probabilisticPCA.cpp

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/***************************************************************************
 *
 * Author:    Itziar Benito Ortega     (2013)
 *
 * Unidad de  Bioinformatica of Centro Nacional de Biotecnologia , CSIC
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
 * 02111-1307  USA
 *
 *  All comments concerning this program package may be sent to the
 *  e-mail address 'xmipp@cnb.csic.es'
 ***************************************************************************/

#include "probabilisticPCA.h"
#include "core/multidim_array.h"
#include "core/xmipp_funcs.h"

void ProbabilisticPCA::setSpecificParameters(size_t Niters)
{
    this->Niters=Niters;
}

void ProbabilisticPCA::reduceDimensionality()
{
    size_t N=MAT_YSIZE(*X);  // N= number of rows of X
    size_t D=MAT_XSIZE(*X);  // D= number of columns of X

    bool converged=false;
    size_t iter=0;
    double sigma2=rnd_unif()*2;
    double Q=MAXDOUBLE, oldQ;

    Matrix2D<double> S, W, inW, invM, Ez, WtX, Wp1, Wp2, invWp2, WinvM, WinvMWt, WtSDIW, invCS;

    // Compute variance and row energy
    subtractColumnMeans(*X);
    matrixOperation_AtA(*X,S);
    S/=(double)N;
    Matrix1D<double> normX;
    X->rowEnergySum(normX);

    W.initRandom(D,outputDim,0,2,RND_UNIFORM);
    matrixOperation_AtA(W,inW);

    MultidimArray <double> Ezz(N,outputDim,outputDim);
    while (!converged && iter<=Niters)
    {
        ++iter;

        // Perform E-step
        // Ez=(W^t*W)^-1*W^t*X^t
        for (size_t i=0; i<outputDim; ++i)
            MAT_ELEM(inW,i,i)+=sigma2;
        inW.inv(invM);
        matrixOperation_AtBt(W,*X,WtX);
        matrixOperation_AB(invM,WtX,Ez);

        for (size_t k=0; k<N; ++k)
            FOR_ALL_ELEMENTS_IN_MATRIX2D(invM)
                DIRECT_A3D_ELEM(Ezz,k,i,j)=MAT_ELEM(invM,i,j)*sigma2+MAT_ELEM(Ez,i,k)*MAT_ELEM(Ez,j,k);

        // Perform M-step (maximize mapping W)
        Wp1.initZeros(D,outputDim);
        Wp2.initZeros(outputDim,outputDim);
        for (size_t k=0; k<N; ++k)
        {
            FOR_ALL_ELEMENTS_IN_MATRIX2D(Wp1)
                MAT_ELEM(Wp1,i,j)+=MAT_ELEM(*X,k,i)*MAT_ELEM(Ez,j,k);
            FOR_ALL_ELEMENTS_IN_MATRIX2D(Wp2)
                MAT_ELEM(Wp2,i,j)+=DIRECT_A3D_ELEM(Ezz,k,i,j);
        }

        Wp2.inv(invWp2);
        matrixOperation_AB(Wp1,invWp2,W);
        matrixOperation_AtA(W,inW);

        // Update sigma2
        double sigma2_new=0;
        for (size_t k=0; k<N; ++k){
            double EzWtX=0;
            FOR_ALL_ELEMENTS_IN_MATRIX2D(W)
                EzWtX+=MAT_ELEM(*X,k,i)*MAT_ELEM(W,i,j)*MAT_ELEM(Ez,j,k);

            double t=0;
            for (size_t i = 0; i < outputDim; ++i)
            {
                double aux=0.;
                for (size_t kk = 0; kk < outputDim; ++kk)
                    aux += DIRECT_A3D_ELEM(Ezz,k,i,kk) * MAT_ELEM(inW, kk, i);
                t+=aux;
            }

            sigma2_new += VEC_ELEM(normX,k) - 2 * EzWtX + t;
        }
        sigma2_new/=(double) N * (double) D;

        //Compute likelihood of new model
        oldQ = Q;

        if (iter > 1)
        {
            matrixOperation_AB(W,invM,WinvM);
            matrixOperation_ABt(WinvM,W,WinvMWt);
            matrixOperation_IminusA(WinvMWt);
            WinvMWt*=1/sigma2_new;

            matrixOperation_AtA(W,WtSDIW);
            WtSDIW*=1/sigma2_new;
            matrixOperation_IplusA(WtSDIW);

            double detC = pow(sigma2_new,D)* WtSDIW.det();

            matrixOperation_AB(WinvMWt,S,invCS);
            Q = (N*(-0.5)) * (D * log (2*PI) + log(detC) + invCS.trace());
        }

        // Stop condition to detect convergence
        // Must not apply to the first iteration, because then it will end inmediately
        if (iter>2 && abs(oldQ-Q) < 0.001)
            converged=true;

        sigma2=sigma2_new;
    }

    //mapping.M = (inW \ W')';
    matrixOperation_ABt(W,inW.inv(),A);
    matrixOperation_AB(*X,A,Y);
    if (fnMapping!="")
        A.write(fnMapping);
}