This is the code I used to classify the handwritten digits of MNist database using back-propagation algorithm on an one-layered perceptron with 10 neurons. The digits are saved in an expanded (1
's in last column) integer 2d matrix images[60000][785]
and the labels in int tlabels[60000][10]
. Every label contains a 1
in the position corresponding to the digits value and 0
's in the rest (digits are 0
–9
).
// weights1[785][10] has been initialized to random values on [-0.5,0.5] in the constructor.
// bias of neurons have been taken into account as the last row of the matrix.
// b is the learning rate , equal to 0.5.
const int Ninput=784;
const int Noutput=10;
float result[Noutput];
for (int epoch =0 ; epoch < 30 ; epoch ++) {
float error =0;
for (int sample=0 ; sample < 1000 ; sample++) {
for (int output= 0 ; output< Noutput; output++) {
float sum = 0;
for (int input = 0 ; input < Ninput+1; input++)
sum += weights1[input][output]*images[sample][input];
result[output] = sum;
}
float delta[Noutput];
for (int output= 0 ; output< Noutput; output++) {
delta[output]=(tlabels[sample][output]-sigmoid(result[output]))*sigmoidDerivative(result[output]);
error+= pow((tlabels[sample][output]-sigmoid(result[output])),2.0);
}
for (int output= 0 ; output< Noutput; output++)
for (int input=0 ; input < Ninput+1 ; input++)
weights1[input][output] = weights1[input][output] +b*delta[output]*images[sample][input];
}
cout << error / 1000.0;
}
The error
variable converges to 0.9 , meaning this code classifies all the digits into one of the classes, even though the samples are equally distributed among the classes. Is there a logical error in the code, or should I try different sets of parameters until the results become acceptable?