ProbabilisticPCA Class Reference

#include <probabilisticPCA.h>

Inheritance diagram for ProbabilisticPCA:

Collaboration diagram for ProbabilisticPCA:

Public Member Functions
void	setSpecificParameters (size_t Niters=200)
	Set specific parameters. More...
void	reduceDimensionality ()
	Reduce dimensionality. More...
Public Member Functions inherited from DimRedAlgorithm
	DimRedAlgorithm ()
	Empty constructor. More...
void	setInputData (Matrix2D< double > &X)
	Set input data. More...
void	setOutputDimensionality (size_t outputDim)
	Set output dimensionality. More...
const Matrix2D< double > &	getReducedData ()
	Get reduced data. More...

Public Attributes
size_t	Niters
Matrix2D< double >	A
Public Attributes inherited from DimRedAlgorithm
Matrix2D< double > *	X
	Pointer to input data. More...
size_t	outputDim
	Output dim. More...
Matrix2D< double >	Y
	Output data. More...
DimRedDistance2	distance
	Distance function. More...
FileName	fnMapping
	Save mapping. More...

Detailed Description

Class for making a Probabilistic PCA dimensionality reduction

Definition at line 35 of file probabilisticPCA.h.

Member Function Documentation

reduceDimensionality()

void ProbabilisticPCA::reduceDimensionality ( )

virtual

Reduce dimensionality.

Implements DimRedAlgorithm.

Definition at line 35 of file probabilisticPCA.cpp.

{
    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);
}

setSpecificParameters()

void ProbabilisticPCA::setSpecificParameters

(

size_t

Niters = 200

)

Set specific parameters.

Definition at line 30 of file probabilisticPCA.cpp.

{
    this->Niters=Niters;
}

Member Data Documentation

A

Matrix2D<double> ProbabilisticPCA::A

Definition at line 40 of file probabilisticPCA.h.

Niters

size_t ProbabilisticPCA::Niters

Definition at line 38 of file probabilisticPCA.h.

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The documentation for this class was generated from the following files:

• xmipp/libraries/dimred/probabilisticPCA.h
• xmipp/libraries/dimred/probabilisticPCA.cpp