Simple BackPropagation Algorithm
I've read some neural net tutorials and decided to build a simple app: create simple perceptrons capable to recognize 2D black&white block representations of digits.
My problem comes with the weights' updating - i didn't fully understand the mechanics. On the tutorial page the formula was http://www.generation5.org/content/1...ges/pn_eq2.png. I've highlighted the part of code i need help with.
How should i update the weights?
Code:
int zero[]= {0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0};
int one[]= {0,
0,0,1,0,
0,1,1,0,
0,0,1,0,
0,0,1,0,
0,0,1,0,
0,1,1,1};
int one_blurred[]= {0,
0,1,1,0,
0,0,1,0,
1,0,0,0,
1,0,1,0,
0,0,1,0,
0,1,1,1};
int two[]= {0,
0,1,1,0,
1,0,0,1,
0,0,0,1,
0,0,1,0,
0,1,0,0,
1,1,1,1};
..
//Neuron
class Neuron_c
{
private:
int iNumInputs;
int i;
int p;
vector<double> vWeights;
vector<double>::iterator it;
double delta;
public:
Neuron_c(int iNumInputs);
~Neuron_c();
void Update(int * iInput, int iOutput);
double Check(int * iInput);
double Sigmoid(double iActivation);
};
//Constructor
Neuron_c::Neuron_c(int iNumInputs)
{
p = 1;
this->iNumInputs = iNumInputs +1;
for( i = 0; i < iNumInputs; i++)
{
vWeights.push_back((i*i)/(e*(i-e*e)));
random_shuffle(vWeights.begin(), vWeights.end());
}
for( i = 0; i <iNumInputs+1; i++)
{
cout<<vWeights[i]<<" ";
}
}
//Destructor
Neuron_c::~Neuron_c()
{
}
//Sigmoid
double Neuron_c::Sigmoid(double iActivation)
{
return 1/(1 + pow(e,-iActivation/p));
}
void Neuron_c::Update(int * iInput, int iOutput)
{
//Get current output
delta = iOutput - Check(iInput);
cout<<"Desired output: "<<iOutput<<"\n";
cout<<"Error: "<<delta<<"\n";
i = 0;
for ( it = vWeights.begin(); it <vWeights.end(); it++)
{
i++;
*it = *it + 0.9 * ( iInput[i] * delta) ;
}
}
double Neuron_c::Check(int * iInput)
{
double activation = 0;
i = 0;
for ( it = vWeights.begin(); it < vWeights.end(); it++)
{
i++;
activation =activation + iInput[i]* *it;
}
cout<<"Activation: "<<activation<<"\n";
return Sigmoid(activation);
int main()
{
/*
initwindow(width, height, title);
Image_c Image(width/2, height/2, 30, two);
Image.Paint();
*/
Neuron_c Perceptron_one(24);
cout<<"Initial check: "<<Perceptron_one.Check( one )<<"\n";
int x = 30;
while( x> 0 )
{
Perceptron_one.Update(one, 1);
Perceptron_one.Update(two, 0);
Perceptron_one.Update(zero, 0);
x--;
}
cout<<"Check Neuron_one for 0: "<<Perceptron_one.Check( zero )<<"\n";
cout<<"Check Neuron_one for 1: "<<Perceptron_one.Check( one )<<"\n";
cout<<"Check Neuron_one for 1_blurred: "<<Perceptron_one.Check( one_blurred )<<"\n";
cout<<"Check Neuron_one for 2: "<<Perceptron_one.Check( two )<<"\n";
cin.get();
return 0;
}
}
Output:
Code:
Check Neuron_one for 0: 3.01565e-011
Check Neuron_one for 1: 1
Check Neuron_one for 1_blurred: 1
Check Neuron_one for 2: 0.00355031
