mlpRegression.C
/// \file
/// \ingroup tutorial_mlp
/// This macro shows the use of an ANN for regression analysis:
/// given a set {i} of input vectors i and a set {o} of output vectors o,
/// one looks for the unknown function f(i)=o.
/// The ANN can approximate this function; TMLPAnalyzer::DrawTruthDeviation
/// methods can be used to evaluate the quality of the approximation.
///
/// For simplicity, we use a known function to create test and training data.
/// In reality this function is usually not known, and the data comes e.g.
/// from measurements.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Axel Naumann, 2005-02-02
Double_t theUnknownFunction(Double_t x, Double_t y) {
return sin((1.7+x)*(x-0.3)-2.3*(y+0.7));
}
void mlpRegression() {
// create a tree with train and test data.
// we have two input parameters x and y,
// and one output value f(x,y)
TNtuple* t=new TNtuple("tree","tree","x:y:f");
TRandom r;
for (Int_t i=0; i<1000; i++) {
Float_t x=r.Rndm();
Float_t y=r.Rndm();
// fill it with x, y, and f(x,y) - usually this function
// is not known, and the value of f given an x and a y comes
// e.g. from measurements
t->Fill(x,y,theUnknownFunction(x,y));
}
// create ANN
TMultiLayerPerceptron* mlp=new TMultiLayerPerceptron("x,y:10:8:f",t,
"Entry$%2","(Entry$%2)==0");
mlp->Train(150,"graph update=10");
// analyze it
TMLPAnalyzer* mlpa=new TMLPAnalyzer(mlp);
mlpa->GatherInformations();
mlpa->CheckNetwork();
mlpa->DrawDInputs();
// draw statistics shows the quality of the ANN's approximation
TCanvas* cIO=new TCanvas("TruthDeviation", "TruthDeviation");
cIO->Divide(2,2);
cIO->cd(1);
// draw the difference between the ANN's output for (x,y) and
// the true value f(x,y), vs. f(x,y), as TProfiles
mlpa->DrawTruthDeviations();
cIO->cd(2);
// draw the difference between the ANN's output for (x,y) and
// the true value f(x,y), vs. x, and vs. y, as TProfiles
mlpa->DrawTruthDeviationInsOut();
cIO->cd(3);
// draw a box plot of the ANN's output for (x,y) vs f(x,y)
mlpa->GetIOTree()->Draw("Out.Out0-True.True0:True.True0>>hDelta","","goff");
TH2F* hDelta=(TH2F*)gDirectory->Get("hDelta");
hDelta->SetTitle("Difference between ANN output and truth vs. truth");
hDelta->Draw("BOX");
cIO->cd(4);
// draw difference of ANN's output for (x,y) vs f(x,y) assuming
// the ANN can extrapolate
Double_t vx[225];
Double_t vy[225];
Double_t delta[225];
Double_t v[2];
for (Int_t ix=0; ix<15; ix++) {
v[0]=ix/5.-1.;
for (Int_t iy=0; iy<15; iy++) {
v[1]=iy/5.-1.;
Int_t idx=ix*15+iy;
vx[idx]=v[0];
vy[idx]=v[1];
delta[idx]=mlp->Evaluate(0, v)-theUnknownFunction(v[0],v[1]);
}
}
TGraph2D* g2Extrapolate=new TGraph2D("ANN extrapolation",
"ANN extrapolation, ANN output - truth",
225, vx, vy, delta);
g2Extrapolate->Draw("TRI2");
}