#include "AliKMeansClustering.h"
#include <TMath.h>
#include <TRandom.h>
+#include <TH1F.h>
ClassImp(AliKMeansClustering)
Double_t AliKMeansClustering::fBeta = 10.;
+
-void AliKMeansClustering::SoftKMeans(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my , Double_t* rk )
+Int_t AliKMeansClustering::SoftKMeans(Int_t k, Int_t n, const Double_t* x, const Double_t* y, Double_t* mx, Double_t* my , Double_t* rk )
{
//
// The soft K-means algorithm
for (j = 0; j < n; j++) {r[j] = new Double_t[k];}
//
// (2b) Normalisation
- Double_t* nr = new Double_t[n];
-
+ Double_t* nr = new Double_t[n];
// (3) Iterations
Int_t nit = 0;
delete[] nr;
for (j = 0; j < n; j++) delete[] r[j];
delete[] r;
+//
+ return (nit < 1000);
+
}
-void AliKMeansClustering::SoftKMeans2(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my , Double_t* sigma2, Double_t* rk )
+Int_t AliKMeansClustering::SoftKMeans2(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my , Double_t* sigma2, Double_t* rk )
{
//
// The soft K-means algorithm
//
Int_t i,j;
//
- // (1) Initialisation of the k means
+ // (1) Initialisation of the k means using k-means++ recipe
//
- // (there is an optimized version for initialisation called kmeans++)
- for (i = 0; i < k; i++) {
- mx[i] = 2. * TMath::Pi() * gRandom->Rndm();
- my[i] = -1. + 2. * gRandom->Rndm();
- }
-
+ OptimalInit(k, n, x, y, mx, my);
//
// (2a) The responsibilities
Double_t** r = new Double_t*[n]; // responsibilities
// (2c) Weights
Double_t* pi = new Double_t[k];
//
+ //
// (2d) Initialise the responsibilties and weights
for (j = 0; j < n; j++) {
nr[j] = 0.;
} // mean i
pi[i] = rk[i] / Double_t(n);
} // data point j
-
-
// (3) Iterations
Int_t nit = 0;
-
+
while(1) {
nit++;
//
for (j = 0; j < n; j++) {
nr[j] = 0.;
for (i = 0; i < k; i++) {
- r[j][i] = pi[i] * TMath::Exp(- fBeta * d(mx[i], my[i], x[j], y[j]))
- / (TMath::Sqrt(2. * sigma2[i]) * TMath::Pi());
+ r[j][i] = pi[i] * TMath::Exp(- d(mx[i], my[i], x[j], y[j]) / sigma2[i] )
+ / (2. * sigma2[i] * TMath::Pi() * TMath::Pi());
nr[j] += r[j][i];
} // mean i
} // data point j
mx[i] = x[0];
my[i] = y[0];
rk[i] = r[0][i];
-
for (j = 1; j < n; j++) {
Double_t xx = x[j];
//
Double_t dx = mx[i] - x[j];
if (dx > TMath::Pi()) xx += 2. * TMath::Pi();
if (dx < -TMath::Pi()) xx -= 2. * TMath::Pi();
- mx[i] = mx[i] * rk[i] + r[j][i] * xx;
- my[i] = my[i] * rk[i] + r[j][i] * y[j];
- rk[i] += r[j][i];
- mx[i] /= rk[i];
- my[i] /= rk[i];
+ if (r[j][i] > 1.e-15) {
+ mx[i] = mx[i] * rk[i] + r[j][i] * xx;
+ my[i] = my[i] * rk[i] + r[j][i] * y[j];
+ rk[i] += r[j][i];
+ mx[i] /= rk[i];
+ my[i] /= rk[i];
+ }
if (mx[i] > 2. * TMath::Pi()) mx[i] -= 2. * TMath::Pi();
if (mx[i] < 0. ) mx[i] += 2. * TMath::Pi();
} // Data
di += d(mx[i], my[i], oldx, oldy);
+
} // means
//
// Sigma
for (i = 0; i < k; i++) {
sigma2[i] = 0.;
- for (j = 1; j < n; j++) {
- sigma2[i] += 2. * r[j][i] * d(mx[i], my[i], x[j], y[j]);
+ for (j = 0; j < n; j++) {
+ sigma2[i] += r[j][i] * d(mx[i], my[i], x[j], y[j]);
} // Data
sigma2[i] /= rk[i];
+ if (sigma2[i] < 0.0025) sigma2[i] = 0.0025;
+ } // Clusters
+ //
+ // Fractions
+ for (i = 0; i < k; i++) pi[i] = rk[i] / Double_t(n);
+ //
+// ending condition
+ if (di < 1.e-8 || nit > 1000) break;
+ } // while
+
+// Clean-up
+ delete[] nr;
+ delete[] pi;
+ for (j = 0; j < n; j++) delete[] r[j];
+ delete[] r;
+//
+ return (nit < 1000);
+}
+
+Int_t AliKMeansClustering::SoftKMeans3(Int_t k, Int_t n, Double_t* x, Double_t* y, Double_t* mx, Double_t* my ,
+ Double_t* sigmax2, Double_t* sigmay2, Double_t* rk )
+{
+ //
+ // The soft K-means algorithm
+ //
+ Int_t i,j;
+ //
+ // (1) Initialisation of the k means using k-means++ recipe
+ //
+ OptimalInit(k, n, x, y, mx, my);
+ //
+ // (2a) The responsibilities
+ Double_t** r = new Double_t*[n]; // responsibilities
+ for (j = 0; j < n; j++) {r[j] = new Double_t[k];}
+ //
+ // (2b) Normalisation
+ Double_t* nr = new Double_t[n];
+ //
+ // (2c) Weights
+ Double_t* pi = new Double_t[k];
+ //
+ //
+ // (2d) Initialise the responsibilties and weights
+ for (j = 0; j < n; j++) {
+ nr[j] = 0.;
+ for (i = 0; i < k; i++) {
+
+ r[j][i] = TMath::Exp(- fBeta * d(mx[i], my[i], x[j], y[j]));
+ nr[j] += r[j][i];
+ } // mean i
+ } // data point j
+
+ for (i = 0; i < k; i++) {
+ rk[i] = 0.;
+ sigmax2[i] = 1./fBeta;
+ sigmay2[i] = 1./fBeta;
+
+ for (j = 0; j < n; j++) {
+ r[j][i] /= nr[j];
+ rk[i] += r[j][i];
+ } // mean i
+ pi[i] = rk[i] / Double_t(n);
+ } // data point j
+ // (3) Iterations
+ Int_t nit = 0;
+
+ while(1) {
+ nit++;
+ //
+ // Assignment step
+ //
+ for (j = 0; j < n; j++) {
+ nr[j] = 0.;
+ for (i = 0; i < k; i++) {
+
+ Double_t dx = TMath::Abs(mx[i]-x[j]);
+ if (dx > TMath::Pi()) dx = 2. * TMath::Pi() - dx;
+ Double_t dy = TMath::Abs(my[i]-y[j]);
+ r[j][i] = pi[i] * TMath::Exp(-0.5 * (dx * dx / sigmax2[i] + dy * dy / sigmay2[i]))
+ / (2. * TMath::Sqrt(sigmax2[i] * sigmay2[i]) * TMath::Pi() * TMath::Pi());
+ nr[j] += r[j][i];
+ } // mean i
+ } // data point j
+
+ for (i = 0; i < k; i++) {
+ for (j = 0; j < n; j++) {
+ r[j][i] /= nr[j];
+ } // mean i
+ } // data point j
+
+ //
+ // Update step
+ Double_t di = 0;
+
+ for (i = 0; i < k; i++) {
+ Double_t oldx = mx[i];
+ Double_t oldy = my[i];
+
+ mx[i] = x[0];
+ my[i] = y[0];
+ rk[i] = r[0][i];
+ for (j = 1; j < n; j++) {
+ Double_t xx = x[j];
+//
+// Here we have to take into acount the cylinder topology where phi is defined mod 2xpi
+// If two coordinates are separated by more than pi in phi one has to be shifted by +/- 2 pi
+
+ Double_t dx = mx[i] - x[j];
+ if (dx > TMath::Pi()) xx += 2. * TMath::Pi();
+ if (dx < -TMath::Pi()) xx -= 2. * TMath::Pi();
+ if (r[j][i] > 1.e-15) {
+ mx[i] = mx[i] * rk[i] + r[j][i] * xx;
+ my[i] = my[i] * rk[i] + r[j][i] * y[j];
+ rk[i] += r[j][i];
+ mx[i] /= rk[i];
+ my[i] /= rk[i];
+ }
+ if (mx[i] > 2. * TMath::Pi()) mx[i] -= 2. * TMath::Pi();
+ if (mx[i] < 0. ) mx[i] += 2. * TMath::Pi();
+ } // Data
+ di += d(mx[i], my[i], oldx, oldy);
+
+ } // means
+ //
+ // Sigma
+ for (i = 0; i < k; i++) {
+ sigmax2[i] = 0.;
+ sigmay2[i] = 0.;
+
+ for (j = 0; j < n; j++) {
+ Double_t dx = TMath::Abs(mx[i]-x[j]);
+ if (dx > TMath::Pi()) dx = 2. * TMath::Pi() - dx;
+ Double_t dy = TMath::Abs(my[i]-y[j]);
+ sigmax2[i] += r[j][i] * dx * dx;
+ sigmay2[i] += r[j][i] * dy * dy;
+ } // Data
+ sigmax2[i] /= rk[i];
+ sigmay2[i] /= rk[i];
+ if (sigmax2[i] < 0.0025) sigmax2[i] = 0.0025;
+ if (sigmay2[i] < 0.0025) sigmay2[i] = 0.0025;
} // Clusters
//
// Fractions
delete[] pi;
for (j = 0; j < n; j++) delete[] r[j];
delete[] r;
+//
+ return (nit < 1000);
}
Double_t AliKMeansClustering::d(Double_t mx, Double_t my, Double_t x, Double_t y)
return (0.5*(dx * dx + (my - y) * (my - y)));
}
+
+
+
+void AliKMeansClustering::OptimalInit(Int_t k, Int_t n, const Double_t* x, const Double_t* y, Double_t* mx, Double_t* my)
+{
+ //
+ // Optimal initialisation using the k-means++ algorithm
+ // http://en.wikipedia.org/wiki/K-means%2B%2B
+ //
+ // k-means++ is an algorithm for choosing the initial values for k-means clustering in statistics and machine learning.
+ // It was proposed in 2007 by David Arthur and Sergei Vassilvitskii as an approximation algorithm for the NP-hard k-means problem---
+ // a way of avoiding the sometimes poor clusterings found by the standard k-means algorithm.
+ //
+ //
+ TH1F d2("d2", "", n, -0.5, Float_t(n)-0.5);
+ d2.Reset();
+
+ // (1) Chose first center as a random point among the input data.
+ Int_t ir = Int_t(Float_t(n) * gRandom->Rndm());
+ mx[0] = x[ir];
+ my[0] = y[ir];
+
+ // (2) Iterate
+ Int_t icl = 1;
+ while(icl < k)
+ {
+ // find min distance to existing clusters
+ for (Int_t j = 0; j < n; j++) {
+ Double_t dmin = 1.e10;
+ for (Int_t i = 0; i < icl; i++) {
+ Double_t dij = d(mx[i], my[i], x[j], y[j]);
+ if (dij < dmin) dmin = dij;
+ } // clusters
+ d2.Fill(Float_t(j), dmin);
+ } // data points
+ // select a new cluster from data points with probability ~d2
+ ir = Int_t(d2.GetRandom() + 0.5);
+ mx[icl] = x[ir];
+ my[icl] = y[ir];
+ icl++;
+ } // icl
+}
+
+
+ClassImp(AliKMeansResult)
+
+
+
+AliKMeansResult::AliKMeansResult(Int_t k):
+ TObject(),
+ fK(k),
+ fMx (new Double_t[k]),
+ fMy (new Double_t[k]),
+ fSigma2(new Double_t[k]),
+ fRk (new Double_t[k]),
+ fTarget(new Double_t[k]),
+ fInd (new Int_t[k])
+{
+// Constructor
+}
+
+AliKMeansResult::AliKMeansResult(const AliKMeansResult &res):
+ TObject(res),
+ fK(res.GetK()),
+ fMx(new Double_t[res.GetK()]),
+ fMy(new Double_t[res.GetK()]),
+ fSigma2(new Double_t[res.GetK()]),
+ fRk(new Double_t[res.GetK()]),
+ fTarget(new Double_t[res.GetK()]),
+ fInd(new Int_t[res.GetK()])
+{
+ // Copy constructor
+ for (Int_t i = 0; i <fK; i++) {
+ fMx[i] = (res.GetMx()) [i];
+ fMy[i] = (res.GetMy()) [i];
+ fSigma2[i] = (res.GetSigma2())[i];
+ fRk[i] = (res.GetRk()) [i];
+ fTarget[i] = (res.GetTarget())[i];
+ fInd[i] = (res.GetInd()) [i];
+ }
+}
+
+AliKMeansResult& AliKMeansResult::operator=(const AliKMeansResult& res)
+{
+ //
+ // Assignment operator
+ if (this != &res) {
+ TObject::operator=(res);
+ if (fK != res.fK) {
+ delete [] fMx;
+ delete [] fMy;
+ delete [] fSigma2;
+ delete [] fRk;
+ delete [] fTarget;
+ delete [] fInd;
+ fK = res.fK;
+ fMx = new Double_t[fK];
+ fMy = new Double_t[fK];
+ fSigma2 = new Double_t[fK];
+ fRk = new Double_t[fK];
+ fTarget = new Double_t[fK];
+ fInd = new Int_t[fK];
+ }
+
+ fK = res.fK;
+ memcpy(fMx, res.fMx, fK*sizeof(Double_t));
+ memcpy(fMy, res.fMy, fK*sizeof(Double_t));
+ memcpy(fSigma2, res.fSigma2, fK*sizeof(Double_t));
+ memcpy(fRk, res.fRk, fK*sizeof(Double_t));
+ memcpy(fTarget, res.fTarget, fK*sizeof(Double_t));
+ memcpy(fInd, res.fInd, fK*sizeof(Int_t));
+ }
+ return *this;
+}
+
+
+AliKMeansResult::~AliKMeansResult()
+{
+// Destructor
+ delete[] fMx;
+ delete[] fMy;
+ delete[] fSigma2;
+ delete[] fRk;
+ delete[] fInd;
+ delete[] fTarget;
+}
+
+void AliKMeansResult::Sort()
+{
+ // Build target array and sort
+ // Sort clusters
+ for (Int_t i = 0; i < fK; i++) {
+ if (fRk[i] > 2.9) {
+ fTarget[i] = fRk[i] / fSigma2[i];
+ }
+ else fTarget[i] = 0.;
+ }
+
+ TMath::Sort(fK, fTarget, fInd);
+}
+
+void AliKMeansResult::Sort(Int_t n, const Double_t* x, const Double_t* y)
+{
+ // Build target array and sort
+ for (Int_t i = 0; i < fK; i++)
+ {
+ Int_t nc = 0;
+ for (Int_t j = 0; j < n; j++)
+ {
+ if (2. * AliKMeansClustering::d(fMx[i], fMy[i], x[j], y[j]) < 2.28 * fSigma2[i]) nc++;
+ }
+
+ if (nc > 2) {
+ fTarget[i] = Double_t(nc) / (2.28 * fSigma2[i]);
+ } else {
+ fTarget[i] = 0.;
+ }
+ }
+
+ TMath::Sort(fK, fTarget, fInd);
+}
+
+void AliKMeansResult::CopyResults(const AliKMeansResult* res)
+{
+ fK = res->GetK();
+ for (Int_t i = 0; i <fK; i++) {
+ fMx[i] = (res->GetMx()) [i];
+ fMy[i] = (res->GetMy()) [i];
+ fSigma2[i] = (res->GetSigma2())[i];
+ fRk[i] = (res->GetRk()) [i];
+ fTarget[i] = (res->GetTarget())[i];
+ fInd[i] = (res->GetInd()) [i];
+ }
+}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff