How to do normalization of data for interpolation with perceptron? - c++

Question

I'm trying to do a normalization of data for a polinomial interpolation with perceptron, I'm using the following formula:
Where:
xi is a data point (x1, x2…xn).
x̄ is the sample mean.
s is the sample standard deviation.
and Z is my new value of input for the perceptron.
I'm programming in C ++, and plotting graph with freeglut.
My function for normalize:
vector<double> Perceptron::normalizar(double x) {
vector<double> aux;
aux.push_back(1.0);
for (unsigned i = 1; i < pesos.size(); i++) {
double t = (pow(x,i) - means[i]) / devianation[i];
aux.push_back(t);
}
return aux;
}
The problem is: before I did the normalization, the polynomial was converging to the points.
But after normalization, the polynomial is converging to other points, and I do not know where it is converging.
The formula for the polynomial would be as follows (with W being the weights of the perceptron):
So I used a mean formula for each value of x.
See the code:
void Perceptron::mean(Points P) { //P is a struct with all x and y values of the points.
means.clear(); //vector that stores the means
for (unsigned i = 0; i < weights.size(); i++) {
double m = 0;
for (unsigned j = 0; j < P.size(); j++) {
m += pow(P[i].x, i);
}
means.push_back(m / P.size());
}
}
void Perceptron::deviation(Points P) {
deviations.clear(); //vector that stores the deviations
for (unsigned i = 0; i < weights.size(); i++) {
double sd = 0;
for (unsigned j = 0; j < P.size(); j++) {
sd += pow(pow(P[j].x, i) - means[i], 2);
}
deviations.push_back(sqrt(sd / P.size()));
}
}