Statistics.PCA Method — Stats Master

Overload List

#	Signature	Description
1	procedure PCA(const Data: TMtx; const PC: TMtx; const ZScores: TMtx; const EigenVec: TVec; const VarPct: TVec; const PCAMode: TPCAMode);	Perform a PCA on Data matrix, where Data columns are variables and rows are the observables.
2	procedure PCA(const CovMat: TMtx; const PC: TMtx; const EigenVec: TVec; const VarPct: TVec);	Performs a principal component analysis (PCA).

Overload 1: procedure PCA(const Data: TMtx; const PC: TMtx; const ZScores: TMtx; const EigenVec: TVec; const VarPct: TVec; const PCAMode: TPCAMode);

Perform a PCA on Data matrix, where Data columns are variables and rows are the observables.

#	Name	Type
1	Data	TMtx
2	PC	TMtx
3	ZScores	TMtx
4	EigenVec	TVec
5	VarPct	TVec
6	PCAMode	TPCAMode

Result: stored in self (calling object)

Remarks:

The (optional) PCAMode parameter defines whether the analysis should be run on correlation or covariance matrix. PCA procedure returns the principal components in matrix PC, the Z-scores (data, transformed in the PC space) in ZScores, the eigenvalues of the covariance matrix (variances) in the EigenVec vector and (optional) the percentage of total variance in VarPct vector. The PC, ZScores, EigenVec and VarPct dimensions are adjusted automatically.

Examples

Uses Statistics, MtxExpr;
procecure Example;
var Data, PC: Matrix;
Variances,VarPercent : Vector;
begin
    Data.SetIt(2,4,false,[1,3,5,2
    2,5,7,9]);

    PCA(data,PC,Variances,VarPercent,PCCovMat);  //works on raw data
    // ... Variances  = [29,0,0,0]
    // VarPercent = [100,0,0,0]
end;

See Also: Statistics.PCAResiduals, Statistics.BartlettTest

Overload 2: procedure PCA(const CovMat: TMtx; const PC: TMtx; const EigenVec: TVec; const VarPct: TVec);

Performs a principal component analysis (PCA).

#	Name	Type
1	CovMat	TMtx
2	PC	TMtx
3	EigenVec	TVec
4	VarPct	TVec

Result: stored in self (calling object)

Remarks:

Perform a PCA by using the original data covariance matrix CovMat. Return the principal components in PC matrix, eigenvalues of the covariance matrix (variances) in vector EigenVec and (optional) the percentage of total variance in vector VarPct. The PC, EigenVec and VarPct dimensions are adjusted automatically.

Examples

Uses MtxExpr, Statistics;
procedure Example;
var Data, PC: Matrix;
Variances, ZS: Vector;
begin
    Data.SetIt(2,4,false,[1,3,5,2,
    2,5,7,9]);

    Covariance(data,covMat,false);
    PCA(covMat,PC,ZS,Variances); //requires cov matrix

    //      Z = [29 ,  0, 0 ,0 ]
    //variance = [100,  0, 0 ,0 ]

end;