Logo ROOT   6.18/05
Reference Guide
mlpRegression.C
Go to the documentation of this file.
1/// \file
2/// \ingroup tutorial_mlp
3/// This macro shows the use of an ANN for regression analysis:
4/// given a set {i} of input vectors i and a set {o} of output vectors o,
5/// one looks for the unknown function f(i)=o.
6/// The ANN can approximate this function; TMLPAnalyzer::DrawTruthDeviation
7/// methods can be used to evaluate the quality of the approximation.
8///
9/// For simplicity, we use a known function to create test and training data.
10/// In reality this function is usually not known, and the data comes e.g.
11/// from measurements.
12///
13/// \macro_image
14/// \macro_output
15/// \macro_code
16///
17/// \author Axel Naumann, 2005-02-02
18
19Double_t theUnknownFunction(Double_t x, Double_t y) {
20 return sin((1.7+x)*(x-0.3)-2.3*(y+0.7));
21}
22
23void mlpRegression() {
24 // create a tree with train and test data.
25 // we have two input parameters x and y,
26 // and one output value f(x,y)
27 TNtuple* t=new TNtuple("tree","tree","x:y:f");
28 TRandom r;
29 for (Int_t i=0; i<1000; i++) {
30 Float_t x=r.Rndm();
31 Float_t y=r.Rndm();
32 // fill it with x, y, and f(x,y) - usually this function
33 // is not known, and the value of f given an x and a y comes
34 // e.g. from measurements
35 t->Fill(x,y,theUnknownFunction(x,y));
36 }
37
38 // create ANN
39 TMultiLayerPerceptron* mlp=new TMultiLayerPerceptron("x,y:10:8:f",t,
40 "Entry$%2","(Entry$%2)==0");
41 mlp->Train(150,"graph update=10");
42
43 // analyze it
44 TMLPAnalyzer* mlpa=new TMLPAnalyzer(mlp);
45 mlpa->GatherInformations();
46 mlpa->CheckNetwork();
47 mlpa->DrawDInputs();
48
49 // draw statistics shows the quality of the ANN's approximation
50 TCanvas* cIO=new TCanvas("TruthDeviation", "TruthDeviation");
51 cIO->Divide(2,2);
52 cIO->cd(1);
53 // draw the difference between the ANN's output for (x,y) and
54 // the true value f(x,y), vs. f(x,y), as TProfiles
55 mlpa->DrawTruthDeviations();
56
57 cIO->cd(2);
58 // draw the difference between the ANN's output for (x,y) and
59 // the true value f(x,y), vs. x, and vs. y, as TProfiles
61
62 cIO->cd(3);
63 // draw a box plot of the ANN's output for (x,y) vs f(x,y)
64 mlpa->GetIOTree()->Draw("Out.Out0-True.True0:True.True0>>hDelta","","goff");
65 TH2F* hDelta=(TH2F*)gDirectory->Get("hDelta");
66 hDelta->SetTitle("Difference between ANN output and truth vs. truth");
67 hDelta->Draw("BOX");
68
69 cIO->cd(4);
70 // draw difference of ANN's output for (x,y) vs f(x,y) assuming
71 // the ANN can extrapolate
72 Double_t vx[225];
73 Double_t vy[225];
74 Double_t delta[225];
75 Double_t v[2];
76 for (Int_t ix=0; ix<15; ix++) {
77 v[0]=ix/5.-1.;
78 for (Int_t iy=0; iy<15; iy++) {
79 v[1]=iy/5.-1.;
80 Int_t idx=ix*15+iy;
81 vx[idx]=v[0];
82 vy[idx]=v[1];
83 delta[idx]=mlp->Evaluate(0, v)-theUnknownFunction(v[0],v[1]);
84 }
85 }
86 TGraph2D* g2Extrapolate=new TGraph2D("ANN extrapolation",
87 "ANN extrapolation, ANN output - truth",
88 225, vx, vy, delta);
89
90 g2Extrapolate->Draw("TRI2");
91}
SVector< double, 2 > v
Definition: Dict.h:5
ROOT::R::TRInterface & r
Definition: Object.C:4
int Int_t
Definition: RtypesCore.h:41
double Double_t
Definition: RtypesCore.h:55
float Float_t
Definition: RtypesCore.h:53
#define gDirectory
Definition: TDirectory.h:218
double sin(double)
The Canvas class.
Definition: TCanvas.h:31
TVirtualPad * cd(Int_t subpadnumber=0)
Set current canvas & pad.
Definition: TCanvas.cxx:693
Graphics object made of three arrays X, Y and Z with the same number of points each.
Definition: TGraph2D.h:40
virtual void Draw(Option_t *option="P0")
Specific drawing options can be used to paint a TGraph2D:
Definition: TGraph2D.cxx:707
virtual void SetTitle(const char *title)
See GetStatOverflows for more information.
Definition: TH1.cxx:6309
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:2981
2-D histogram with a float per channel (see TH1 documentation)}
Definition: TH2.h:248
void DrawDInputs()
Draws the distribution (on the test sample) of the impact on the network output of a small variation ...
THStack * DrawTruthDeviationInsOut(Int_t outnode=0, Option_t *option="")
Creates a profile of the difference of the MLP output outnode minus the true value of outnode vs the ...
void CheckNetwork()
Gives some information about the network in the terminal.
void GatherInformations()
Collect information about what is usefull in the network.
THStack * DrawTruthDeviations(Option_t *option="")
Creates TProfiles of the difference of the MLP output minus the true value vs the true value,...
TTree * GetIOTree() const
Definition: TMLPAnalyzer.h:67
Double_t Evaluate(Int_t index, Double_t *params) const
Returns the Neural Net for a given set of input parameters #parameters must equal #input neurons.
void Train(Int_t nEpoch, Option_t *option="text", Double_t minE=0)
Train the network.
A simple TTree restricted to a list of float variables only.
Definition: TNtuple.h:28
virtual Int_t Fill()
Fill a Ntuple with current values in fArgs.
Definition: TNtuple.cxx:170
virtual void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0)
Automatic pad generation by division.
Definition: TPad.cxx:1166
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
virtual void Draw(Option_t *opt)
Default Draw method for all objects.
Definition: TTree.h:371
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17