i].neurons[j].deltaError *= (layers[i].neurons[j].neuronOutputValue * (1-layers[i].neurons[j].neuronOutputValue));
            }
            /* Now that you have all the necessary fields populated, you can now Train this hidden layer and then clear the Expected outputs, ready for the next round. */
            layers[i].trainLayer(learningRate);
            layers[i].clearExpectedOUTPUT();
          }
        }
      }
       
       
       
       
       
      /* Function to train the entire network, using an array of input and expected data within an ArrayList */
      void trainingCycle(ArrayList trainingInputData, ArrayList trainingExpectedData, Boolean trainRandomly){
          int dataIndex;
           
          /* re-initialise the training Error with every cycle */
          trainingError=0;
           
          /* Cycle through the training data either randomly or sequentially */
          for(int i=0; i<trainingInputData.size(); i++){
            if(trainRandomly){
              dataIndex=(int) (random(trainingInputData.size()));
            } else {
              dataIndex=i;
            }
      
            trainNetwork((float[]) trainingInputData.get(dataIndex),(float[]) trainingExpectedData.get(dataIndex));
             
            /* Use the networkError variable which is calculated at the end of each individual training session to calculate the entire trainingError. */
            trainingError+=abs(networkError);
          }
      }
       
       
       
       
       
      /* Function to train the network until the Error is below a specific threshold */
      void autoTrainNetwork(ArrayList trainingInputData, ArrayList trainingExpectedData, float trainingErrorTarget, int cycleLimit){
        trainingError=9999;
        int trainingCounter=0;
         
         
        /* cycle through the training data until the trainingError gets below trainingErrorTarget (eg. 0.0005) or the training cycles have exceeded the cycleLimit
     
    variable (eg. 10000). */
        while(trainingError>trainingErrorTarget && trainingCounter<cycleLimit){
           
          /* re-initialise the training Error with every cycle */
          trainingError=0;
           
          /* Cycle through the training data randomly */
          trainingCycle(trainingInputData, trainingExpectedData, true);
           
          /* increment the training counter to prevent endless loop */
          trainingCounter++;
        }
         
        /* Due to the random nature in which this neural network is trained. There may be occasions when the training error may drop below the threshold
           To check if this is the case, we will go through one more cycle (but sequentially this time), and check the trainingError for that cycle
           If the training error is still below the trainingErrorTarget, then we will end the training session.
           If the training error is above the trainingErrorTarget, we will continue to train. It will do this check a  Maximum of 9 times. */
        if(trainingCounter<cycleLimit){
           trainingCycle(trainingInputData, trainingExpectedData, false);
           trainingCounter++;
           
           if(trainingError>trainingErrorTarget){
             if (retrainChances<10){
               retrainChances++;
               autoTrainNetwork(trainingInputData, trainingExpectedData,trainingErrorTarget, cycleLimit);
             }
           }
            
        } else {
          println("CycleLimit has been reached. Has been retrained " + retrainChances + " times.  Error is = " + trainingError);
        }  
      }
    }   
    
    The above code was formatted using hilite.me

    14 August 2011

    Neural Network (Part 6) : Back Propagation, a worked example

    A worked example of a Back-propagation training cycle.




    In this example we will create a 2 layer network (as seen above), to accept 2 readings, and produce 2 outputs. The readings are (0,1) and the expectedOutputs in this example are (1,0).

    Step 1: Create the network

    NeuralNetwork NN = new NeuralNetwork();   
    NN.addLayer(2,2);
    NN.addLayer(2,2);
    float[] readings = {0,1};
    float[] expectedOutputs = {1,0};
    NN.trainNetwork(readings,expectedOutputs);

    This neural network will have randomised weights and biases when created.
    Let us assume that the network generates the following random variables:

    LAYER1.Neuron1
    Layer1.Neuron1.Connection1.weight = cW111 = 0.3
    Layer1.Neuron1.Connection2.weight = cW112 = 0.8
    Layer1.Neuron1.Bias = bW11 = 0.5

    LAYER1.Neuron2
    Layer1.Neuron2.Connection1.weight = cW121 =  0.1
    Layer1.Neuron2.Connection2.weight = cW122 =  0.1
    Layer1.Neuron2.Bias = bW12 = 0.2

    LAYER2.Neuron1
    Layer2.Neuron1.Connection1.weight = cW211 = 0.6
    Layer2.Neuron1.Connection2.weight = cW212 = 0.4
    Layer2.Neuron1.Bias = bW21 = 0.4

    LAYER2.Neuron2
    Layer2.Neuron2.Connection1.weight = cW221 = 0.9
    Layer2.Neuron2.Connection2.weight = cW222 = 0.9
    Layer2.Neuron2.Bias = bW22 = 0.5




    Step 2: Process the Readings through the Neural Network

    a) Provide the Readings to the first layer, and calculate the neuron outputs

    The readings provided to the neural network is (0,1), which go straight through to the first layer (layer1).
    Starting with Layer 1:
    Layer1.INPUT1 = 0
    Layer1.INPUT2 =1

       Calculate Layer1.Neuron1.NeuronOutput
       ConnExit (cEx111) = ConnEntry (cEn111)  x Weight (cW111) = 0 x 0.3 = 0;
       ConnExit (cEx112) = ConnEntry (cEn112)  x Weight (cW112) = 1 x 0.8 = 0.8;
       Bias (bEx11) = ConnEntry (1) x Weight (bW11) = 1 x 0.4 = 0.4
       NeuronInputValue11 = 0 + 0.8 + 0.4 = 1.2
       NeuronOutputValue11 = 1/(1+EXP(-1 x 1.2)) = 0.768525
      
      Calculate Layer1.Neuron2.NeuronOutput
       ConnExit (cEx121) = ConnEntry (cEn121)  x Weight (cW121) = 0 x 0.1 = 0;
       ConnExit (cEx122) = ConnEntry (cEn122)  x Weight (cW122) = 1 x 0.1 = 0.1;
       Bias (bEx12) = ConnEntry (1) x Weight (bW12) = 1 x 0.2 = 0.2
       NeuronInputValue12 = 0 + 0.1 + 0.2 = 0.3
       NeuronOutputValue12 = 1/(1+EXP(-1 x 0.3)) = 0.574443


    b) Provide LAYER2 with Layer 1 Outputs.

    Now lets move to  Layer 2:
    Layer2.INPUT1 = NeuronOutputValue11 = 0.768525
    Layer2.INPUT2 = NeuronOutputValue12 = 0.574443

       Calculate Layer2.Neuron1.NeuronOutput
       ConnExit (cEx211) = (cEn211)  x Weight (cW211) = 0.768525 x 0.6 = 0.461115;
       ConnExit (cEx212) = (cEn212)  x Weight (cW212) = 0.574443 x 0.4 = 0.229777;
       Bias (bEx21) = ConnEntry (1) x Weight (bW21) = 1 x 0.4 = 0.4
       NeuronInputValue21 = 0.461115 + 0.229777 + 0.4 = 1.090892
       NeuronOutputValue21 = 1/(1+EXP(-1 x 1.090892)) = 0.74855
      
      Calculate Layer2.Neuron2.NeuronOutput
       ConnExit (cEx221) = (cEn221)  x Weight (cW221) = 0.768525  x 0.1 = 0.076853;
       ConnExit (cEx222) = (cEn222)  x Weight (cW222) = 0.574443  x 0.1 = 0.057444;
       Bias(bEx22) = ConnEntry (1) x Weight (bW22) = 1 x 0.5 = 0.5
       NeuronInputValue22 = 0.076853 + 0.057444 + 0.5 = 0.634297  
       NeuronOutputValue22 = 1/(1+EXP(-1 x 0.634297)) = 0.653463



    Step 3) Calculate the delta error for neurons in layer 2
         -Because layer 2 is the last layer in this neural network -
          we will use the expected output data (1,0) to calculate the delta error.
       
    LAYER2.Neuron1:
    Let Layer2.ExpectedOutput1 = eO21 = 1    
          Layer2.ActualOutput1= aO21 = NeuronOutputValue21= 0.74855         
          Layer2.Neuron1.deltaError1 = dE21

    dE21 =     aO21       x      (1 - aO21)     x  (eO21 - aO21)
           =  (0.74855)  x  (1 - 0.74855)  x  (1 - 0.74855)
            = (0.74855)  x     (0.25145)     x    (0.25145)
            = 0.047329



    LAYER2.Neuron2:
    Let Layer2.ExpectedOutput2 = eO22 = 0         
          Layer2.ActualOutput2     = aO22 = NeuronOutputValue22 = 0.653463      
          Layer2.Neuron2.deltaError = dE22

    dE22  =      aO22       x      (1 - aO22)       x  (eO22 - aO22)
            = (0.653463)  x  (1 - 0.653463)  x  (0 - 0.653463)
            = (0.653463)  x     (0.346537)     x    (-0.653463)
            = -0.14797




    Step 4) Calculate the delta error for neurons in layer 1

    LAYER1.Neuron1 delta Error calculation

    Let              Layer1.Neuron1.deltaError  = dE11 
                                Layer1.actualOutput1  = aO11 = NeuronOutputValue11 =  0.768525
          Layer2.Neuron1.Connection1.weight = cW211   =  0.6
                         Layer2.Neuron1.deltaError = dE21 =  0.047329
          Layer2.Neuron2.Connection1.weight = cW221   =  0.9
                         Layer2.Neuron2.deltaError = dE22 = -0.14797

    dE11 = (aO11)          x  (1 -   aO11)         x ( [cW211   x   dE21]      +   [cW221  x    dE22] )
               = (0.768525) x   (1 - 0.768525)     x   ([0.6        x  0.047329]  +   [  0.9      x  -0.14797]  )
               = -0.01864

    LAYER1.Neuron2 delta Error calculation

    Let              Layer1.Neuron2.deltaError  = dE12 
                                Layer1.actualOutput2  = aO12    = NeuronOutputValue12 =  0.574443
          Layer2.Neuron1.Connection2.weight = cW212   =  0.4
                         Layer2.Neuron1.deltaError = dE21 =  0.047329
          Layer2.Neuron2.Connection2.weight = cW222   =  0.9
                         Layer2.Neuron2.deltaError = dE22 = -0.14797

    dE12  = (aO12)          x  (1 -   aO12)         x ( [cW212  x     dE21]      +   [cW222  x    dE22] )
               = (0.574443) x   (1 - 0.574443)  x     ([0.4      x  0.047329]  +      [  0.9      x  -0.14797]  )
               = -0.02793





    Step 5) Update Layer_2 neuron connection weights and bias (with a learning rate (LR) = 0.1)


    Layer 2, Neuron 1 calculations:

    Let
    Layer2.Neuron1.Connection1.New_weight = New_cW211
    Layer2.Neuron1.Connection1.Old_weight   =   Old_cW211   = 0.6
    Layer2.Neuron1.Connection1.connEntry =                 cEn211 = 0.768525
    Layer2.Neuron1.deltaError =                                       dE21 = 0.047329

    New_cW211 = Old_cW211 + (LR x cEn211 x dE21)
                         =    0.6            + (0.1 x 0.768525 x 0.047329)
                         =    0.6            + ( 0.003627)
                         =    0.603627



    Layer2.Neuron1.Connection2.New_weight = New_cW212
    Layer2.Neuron1.Connection2.Old_weight   =   Old_cW212 = 0.4
    Layer2.Neuron1.Connection2.connEntry =                cEn212 = 0.574443
    Layer2.Neuron1.deltaError =                                      dE21 = 0.047329

    New_cW212 = Old_cW212 + (LR x cEn212 x dE21)
                         =    0.4            + (0.1 x 0.574443 x 0.047329)
                         =    0.4            + (0.002719)
                         =    0.402719



    Layer2.Neuron1.New_Bias = New_Bias21
    Layer2.Neuron1.Old_Bias =    Old_Bias21 = 0.4
    Layer2.Neuron1.deltaError =             dE21 = 0.047329

    New_Bias21 = Old_Bias21 + (LR x  1  x  de21)
                         =  0.4              + (0.1 x 1  x 0.047329)
                         =  0.4              + (0.0047329)
                         =  0.4047329


    --------------------------------------------------------------------

    Layer 2, Neuron 2 calculations:

    Layer2.Neuron2.Connection1.New_weight = New_cW221
    Layer2.Neuron2.Connection1.Old_weight =    Old_cW221 = 0.9
    Layer2.Neuron2.Connection1.connEntry =               cEn221 = 0.768525
    Layer2.Neuron2.deltaError =                                     dE22 = -0.14797

    New_cW221 = Old_cW221 + (LR x cEn221 x dE22)
                         =    0.9            + (0.1 x 0.768525 x -0.14797)
                         =    0.9            + ( -0.01137)
                         =    0.88863


    Layer2.Neuron2.Connection2.New_weight = New_cW222
    Layer2.Neuron2.Connection2.Old_weight =    Old_cW222 = 0.9
    Layer2.Neuron2.Connection2.connEntry =              cEn222 = 0.574443
    Layer2.Neuron2.deltaError =                                    dE22 = -0.14797

    New_cW222 = Old_cW222 + (LR x cEn222 x dE22)
                         =    0.9            + (0.1 x 0.574443 x -0.14797)
                         =    0.9            + (-0.0085)
                         =    0.8915


    Layer2.Neuron2.New_Bias = New_Bias22
    Layer2.Neuron2.Old_Bias =    Old_Bias22 =  0.5
    Layer2.Neuron2.deltaError =             dE22 = -0.14797

    New_Bias22 = Old_Bias22 + (LR x  1  x  de22)
                         =  0.5              + (0.1 x  1  x  -0.14797)
                         =  0.5            +   (-0.014797)
                         =  0.485203



    --------------------------------------------------------------------------


    Step 6) Update Layer_1 neuron connection weights and bias.

    Layer 1, Neuron 1 calculations:

    Let
    Layer1.Neuron1.Connection1.New_weight = New_cW111
    Layer1.Neuron1.Connection1.Old_weight   =   Old_cW111   =  0.3
    Layer1.Neuron1.Connection1.connEntry =                 cEn111 = 0
    Layer1.Neuron1.deltaError =                                       dE11 = -0.01864

    New_cW111 = Old_cW111 + (LR   x  cEn111   x   dE11)
                         =  0.3              +   (0.1   x     0      x    -0.01864)
                         =  0.3              +   ( 0 )
                         =  0.3    


    Layer1.Neuron1.Connection2.New_weight = New_cW112
    Layer1.Neuron1.Connection2.Old_weight   =   Old_cW112 = 0.8
    Layer1.Neuron1.Connection2.connEntry =               cEn112 = 1
    Layer1.Neuron1.deltaError =                                      dE11 = -0.01864

    New_cW112 = Old_cW112 + (LR   x  cEn112   x   dE11)
                         =  0.8    +            (0.1     x    1     x     -0.01864)
                         =  0.8    +            (-0.001864)
                         =  0.798136   


    Layer1.Neuron1.New_Bias = New_Bias11
    Layer1.Neuron1.Old_Bias =    Old_Bias11 = 0.5
    Layer1.Neuron1.deltaError =             dE11 = -0.01864

    New_Bias11 = Old_Bias11 + (LR   x  1   x  dE11)
                         =  0.5              + (0.1   x 1   x -0.01864 )
                         =  0.5              + (-0.001864)
                         =  0.498136

    --------------------------------------------------------------------

    Layer 1, Neuron 2 calculations:

    Layer1.Neuron2.Connection1.New_weight = New_cW121
    Layer1.Neuron2.Connection1.Old_weight =    Old_cW121 = 0.1
    Layer1.Neuron2.Connection1.connEntry =               cEn121 = 0
    Layer1.Neuron2.deltaError =                                     dE12 =   -0.02793

    New_cW121 = Old_cW121 + (LR  x  cEn121 x dE12)
                         =  0.1               + (0.1  x     0     x  -0.02793 )
                         =  0.1   +   (0)
                         =  0.1




    Layer1.Neuron2.Connection2.New_weight = New_cW122
    Layer1.Neuron2.Connection2.Old_weight =    Old_cW122 = 0.1
    Layer1.Neuron2.Connection2.connEntry =              cEn122 = 1
    Layer1.Neuron2.deltaError =                                    dE12 =  -0.02793

    New_cW122 = Old_cW122 + (LR  x  cEn122  x   dE12)
                         =  0.1                + (0.1   x    1      x  -0.02793)
                         =  0.1    +  (-0.002793)
                         =  0.097207



    Layer1.Neuron2.New_Bias = New_Bias12
    Layer1.Neuron2.Old_Bias =    Old_Bias12 =  0.2
    Layer1.Neuron2.deltaError =             dE12 =  -0.02793

    New_Bias12 = Old_Bias12 + (LR    x  1  x  de12)
                         =  0.2             +   (0.1  x  1  x  -0.02793)
                         =  0.2             +  (-0.002793)
                         =  0.197207


    ----------------------------------------------------------------------

    All done. That was just one training cycle. Thank goodness we have computers !
    A computer can process these calculations really quickly, and depending on how complicated your neural network is (ie. number of layers, and number of neurons per layer), you may find that the training procedure may take some time. But believe me, if you have designed it right, it is well worth the wait.
    Because once you have the desired weights and bias values set up, you are good to go, and as you receive data, the computer can do a single forward pass in a fraction of a second, and you will get your desired output, hopefully :)

    Here is a complete Processing.org script that demonstrates the use of my neural network.
    Neural Network (Part 7): Cut and Paste Code (click here).

    If you liked my tutorial - please let me know in the comments. It is sometimes hard to know if anyone is actually reading this stuff. If you use my code in your own project, I am also happy for you to leave a link to a YouTube video etc in the comments also.

    To go back to the table of contents click here