Posts with «neural network» label

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.

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

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

01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
/* 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);
}



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

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

      1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275
    276
    277
    278
    279
    280
    281
    282
    283
    284
    285
    286
    287
    288
    289
    290
    291
    292
    293
    294
    295
    296
    297
    298
    299
    300
    301
    302
    303
    304
    305
    306
    307
    308
    309
    310
    311
    312
    313
    314
    315
    316
    317
    318
    319
    320
    321
    322
    323
    324
    325
    326
    327
    328
    329
    330
    331
    332
    333
    334
    335
    336
    337
    338
    339
    340
    341
    342
    343
    344
    345
    346
    347
    348
    349
    350
    351
    352
    353
    354
    355
    356
    357
    358
    359
    360
    361
    362
    363
    364
    365
    366
    367
    368
    369
    370
    371
    372
    373
    374
    375
    376
    377
    378
    379
    380
    381
    382
    383
    384
    385
    386
    387
    388
    389
    390
    391
    392
    393
    394
    395
    396
    397
    398
    399
    400
    401
    402
    403
    404
    405
    406
    407
    408
    409
    410
    411
    412
    413
    414
    415
    416
    417
    418
    419
    420
    421
    422
    423
    424
    425
    426
    427
    428
    429
    430
    431
    432
    433
    434
    435
    436
    437
    438
    439
    440
    441
    442
    443
    444
    445
    446
    447
    448
    449
    450
    451
    452
    453
    454
    455
    456
    457
    458
    459
    460
    461
    462
    463
    464
    465
    466
    467
    468
    469
    470
    471
    472
    473
    474
    475
    476
    477
    478
    479
    480
    481
    482
    483
    484
    485
    486
    487
    488
    489
    490
    491
    492
    493
    494
    495
    496
    497
    498
    499
    500
    501
    502
    503
    504
    505
    506
    507
    508
    509
    510
    511
    512
    513
    514
    515
    516
    517
    518
    519
    520
    521
    522
    523
    524
    525
    526
    527
    528
    529
    530
    531
    532
    533
    534
    535
    536
    537
    538
    539
    540
    541
    542
    543
    544
    545
    546
    547
    548
    549
    550
    551
    552
    553
    554
    555
    556
    557
    558
    559
    560
    561
    562
    563
    564
    565
    566
    567
    568
    569
    570
    571
    572
    573
    /*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

    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

    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):



    To go back to the table of contents click here



    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:



    processing code Neural Network Class

    01
    02
    03
    04
    05
    06
    07
    08
    09
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    /* -------------------------------------------------------------------------------------
    
    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 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

    Neural Network (Part 3): The Layer


    The Layer

    The purpose of a layer is mainly to group and manage neurons that are functionally similar, and provide a means to effectively control the flow of information through the network (forwards and backwards). The forward pass is when you convert input values into output values, the backwards pass is only done during network training.

    In my neural network, the Layer is an essential building block of the neural network. They can work individually or as a team. Let us just focus on one layer for now

    This is what a layer with two neurons looks like in my neural network:



    As you can see from the picture above, I tend to treat each neuron as an individual.
    Both neurons have the same connEntry values (cEn11 = cEn21) and (cEn12 = cEn22), which stem from the layerINPUTs. Other than that, the rest is different.  Which means that Neuron1 could produce an output value close to 1, and at the same time Neuron2 could produce an output close to 0, even though they have the same connEntry values at the start.


    The following section will describe how the layerINPUTs get converted to actualOUTPUTs.

    Step1: Populate the layerINPUTs:
    layerINPUTs are just a placeholder for values that have been fed into the neural network, or come from a previous layer within the same neural network. If this is the first layer in the network, then the layerINPUTs would be the Neural Network's input values (eg Sensor data). If this is the 2nd layer in the network, then the layerINPUTs would equal the actualOUTPUTs of Layer One



    Step2: Send each layerINPUT to the neuron's connection in the layer.
    You will notice that every neuron in the same layer will have the same number of connections. This is because each neuron will connect only once to each of the layerINPUTs. The relationship between layerINPUTs and the connEntry values of a neuron are as follows.

              layerINPUTs1:                                                                                 
              cEn11 = layerINPUTs1                  Neuron1.Connection1.connEntry
              cEn21 = layerINPUTs1                  Neuron2.Connection1.connEntry


              layerINPUTs2:                                                                                  
              cEn12 = layerINPUTs2                  Neuron1.Connection2.connEntry
              cEn22 = layerINPUTs2                  Neuron2.Connection2.connEntry

    Therefore, the connEntry of the first connection of every neuron in this layer will equal the first layerINPUT value in this layer.




    Step3: Calculate the connExit values of each connection (including bias)

               Neuron 1:                       
               cEx11 = cEn11  x  cW11
               cEx12 = cEn12  x  cW12
                 bEx1 =    1      x    bW1

               Neuron 2:                       
               cEx21 = cEn21  x  cW21
               cEx22 = cEn22  x  cW22
                 bEx2 =    1      x    bW2




    Step4: Calculate the NeuronInputValue for each neuron

              Neuron1:                                                                       
              Neuron1.NeuronInputValue = cEx11  +  cEx12  +  bEx1


              Neuron2:                                                                       
              Neuron2.NeuronInputValue = cEx21  +  cEx22  +  bEx2




    Step5: Send the NeuronInputValues through an Activation function to produce a NeuronOutputValue

              Neuron1:                                                                                                        
              Neuron1.NeuronOutputValue= 1/(1+EXP(-1 x Neuron1.NeuronInputValue))


              Neuron2:                                                                                                 
              Neuron2.NeuronOutputValue= 1/(1+EXP(-1 x Neuron2.NeuronInputValue))


              Please note that the NeuronInputValues for each neuron are different !





    Step6: Send the NeuronOutputValues to the layer's actualOUTPUTs
    • actualOUTPUT1 = Neuron1.NeuronOutputValue
    • actualOUTPUT2 = Neuron2.NeuronOutputValue



    The NeuronOutputValues become the actualOUTPUTs of this layer, which then become the layerINPUTs of the next layer. And the process is repeated over and over until you reach the final layer, where the actualOUTPUTs become the outputs of the entire neural network.


    Here is the code for the Layer class:


    processing code Layer Class

    01
    02
    03
    04
    05
    06
    07
    08
    09
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    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);
    }
    }
    }
    }

    Within each layer, you have neuron(s) and their associated connection(s). Therefore it makes sense to have a constructor that automatically sets these up.


    If you create a new Layer(2,3), this would automatically
    • add 3 neurons to the layer
    • create 2 connections for each neuron in this layer (to connect to the previous layer neurons).
    • randomise each neuron bias and connection weights.
    • add 3 actualOUTPUT slots to hold the neuron output values.


                                                                                                                                             
    Here are the functions of the Layer class:
    • addNeuron() : adds a neuron to the layer
    • getNeuronCount() : returns the number of neurons in this layer
    • addActualOUTPUT() : adds an actualOUTPUT slot to the layer.
    • setExpectedOUTPUTs() : sets the entire expectedOUTPUTs array in one go.
    • clearExpectedOUTPUT() : clear all values within the expectedOUTPUTs array.
    • setLearningRate() : sets the learning rate of the layer.
    • setInputs() : sets the inputs of the layer.
    • processInputsToOutputs() : convert all layer input values into output values
    • getLayerError() : returns the error of this layer
    • setLayerError() : sets the error of this layer
    • increaseLayerErrorBy() : increases the layer error by a specified amount.
    • setDeltaError() : calculate and set the deltaError for each neuron in this layer
    • trainLayer() : uses a training set to adjust the connection weights and biases of the neurons in this layer
    There are a few functions mentioned above, which I have not yet discussed, and are used for neural network training (back-propagation). Don't worry, we'll go through them in the "back-propagation" section of the tutorial.


    Next up:  Neural Network (Part 4) : The Neural Network class



    To go back to the table of contents click here


    Neural Network (Part 2) : The Neuron

    The Neuron

    The main purpose of the Neuron is to store the values that flow through the neural network. They also do a bit of processing through the use of an Activation function. The activation function is quite an important feature of the neural network. It essentially enables the neuron to make decisions (yes/no and greyzone) based on the values provided to them. The other feature of activation functions is the ability to map values of infinite size to a range of 0 to 1. We will be using the Sigmoid function.





    The neuron accumulates signals from one or more connections, adds a bias value, and then sends this value through the activation function to produce a neuron output. Each neuron output will be within the range of 0 to 1 (due to the activation function).

    So lets take a look at  a single neuron with 2 connections (+ bias) feeding into it.
    As seen below.




    connEntry                                                       weight                                             
    Neuron.Connection1.connEntry = cEn1           Neuron.Connection1.weight = cW1
    Neuron.Connection2.connEntry = cEn2           Neuron.Connection2.weight = cW2
    Neuron.Bias.connEntry = bEn = 1 (always)                Neuron.Bias.weight = bW

    connExit                                             
    Neuron.Connection1.connExit = cEx1
    Neuron.Connection2.connExit = cEx2
    Neuron.Bias.connExit = bEx

    You need to multiply the connEntry value by the weight to get the connExit value.

    Connection #1:                      
             cEx1 = cW1  x   cEn1


    Connection # 2:                      
              cEx2 = cW2  x  cEn2


    Bias:                                       
                          bEx = bW x 1

    As you can see from the Bias calculation, the Bias.connEntry (bEn) value is always 1, which means that the Bias.connExit (bEx) value is always equal to the Bias.weight (bW) value.




    The Neuron Input Value is equal to the sum of all the connExit values (cEx1 and cEx2 in this case) plus the bias (bEx), and can be represented by the following formula.

    Neuron Input Value:                                                                                                    
    Neuron Input Value = cEx1 + cEx2 + bEx      
     or
    Neuron Input Value = [cW1 x cEn1] + [cW2 x cEn2] + [bW x 1]




    Now that we have the Neuron Input Value, we can put this through the Activation Function to get the Neuron Output Value. This can be represented by the following formula.

    Neuron Output Value:                                                                                                  
    Neuron Output Value = 1 / (1 + EXP(-1 x Neuron Input Value))





    We will use this Neuron Output value as an input to the next layer, therefore it automatically becomes a connEntry for one of the neuron connections in the next layer.

    Now that we know what a neuron does, let us create a neuron class. See the code below.




    processing code Neuron Class

    01
    02
    03
    04
    05
    06
    07
    08
    09
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    /* ------------------------------------------------------------------------
    
    A neuron does all the calculations to convert an input to 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 Neuron
    void setBias(float tempBias){
    bias = tempBias;
    }

    //Function to randomise the bias of this Neuron
    void randomiseBias(){
    setBias(random(1));
    }

    //Function to convert the neuronInputValue to an neuronOutputValue
    //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.
    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;
    }

    //Sigmoid Activation function
    float Activation(float x){
    float activatedValue = 1 / (1 + exp(-1 * x));
    return activatedValue;
    }

    }



    When you create a new Neuron, you have the option to create the basic neuron shell with the Neuron() constructor, however, you are more likely to call the 2nd constructor, which allows you to set the number of input connections attached to this neuron.
    For example, if I create a neuron using New Neuron(4), then this will automatically
    • attach and associate four connections with this neuron
    • randomise the weight of each connection
    • randomise the bias of this neuron


    These are the functions within the Neuron Class:
    • addConnection():  adds a new connection to this neuron
    • getConnectionCount(): returns the number of connections associated with this neuron
    • setBias(): sets the Bias of the neuron to a specific value.
    • randomiseBias() : randomises the Bias of this neuron
    • getNeuronOutput() : values are fed through the neuron's connections to create the neuronInputValue, which is then sent through the Sigmoid Activation function to create the neuronOutputValue.
    • Activation() :  is the function used by the getNeuronOutput() function to generate the neuronOutputValue.







    Up next:  Neural Network (Part 3)  : The Layer



    To go back to the table of contents click here