Posts with «neural network» label

Full Self-Driving, on a Budget

Self-driving is currently the Holy Grail in the automotive world, with a number of companies racing to build general-purpose autonomous vehicles that can get from point A to point B with no user input. While no one has brought one to market yet, at least one has promised this feature and had customers pay for it, but continually moved the goalposts for delivery due to how challenging this problem turns out to be. But it doesn’t need to be that hard or expensive to solve, at least in some situations.

The situation in question is driving on a single stretch of highway, and only focuses on steering, so it doesn’t handle the accelerator or brake pedal input. The highway is driven normally, using a webcam to take images of the route and an Arduino to capture data about the steering angle. The idea here is that with enough training the Arduino could eventually steer the car. But first some math needs to happen on the training data since the steering wheel is almost always not turning the car, so the Arduino knows that actual steering events aren’t just statistical anomalies. After the training, the system does a surprisingly good job at “driving” based on this data, and does it on a budget not much larger than laptop, microcontroller, and webcam.

Admittedly, this project was a proof-of-concept to investigate machine learning, neural networks, and other statistical algorithms used in these sorts of systems, and doesn’t actually drive any cars on any roadways. Even the creator says he wouldn’t trust it himself, but that he was pleasantly surprised by the results of such a simple system. It could also be expanded out to handle brake and accelerator pedals with separate neural networks as well. It’s not our first budget-friendly self-driving system, either. This one makes it happen with the enormous computing resources of a single Android smartphone.

Hack a Day 17 Oct 21:00

arduino car machine learning neural network self-driving statistics steering vehicle webcam

Mind-Controlled Flamethrower

Mind control might seem like something out of a sci-fi show, but like the tablet computer, universal translator, or virtual reality device, is actually a technology that has made it into the real world. While these devices often requires on advanced and expensive equipment to interpret brain waves properly, with the right machine learning system it’s possible to do things like this mind-controlled flame thrower on a much smaller budget. (Video, embedded below.)

[Nathaniel F] was already experimenting with using brain-computer interfaces and machine learning, and wanted to see if he could build something practical combining these two technologies. Instead of turning to an EEG machine to read brain patterns, he picked up a much less expensive Mindflex and paired it with a machine learning system running TensorFlow to make up for some of its shortcomings. The processing is done by a Raspberry Pi 4, which sends commands to an Arduino to fire the flamethrower when it detects the proper thought patterns. Don’t forget the flamethrower part of this build either: it was designed and built entirely by [Nathanial F] as well using gas and an arc lighter.

While the build took many hours of training to gather the proper amount of data to build the neural network and works as the proof of concept he was hoping for, [Nathaniel F] notes that it could be improved by replacing the outdated Mindflex with a better EEG. For now though, we appreciate seeing sci-fi in the real world in projects like this, or in other mind-controlled projects like this one which converts a prosthetic arm into a mind-controlled music synthesizer.

Hack a Day 12 May 12:00

arduino flamethrower machine learning mind control neural network raspberry pi tensorflow tensorflow lite

Wiping Your Windscreen To The Beat

Nothing spoils your mood quite like your windscreen wipers not feeling it when the beat drops. Every major car manufacturer is focused on trying to build the electric self driving vehicle for the masses, yet ignoring this very real problem. Well [Ian Charnas] is taking charge, and has successfully slaved his car’s wipers to beat of its stereo.

Starting with the basics, [Ian] first needed to control the speed of the wiper motor. This was done using a custom power supply adapted from another project. The brain of the system is a Raspberry Pi 3B+ which runs a phase locked loop algorithm to sync the music and the motor. Detecting the beat turned out to be the most difficult part of the project, and from the research [Ian] did, there is no standard solution. He ended up settling on “madmom“, a Python audio and music signal processing library, which runs a neural net to detect the beat in real time. The Raspi sends the required PWM and Enable signals to an Arduino over serial, which in turn controls the power supply. The entire system was neatly integrated in the car, with a switch in the dash that connects the motor to the new power supply on demand, to allow the wipers to still be used normally (and safely).

[Ian] filed a provisional patent application for the idea, and will be putting it on auction on eBay soon, with the hope that some major car manufacturer would be interested. For older cars, you can shove an Arduino into the stereo, or do a super cheap bluetooth upgrade. Check out the video after the break.

Hack a Day 25 Oct 00:00

arduino car stereo machine learning music musical hacks neural network raspberry pi transportation hacks

Modern Wizard Summons Familiar Spirit

In European medieval folklore, a practitioner of magic may call for assistance from a familiar spirit who takes an animal form disguise. [Alex Glow] is our modern-day Merlin who invoked the magical incantations of 3D printing, Arduino, and Raspberry Pi to summon her familiar Archimedes: The AI Robot Owl.

The key attraction in this build is Google’s AIY Vision kit. Specifically the vision processing unit that tremendously accelerates image classification tasks running on an attached Raspberry Pi Zero W. It no longer consumes several seconds to analyze each image, classification can now run several times per second, all performed locally. No connection to Google cloud required. (See our earlier coverage for more technical details.) The default demo application of a Google AIY Vision kit is a “joy detector” that looks for faces and attempts to determine if a face is happy or sad. We’ve previously seen this functionality mounted on a robot dog.

[Alex] aimed to go beyond the default app (and default box) to create Archimedes, who was to reward happy people with a sticker. As a moving robotic owl, Archimedes had far more crowd appeal than the vision kit’s default cardboard box. All the kit components have been integrated into Archimedes’ head. One eye is the expected Pi camera, the other eye is actually the kit’s piezo buzzer. The vision kit’s LED-illuminated button now tops the dapper owl’s hat.

Archimedes was created to join in Google’s promotion efforts. Their presence at this Maker Faire consisted of two tents: one introductory “Learn to Solder” tent where people can create a blinky LED badge, and the other tent is focused on their line of AIY kits like this vision kit. Filled with demos of what the kits can do aside from really cool robot owls.

Hopefully these promotional efforts helped many AIY kits find new homes in the hands of creative makers. It’s pretty exciting that such a powerful and inexpensive neural net processor is now widely available, and we look forward to many more AI-powered hacks to come.

Nematoduino: A Roundworm Neural Model on an Arduino

When it comes to building a neural network to simulate complex behavior, Arduino isn’t exactly the first platform that springs to mind. But when your goal is to model the behavior of an organism with only a handful of neurons, the constraints presented by an Arduino start to make sense.

It may be the most important non-segmented worm you’ve never heard of, but Caenorhabditis elegans, mercifully abbreviated C. elegans, is an important model organism for neurobiology, having had its entire nervous system mapped in 2012. [Nathan Griffith] used this “connectome” to simulate a subset of the diminutive nematode’s behaviors, specifically movements toward attractants and away from obstacles. Riding atop a small robot chassis, the Arduino sends signals to the motors when the model determines it’s time to fire the virtual worm’s muscles. An ultrasonic sensor stands in for the “nose touch” neurons of the real worm, and when the model is not busy avoiding a touch, it’s actively seeking something to eat using the “chemotaxis” behavior. The model is up on GitHub and [Nathan] hopes it provides an approachable platform for would-be neuroroboticists.

This isn’t the first time someone has modeled the nematode’s connectome in silico, but kudos to [Nathan] for accomplishing it within the constraints an Arduino presents.

Filed under: Arduino Hacks, misc hacks

Hack a Day 13 Oct 09:00

arduino arduino hacks c. elegans connectome misc hacks neural network neurons roundworm simulation

Poor Man's Colour Detector (Part 2) - The project

In this project we will be detecting the colour of 3 different Mega Blok colours (Red, Yellow and Green). We will be using an Arduino UNO connected to 2 LEDs (one Yellow and one Red LED) as light detectors, and an RGB LED to illuminate the subject. We will use a Photocell to account for varying ambient light levels.

The signals from the LED light sensors will be sent to a Processing.org program via a Serial command. The computer program will make use of my Neural Network to classify the pattern of results and hopefully provide the correct colour "answer". The program should change the colour of the computer screen background to coincide with the colour of the Mega Blok.

The Video

Parts Required:

Arduino UNO...........x1
Red LED .................x1
Yellow LED.............x1
330 Ohm resistors... x 5 (for the LEDs)
Photocell .................x1
10K Ohm resistor....x1 (for the Photocell)
Around 11 wires and a Breadboard (or two) to put it all together

Here is the Fritzing Sketch: (made with Fritzing)

The Arduino Code

Load the following code into the Arduino.

arduino code Arduino: Colour Detector

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/* Define the pin for the PhotoResistor */
#define PhotoR_Pin 0

/* Define the pins for the Red LED Sensor */
#define Red_LED_Sensor_POS 4
#define Red_LED_Sensor_NEG 5

/* Define the pins for the Yellow LED Sensor */
#define Yellow_LED_Sensor_POS 7
#define Yellow_LED_Sensor_NEG 8

/* Define the pin for the RGB LED torch */
#define RGB_LED_RedPin 11
#define RGB_LED_GreenPin 10
#define RGB_LED_BluePin 9

/* Controls the brightness of the RGB LED */
int intensity=255;


/* Define the maximum cycles/time allowed for each LED to capture light */
long max_darkness=80000;


void setup(){
  /* Setup the RED LED Sensor */
  pinMode(Red_LED_Sensor_POS,OUTPUT);
  digitalWrite(Red_LED_Sensor_POS,LOW);
  
  /* Setup the YELLOW LED Sensor */
  pinMode(Yellow_LED_Sensor_POS,OUTPUT);
  digitalWrite(Yellow_LED_Sensor_POS,LOW);
  
  /* No need to setup the RGB LED Pins */
    
  /* Turn on Serial Protocol */
  Serial.begin(9600);
}

void loop()
{      
  byte byteRead;

   /*  check if data has been sent from the computer: */
  if (Serial.available()) {

    /* read the most recent byte (which will be from 0 to 255): */
    byteRead = Serial.read();
    
    if(byteRead==0){

      /* Turn off if the byte Read was 0 */
      set_RGB_LED(0,0,0,false);

    }else{

      /* set the brightness of the LED and then take readings: */
      set_RGB_LED(0,0,0,false);
      photoR_Read();
      set_RGB_LED(0,0,0,true);
      set_RGB_LED(intensity,0,0,true);
      set_RGB_LED(0,intensity,0,true);
      set_RGB_LED(0,0,intensity,true);
    }
  }
}

void photoR_Read(){
  int ambiLight = analogRead(PhotoR_Pin); 
  ambiLight = map(ambiLight, 0, 900, 0, 50); 
  ambiLight = constrain(ambiLight, 0, 50);
  
   /* Print the Ambient light level to the serial port */
  Serial.println(ambiLight);
}

void set_RGB_LED(int redInt, int greenInt, int blueInt, boolean takeReadings ){
  /* set the brightness and colour of the RGB LED: */
    analogWrite(RGB_LED_RedPin, redInt);
    analogWrite(RGB_LED_GreenPin, greenInt);
    analogWrite(RGB_LED_BluePin, blueInt);
  
  /* If takeReadings is true - then take Readings. */
  if(takeReadings){

    /* Read the amount of Yellow light */
    read_LED('Y', Yellow_LED_Sensor_NEG);
  
    /* Read the amount of Red light */
    read_LED('R', Red_LED_Sensor_NEG);
  }
}

void read_LED(char LED_Colour, int LED_Pin){

  /* Charge the LED by applying voltage in the opposite direction */
  pinMode(LED_Pin,OUTPUT);
  digitalWrite(LED_Pin,HIGH);
  
  /* Read the amount of Light coming into the LED sensor */
  long darkness=0;
  int lightLevel=0;
  pinMode(LED_Pin,INPUT);
  digitalWrite(LED_Pin,LOW);
  
  while((digitalRead(LED_Pin)!=0) && darkness < max_darkness){
     darkness++;
  }
  
  lightLevel=((max_darkness-darkness)+1)/80;
  
  /* Print the light level to the serial port */
  Serial.println(lightLevel);
}

code formatter

The Processing Code:

The processing code is very long:
Please visit this link to copy and paste the code into your Processing sketch.
http://www.openprocessing.org/visuals/?visualID=34210

Make sure to select "Source Code" when you get there: (as displayed below)

If you have any problems with accessing the code - please let me know in the comments section of this blog.

This sketch utilises a simple feed forward Neural Network (that I developed from scratch). For more detailed information about this neural network please navigate through my previous blog postings.

Neural Network

So there you go, a simple idea, a simple outcome, and a lot of "stuff" happening in the background.
I am sorry. This project is not basic, but hopefully someone out there will get some use out of it.

Have fun !

ScottC

ScottC 19 Aug 15:11

arduino arduinobasics best arduino blog code color colour led as sensor mega bloks neural network photocell processing project uno

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

/*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

ScottC 15 Aug 14:06

arduinobasics back propagation best arduino blog code example neural network processing processing.org project tutorial

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);

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

ScottC 14 Aug 10:11

arduinobasics back propagation best arduino blog feed forward neural network processing.org project training tutorial

Neural Network (Part 5): The Back Propagation process

Back-propagation

Back propagation is the process by which you move backwards through the neural network to adjust the weights and biases so as to reduce the total error of the network. The total error of the network is essentially the difference between the end results (actual Outputs) and the expected results. If you expected to get a result of 1, but instead got a 0: you would go back through the network and tweak each of the weights (and bias) values so that your end result was a little bit closer to 1 than before.

The process of back-propagation is such that larger errors and larger weights and biases that create those errors are penalised more than their smaller counterparts. Bigger weights have a bigger influence on the final outcome than smaller weights, and are therefore penalised more for incorrect answers.

After many training cycles, the neural network reaches a stage of equilibrium (not quite, but close enough), whereby the tweaking is insignificant to the final outcome.

If you under-train, then you will get the wrong result more often than desired.

If you over-train, then the neural network will not be able to "think outside the sqaure", so to speak.

So how do you propagate backwards ??

Step 1: Feed-forward pass through:

Send some data through the network to populate all the variables. This feed-forward pass allows you calculate your actualOUTPUTs, which you will use to compare against your expectedOUTPUTs.

Step 2: Calculate delta-error for the neurons in the last layer (output layer).

The delta-error calculation for the neuron(s) in the last layer of the neural network is a liitle bit different than the other layers. You can work this out once you calculate the actualOUTPUTs from the feedforward pass.

Let Last Layer Neuron1.deltaError = LLN1.dE

Last Layer.actualOutput1 = aO1 <--- This is the same as the Neuron1 Output Value

Last Layer.expectedOutput1 = exO1

LLN1.dE = (aO1) x (1-aO1) x (exO1 - aO1);

Once you have calculated the deltaError for every neuron in the last layer (output layer), you can move onto the next step.

Step 3: Calculate the delta-error for the hidden layer neurons

The hidden layers for this neural network, is any layer in the neural network, that is not the last layer. However, each layer should sit like ducks in a row. And we are now going to calculate the delta error for the second last layer in the neural network. This could in theory be the first layer in the network (if this network only had 2 layers).

HLN = Hidden Layer Neuron,

LLN = Last Layer Neuron,

aO=actualOUTPUT,

dE=deltaError

HLN.dE = (HLN.aO) x (1-HLN.aO) x (Sum of [LLN.dE x LLN to HLN connection weight])

Keep moving back through the network layers until you reach the 1st layer (ie, you run out of layers).

Step 4: Update the weights of the connections and Bias of neuron.

a) Multiply the neuron's deltaError which was calculated in either step 2 or 3, by the learning rate (0.1), and by the connection's connEntry value.

b) Then add this calculated value (in Step (4a)) to the current weight of the connection.

neuron.connections[i].weight += (learningRate * neuron.connections[i].connEntry * neuron.deltaError);

The bias is like a connection with a constant connEntry of 1, therefore the calculation is

neuron.bias += (learningRate * 1 * neuron.deltaError);

Up Next: Neural Network (Part 6):

Back Propagation - a fully worked example.

To go back to the table of contents click here

ScottC 12 Aug 16:27

arduinobasics back propagation best arduino blog learning neural network neuron processing.org programming project tutorial

Neural Network (Part 4): The Neural Network class

The Neural Network

Finally, we made it to the Neural Network class. This is the top level class that manages the communication between the layers. This class provides the necessary glue to hold all the layers together. It also controls the flow of information forwards and backwards from layer to layer. Lets have a look at a simple 2 layer neural network.

The above neural network starts with 2 inputs in Layer1 and finishes with 2 outputs in Layer 2.

This Neural Network structure is very modular in design. Layers can be added quite easily without affecting the functionality of the neural network code. The only layer that is treated a little bit differently from other layers in the neural network, is the last layer. However, any/all preceding layers are treated exactly the same. And the differences in the last layer, only really come into effect in Neural Network training.

When building my network, I just need to make sure that the number of outputs (or neurons) in the current layer match the number of connections in the next. If I wanted to create a neural network, that accepted 3 input signals from the outside world, to process them with 10 neurons, but only wanted to output one result... I could build the neural network in the following way.

addLayer(3,10) : This first layer would have 3 layerINPUTs and 10 neurons

addLayer(10,1) : This second (and last) layer would have 10 layerINPUTs and 1 neuron

The neural network class would manage these two layers, to ensure that information was passed from one to the other seemlessly. Here is the code for the Neural Network class that would make it possible:

/* -------------------------------------------------------------------------------------

   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);

    }   

  } 

}

code formatter

The neural network constructor: NeuralNetwork() - automatically sets the learning rate to 0.1. Other than that, the Neural Network object is an empty shell waiting to be filled. The main setup function of the Neural Network class is the addLayer() function, which adds a layer with a specified number of connections and neurons.

Here are the functions of the Neural Network (NN) class:

addLayer() : adds a layer to the NN (from left to right)
getLayerCount() : returns the number of layers in the NN
setLearningRate(): sets the learning Rate to a specified value.
setInputs(): sets the inputs of the NN, and become the layerINPUTs of the 1st layer
setLayerInputs(): set the inputs of a specified layer
setOutputs(): set the outputs of the NN= same as the actualOUTPUTs of the last layer.
getOutputs(): returns the outputs of the NN
processInputsToOutputs(): Converts the NN inputs into outputs by feeding through layers.
trainNetwork(): uses a training set to train the neural network (using an Array).
trainingCycle(): uses a training set to train the neural network (using an ArrayList).
autoTrainNetwork(): cycles through the training data until a specific condition is met

Ok - so we now have all of the structural components required to build a feed forward neural network. And here is how you would create it. Let us build a neural network that accepts data from 4 sensors and has 3 layers . The layers will have 6, 8 and 2 neurons respectively...

NeuralNetwork NN = new NeuralNetwork();
NN.addLayer(4,6);
NN.addLayer(6,8);
NN.addLayer(8,2);

Perfect, we have just created an entire neural network, with randomised weights and biases etc etc.

Unfortunately, the neural network is not that useful at the moment. Before we can even start to use it, we need to put it through school. We need to teach it.

Try to imagine a colour that you have never seen before. Hard isn't it ? That is how the Neural Network feels. So before you can get it to make any sort of classifications, you have to show it some examples of what you are looking for. Once the neural network can make sense of your examples, you use a "validation set" to put it through it's paces. If it performs well, then you are good to go, otherwise it is back to school until it can pass the test. My neural network doesn't have a validation set at the moment, but it seems to work quite well without it. This statement is not entirely true. I tend to validate it using the training data, but maybe in future I will fix it up to use a proper validation set.

So how do you train the neural network ? Back-propagation !

Up Next: Neural Network (Part 5): Back Propagation

To go back to the table of contents click here

ScottC 12 Aug 15:47

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