Thursday, November 19, 2015

MLP Neural Network with Backpropagation [MATLAB Code]

This is an implementation for Multilayer Perceptron (MLP) Feed Forward Fully Connected Neural Network with a Sigmoid activation function. The training is done using the Backpropagation algorithm with options for Resilient Gradient Descent, Momentum Backpropagation, and Learning Rate Decrease. The training stops when the Mean Square Error (MSE) reaches zero or a predefined maximum number of epochs is reached.

Four example data for training and testing are included with the project. They are generated by SharkTime Sharky Neural Network.

1- Download Code

2- Network architecture & Training Parameters:
The code configuration parameters are as follows:

1- Numbers of hidden layers and neurons per hidden layer. It’s represented by the variable nbrOfNeuronsInEachHiddenLayer. To have a neural network with 3 hidden layers with number of neurons 4, 10, and 5 respectively; that variable is set to [4 10 5].
2- Number of output layer nits. Usually the number of output units is equal to the number of classes, but it still can be less (≤ log2(nbrOfClasses)). It’s represented by the variable nbrOfOutUnits. The number of input layer units is obtained from the training samples dimension.
3- The selection if the sigmoid activation function is unipolar or polar. It’s represented by the variable unipolarBipolarSelector.
4- The learning rate η.
5- The maximum number of epochs at which the training stops unless MSE reaches zero. It’s represented by the variable nbrOfEpochs_max.
6- Option to enable or disable Momentum Backpropagation. It’s represented by the variable enable_learningRate_momentum.
7- The Momentum Backpropagation rate α. It’s represented by the variable momentum_alpha.
8- Option to enable or disable Resilient Gradient Descent. It’s represented by the variable enable_resilient_gradient_descent.
9- The Resilient Gradient Descent parametersη+η-Δmin, Δmax, represented by the variables learningRate_plus, learningRate_negative, deltas_min, and deltas_max.
10- Option to enable or disable Learning Rate Decrease. It’s represented by the variable enable_decrease_learningRate.
11- The Learning Rate Decrease parameters: and . It’s represented by the variables learningRate_decreaseValue and min_learningRate.

The code also contains a parameter for drawing the decision boundary separating the classes and the MSE curve. The number of epochs after which a figure is drawn and saved on the machine is specified. The figures are saved in a folder named Results besides the m files. This parameter is represented by the variable draw_each_nbrOfEpochs. The variable dataFileName takes the Sharky input points file name as string.

3- Results:
In all of the following four test cases, MCCR=1. The stop condition is that MSE reaches zero in all the cases. A unipolar sigmoid function is chosen.

A) Linear Points Case:
Figure 1. Network: 2-4-2 , Unipolar Sigmoid Activation, No Options, η=0.15.

B) Circle Points Case:

Figure2. Network: 2-10-2 , Unipolar Sigmoid Activation, Resilient Gradient Descent, η+=1.2, η-=0.5, Δmin=10^-6, Δmax=50.

C) Wave Points Case:
Figure 3. Network: 2-10-10-2 , Unipolar Sigmoid Activation, Resilient Gradient Descent, η+=1.2, η-=0.5, Δmin=10^-6, Δmax=50.

D) Spiral Points Case:

Figure 4. Network: 2-10-10-2 , Unipolar Sigmoid Activation, Resilient Gradient Descent, η+=1.2, η-=0.5, Δmin=10^-6, Δmax=50.

The following image shows a magnification for the decision boundary with better resolution.
Figure 5. Magnified decision boundary with better resolution for Spiral points case. 

The following video shows the solving of the Two Spirals problem.

Video 1. Solving the Two Spirals Problem.


Unknown said...

There is something wrong for the original code. It should be added with " if i~= length(Weights)-1", for there is no redundant bias in the last weight matrix.

for i = 1:length(Weights)-1
Weights{i} = 2*rand(nbrOfNodesPerLayer(i), nbrOfNodesPerLayer(i+1))-1; %RowIndex: From Node Number, ColumnIndex: To Node Number
if i~= length(Weights)-1
Weights{i}(:,1) = 0; %Bias nodes weights with previous layer (Redundant step)
Delta_Weights{i} = zeros(nbrOfNodesPerLayer(i), nbrOfNodesPerLayer(i+1));
ResilientDeltas{i} = deltas_start*ones(nbrOfNodesPerLayer(i), nbrOfNodesPerLayer(i+1));

Hesham Eraqi said...

Hello 王健,

Many Thanks. Yes, you are right. This is a mistake.
It will always force the weights connected to the first neuron in the output layer to be zero, instead of starting from random values.

As I say in code comments, this line of code is only for convenience ("Redundant") and can be removed. However, once it's there, it should be protected with an if condition like you've did.

I have corrected the code on MathWorks File Exchange.
Thanks again,

AbdelMonaem AbdAllah said...

Dear Hesham,

How are you ? I wish you are fine.

I'm AbdelMonaem AbdAllah, doing my PhD in UNSW @ Canberra, Australia. I'm still new in NN, so I'm wondering whether your NN can train a function, for example, squares of number of variables or it works on binary values only ?

Please, could you contact me on my e-mail,


Hesham Eraqi said...

Dear AbdelMonaem,

I'm fine, thank you. I wish you best of success with your PhD.

Simply, a neural network is a black box that understands/models the relation between some patterns (feature vectors) and their corresponding labels (classes). The understanding phase is called "training". A trained neural network is used later on to estimate the class (label) of a test pattern, this is called the "testing" or "deployment" phase.

I understand you are asking about the input vector dimensionality. My implementation is generic; it detects and works with the given input dimension whatever its length. The input vectors should be stored row by row in the "Samples" variable, and their corresponding class labels in "TargetClasses". A feature can take any number. If you need more than two output classes, you need to uncomment line 59 and implement the "To-Do" I mention in line 68. Please let me know if you have any difficulties doing it.

Best Regards, Hesham

Unknown said...
This comment has been removed by the author.
Unknown said...

Thank you Hesham for your quick reply. I'm doing PhD in optimization.

Actually, I'm wondering if you have any document that would help me in understanding the parameters that you used in your code, and how they would affect the performance of your NN.

Also, after training, how can I test a new record to be belongs to which class ?


Hesham Eraqi said...

Hello AbdelMonaem,

I'm afraid that I don't have a specific reference in mind to recommend for you. Nevertheless, the parameters of the network, resilient Gradient Descent, decreasing learning rate, momentum, and epochs are widely discussed online. Have a look, and let me know if you have any specific questions.

I wish you best of luck.

Unknown said...

hi,,can u help me?im doing my final project on classifying TB on color features by using multilayered perceptron..n im getting confused on extracting the input and output value from an image

Hesham Eraqi said...

Hi Siti,

I wish you all the best with your final project.
I didn't get what you mean.
Inputs to MLP is your feature and output is the classification result. You should have an output neuron per class, and decide the predicted class by checking the neuron with highest activation value.

Unknown said...

Dear Hesham,

Lovely Stuff mate. Love what you have done!
Im trying to create my own code and was looking at how others have attempted it to get a general idea of how to start coding.

Just a quick question and it may seem a silly one....
but what is the difference between activation_func and activation_func_drev?
As in what does the drev stand for. I understand the function itself is different but what is the reasoning behind that?

Thank you very much

Hesham Eraqi said...

Dear Michael,

Thank you so much for the motivation :)
Very soon, I will post more interesting similar articles about different areas of machine learning.

"Drev" stands for "Derivative", that function returns the value of the derivative (gradient) of the activation function at a query point.

Best Wishes, Hesham

Unknown said...

Hey , Great work.

I am a newbie in ANN and its coding.. But from whatever i have read, this seems to be prefect generic code for "ANY" MLP feedforward network with backpropagation training algorithm. Right?

And if so then, I have generated 1570*7 excel table for my project by Matlab code. Now i want to create a network that takes 5 columns (First five natural frequencies of the structure) as input and takes remaining 2 columns (Size and location of defect) as target.

So my query is, while you have used some other input data format, and I have excel table. So how can i incorporate reading those data format instead of .points data file?

Hesham Eraqi said...

Hello Narendra,

Yes, it is a generic implementation for MLP feedforward network.

Concerning parsing the Excel data in MATLAB, there are many tutorials online for that.

In line 52, the variable 'Samples' should contain the training data, a row for each data sample. In your case it should be a matrix of 1570 rows X 5 columns.

Because, you don't have classes here; i.e. you don't have a single output neuron that should fire for each different class. You should comment the 'for' loop in line 70. And after it, fill the matrix 'TargetOutput' such that each row is the desired output for each data sample. In your case it should be a matrix of 1570 rows X 2 columns.

Also, for the above reason, your training stop criteria is different. So, comment lines 184:195 and line 198, and another code that can estimate how much the neural network is good (calculate 'MSE(Epoch)' using the 'outputs' results for each sample). 'MSE(Epoch)' should be the number of mistakenly classified samples from the neural network divided by the total number of data samples.

It you don't get any of what I mean. I'm happy to get your data and upgrade my code accordingly for you.

Best wishes, Hesham

70R50 said...
This comment has been removed by the author.
70R50 said...

Hello Hesham Eraqi,

First of all, thank you for sharing your work with us.
I'm adapting your source code for digit recognition assignment.

1. And having a problem when evaluating data, how do I calculate MSE and stop the training?
- I have 10 output neuron each for specific digit. (say 0-9)
- on %%Evaluation part outputs variable is 1by10 matrix, value 1 for corresponding digit, 0 for others. (say 5=[0 0 0 0 0 1 0 0 0 0])
- Samples is a 8000by16 matrix, 16 columns are 8 x,y coordinate pairs.( say first row [0.47 1 ... 0.98])
- TargetClasses is 8000by1 matrix, each row represents a correct digit. (say first row [5])
2. Also, assignment requirement is to use logsig activation function, should I replace Activation_func_drev with Activation_func?

Please share your idea and thoughts with me, thank you!

Hesham Eraqi said...

Hello 70R50,

1- Let's speak in terms of code, after getting 'outputs', you need to modify the next if conditions like follows:
if (isequal(outputs,[1 0 0 0 0 0 0 0 0 0]))
ActualClasses(Sample) = 0;
else if (isequal(outputs,[0 1 0 0 0 0 0 0 0 0]))
ActualClasses(Sample) = 1;
else if (isequal(outputs,[0 0 0 0 0 0 0 0 1 0]))
ActualClasses(Sample) = 8;

2- No, you should modify the function in Activation_func.m to be 'logsig' activation. Plus, modifying the function in Activation_func_drev.m to be the derivative of the 'logsig' activation. Which you should figure out for your assignment :-)

Best wishes, Hesham

Hesham Eraqi said...

@70R50: I've forgot to mention that the MSE calculation should change accordingly:
MSE(Epoch) = sum(find(ActualClasses==TargetClasses))/(length(Samples(:,1)));

Unknown said...

Hello Sir,
I am doing my final assignment on Yield forecasting using ANN. First of all, I am a newbie to NN, my background is Agriculture. I wanna ask you about my code either it is true or not.

%% load divided input data set
load annflo.mat

%% define training inputs
trainInp = [trainflo];

%% define targets
T = [targetflo];

net = newff(trainInp,T,[],{},'trainlm');
net = init(net);
net.trainParam.epochs = 1000;
net.trainParam.goal = 0.01;
net.divideParam.trainRatio = 1;
net.divideParam.valRatio = 0;
net.divideParam.testRatio = 0;

net.trainParam.max_fail = 2;
net = train(net,trainInp,T,[],[]);

Y = sim(net,trainInp);

I was using Levenberg-Marquardt as the training algorithm, but then I realized that It was supposed to be Back-propagation as the training algorithm and I had no idea how to change the code. Would you like to help me, Sir?
Thank you :)

Unknown said...

I am new to NN.Can the following code be used for time series prediction?
What modification do i have to do?

ChathuraW said...

Hi Hesham,

I'm trying to adapt your code for 4 inputs and 2 output neurons(no classes). I read your comment given to Narendra. I'm struggling with the evaluation part of the code. Can you please help me out.

Thank you :)

Really Nice work Hesham. Good luck with all your work.

Best Regards


Hesham Eraqi said...

@freakme whatsoever:
You are using MATLAB Neural Network Toolbox. Sorry, I don't have it. But there is a nice example for you here:

Good luck, and I'm here for any questions if you use my code.

Hesham Eraqi said...

@mahum pervez:
Yes NN can solve the series prediction problem. I've uploaded an image for you that summarizes the idea:
Good Luck.

Hesham Eraqi said...

@Chathura: Hi, Thanks for your nice words. Sorry for late replay.
You can simply replace the evaluation code from line 184 to line 195 with this line of code:

[~,ActualClasses(Sample)] = max(outputs) - 1;

Good Luck :)

Unknown said...

Dear Hesam
First of all I want to thank for this awesome and clean MLP implementation
I have a question about my case which doesn't work very well I have 400 samples with 20 features which divided to 3 classes. I almost done all of your advises for changing code base on other questions and comments but in my case code works till 99 epochs and after that this errors comes out!could you please help me?


Error using *
Inner matrix dimensions must agree.

Error in EvaluateNetwork (line 7)
NodesActivations{Layer} = NodesActivations{Layer-1}*Weights{Layer-1};

Error in MLP_NN (line 228)
outputs = EvaluateNetwork([1 x y], NodesActivations, Weights, unipolarBipolarSelector);

Hesham Eraqi said...

Thank you Milad for your nice words, glad it's useful.

You are right, this is because my visualization code only supports problems with 2 features only. But in your case, it's 20.
You have to options to proceed:
- Comment the visualization code section, or set the variable draw_each_nbrOfEpochs to a large number like 10^9, so that visualization won't occur.
- Try to do PCA on your features to reduce them to 2 features, this will make training much faster and visualization feasible. You may even end up with better classification performance (depending on the variance in your features).

Eve said...

Hi Hesham,

I have a classification problem which is to classify the music genres for more than 50,000 songs. Here, I have 10 genres. I've been studying your code for several days and I also read your comment about the multiply outputs problem. But I still cannot figure out how to construct the outputs. The actual labels for the 10 genres are [1,2,...,10]. And I construct a matrix for all the samples with their corresponding labels:
[1 0 0 0 0 0 0 0 0 0;
1 0 0 0 0 0 0 0 0 0;
0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 1];

Here [1 0 0 0 0 0 0 0 0 0] means the label for the sample point is 1 and [0 0 0 0 0 0 0 0 0 1] means the label for this sample point is 10, etc.

The followings are your code:
%% Read Data
importedData = importdata(dataFileName, '\t', 6);
Samples =, 1:length(,:))-1);
TargetClasses =, length(,:)));
TargetClasses = TargetClasses - min(TargetClasses);
ActualClasses = -1*ones(size(TargetClasses));

Problem 1: Do I still needs the above code to construct the TargetClasses and the ActualClasses?
Problem 2: What are the TargetClasses and the ActualClasses in my case?

Thank you!

Hesham Eraqi said...

Hi Eve,

Problem 1: No you won't need that code. Replace it by other code that fills the variables 'Samples', 'TaggetClasses', and 'ActualClasses'.
Please note that the variable 'Samples' should contain your training data, a row for each data sample.

Problem 2: 'TaggetClasses' is the labels matrix you have constructed as you describe above.
'ActualClasses' at that moment is a variable of the same size as 'TaggetClasses'. It is just for allocation, so you can put zeros or any numbers for now. Later on in the "Evaluation" code section, it should be filled with the neural network output for all the samples. You should modify that section as I described in a previous comment.

If it still have problems, I will be happy to upgrade my code if you send me sample of your data via email maybe:

Good luck.

Kris said...

Dear Hesham Eraqi,

can I use your code as classifier ?

As I understand the data there are:
Samples - training data,
TargetClassess - labels for training data (classess).

Where (which variable) can I store the testing data ?
And, how to read a final (predicted) labels of such data ?


Unknown said...

Hi! Congratulations for your code. I'm using it to approximate a function. It's more or less like this: I have five inputs and one output that is the price of a commodity. And I want the Neural Network to learn these prices and give me prices on new five inputs that it hasn't been taught. So I think it is only one output. Ok ? If I just reduce the number of output in your code to one, will it work to approximate the function ?
And another doubt, why do you subtract from the Target Classes its minimum ?
Thank you very much!

Unknown said...

Just to let you know what changes I have made to your code in order to get the nn to calculate an output only (value of a function). I started by changing the number of outputs to one, and importing my data. My data have six input variables and one output. As my target output is a price, I normalized it to be between 0 and 1 with the min max normalization. So my targetclasses are just my prices normalized. Besides, the targetoutputs now, as I guess, must be the same as the targetclasses, because there are no classes at all. So it must be the value of the output itself, that is what I want my nn to evaluate given the inputs. As for the evaluation, I just commented all the stuff that has to do with the actualclasses and inserted in ActuallClasses(sample) = output. After that I commented the visualization part that has not to do with the error. It won't work with this changes becaue the evaluation is evaluating the same value for all my training set. What have I forgot doing ?

Unknown said...

Hi der..I need matlab code for ( training back propagation algorithm ) for wind forecasting....plz rpy to diz mail

PRANA said...

Dear Hesham Eraqi

i'm doing finial year research in university. i'm doing "landslide susceptibility analysis" using ANN back-propagation method, problem is i have 10 input data(images,numerically ) for 1 landslide like wise i have 8 land slide data. Now i wanted create network for finding land slide susceptible.
Can you provided ideas with code.(i'm try to do this with the mathlab)

syafiq said...

Hello Hesham Eraqi,

Good work from you. However, I found that the code only for training. How do you test your data? And if by getting MSE close to 0, how you ensure that your model is not overfitting?


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Hesham Eraqi said...

Christian Sanchez commented on your file MLP Neural Network with Backpropagation :
Hi ,
I am trying to understand backpropagation, and your code is being really helpful, thanks.

I have got a question: your input to the derivative of the sigmoid is "NodesActivations", which has previously gone through the sigmoid function. I do not understand this, shouldnt it be input to the derivative of the sigmoid the input to the activation function? Obviously no, because your code works, but could you help me please to understand this ?
Input to activation function: s
Output from activation function: z=f(s )
Derivative: d/dw z=d/dw f(s) = f(s)(1-f(s))

while in the code it looks like f(z)(1-f(z)) is calculated, because you do :
Line 111-->NodesActivations{Layer} = Activation_func(NodesActivations{Layer}, unipolarBipolarSelector );
Line 121-->gradient = Activation_func_drev(NodesActivations{Layer+1}, unipolarBipolarSelector);


@Christian Sanchez:
You are absolutely correct; to get the derivative of a function you need the input to it (not the output) to substitute with. But if that function is a Sigmoid (which is our case) you can use a beautiful feature that allows calculating the derivative using the output. I've provided the proof in this post:

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