HessianLLE Class Reference

#include <hessianLLE.h>

Inheritance diagram for HessianLLE:

Collaboration diagram for HessianLLE:

Public Member Functions
void	setSpecificParameters (int kNeighbours=12)
	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
int	kNeighbours
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 Hessian LLE dimensionality reduction

Definition at line 34 of file hessianLLE.h.

Member Function Documentation

reduceDimensionality()

void HessianLLE::reduceDimensionality ( )

virtual

Reduce dimensionality.

Implements DimRedAlgorithm.

Definition at line 31 of file hessianLLE.cpp.

{
    Matrix2D<int> neighboursMatrix;
    Matrix2D<double> distanceNeighboursMatrix;

    kNearestNeighbours(*X, kNeighbours, neighboursMatrix, distanceNeighboursMatrix);

    size_t sizeY = MAT_YSIZE(*X);
    size_t dp = outputDim * (outputDim+1)/2;
    Matrix2D<double> weightMatrix, thisX, U, V, Vpr, Yi, Yi_complete, Yt, R, Pii;
    Matrix1D<double> D, vector;

    weightMatrix.initZeros(dp*sizeY,sizeY);

    for(size_t index=0; index<MAT_YSIZE(*X);++index)
    {
        extractNearestNeighbours(*X, neighboursMatrix, index, thisX);
        subtractColumnMeans(thisX);
        thisX = thisX.transpose();
        svdcmp(thisX, U, D, Vpr); // thisX = U * D * Vpr^t

        // Copy the first columns of Vpr onto V
        V.resizeNoCopy(MAT_YSIZE(Vpr),outputDim);
        for (size_t y=0; y<MAT_YSIZE(V); ++y)
            memcpy(&MAT_ELEM(V,y,0),&MAT_ELEM(Vpr,y,0),outputDim*sizeof(double));

        //Basically, the above is applying PCA to the neighborhood of Xi.
        //The PCA mapping that is found (and that is contained in V) is an
        //approximation for the tangent space at Xi.

        //Build Hessian estimator
        buildYiHessianEstimator(V,Yi,outputDim,dp);
        completeYt(V, Yi, Yt);
        orthogonalizeColumnsGramSchmidt(Yt);

        //Get the transpose of the last columns
        size_t indexExtra = outputDim+1;
        size_t Ydim = MAT_XSIZE(Yt)-indexExtra;
        Pii.resizeNoCopy(Ydim,MAT_YSIZE(Yt));
        FOR_ALL_ELEMENTS_IN_MATRIX2D(Pii)
            MAT_ELEM(Pii,i,j) = MAT_ELEM(Yt,j,indexExtra+i);

        //Double check weights sum to 1
        for (size_t j=0; j<dp; j++)
        {
            Pii.getRow(j,vector);
            double sum = vector.sum();
            if(sum > 0.0001)
                vector*=1.0/sum;

            //Fill weight matrix
            for(int k = 0; k<kNeighbours; k++){
                size_t neighbourElem = MAT_ELEM(neighboursMatrix,index,k);
                MAT_ELEM(weightMatrix,index*dp+j,neighbourElem) = VEC_ELEM(vector,k);
            }
        }
    }
    Matrix2D<double> G;
    matrixOperation_AtA(weightMatrix,G);

    Matrix1D<double> v;
    eigsBetween(G,1,outputDim,v,Y);
    Y*=sqrt(sizeY);
}

setSpecificParameters()

void HessianLLE::setSpecificParameters

(

int

kNeighbours = 12

)

Set specific parameters.

Definition at line 26 of file hessianLLE.cpp.

{
    this->kNeighbours = kNeighbours;
}

Member Data Documentation

kNeighbours

int HessianLLE::kNeighbours

Definition at line 37 of file hessianLLE.h.

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

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