/// <summary>
/// Perform CCA analysis on columns of two number tables.
/// </summary>
/// <param name="tableX">A number table.</param>
/// <param name="tableY">A number table.</param>
/// <returns>A PlsResult structure.</returns>
/// <remarks>This method finds directions for tableX and tableY; so that these two tables will
/// have maximal correlation in those directions.</remarks>
public PlsResult DoCCA(INumberTable tableX, INumberTable tableY)
{
double[][] X = (double[][])tableX.Matrix;
double[][] Y = (double[][])tableY.Matrix;
double[][] Cxy = Covariance(X, Y);
double[][] Cyx = Covariance(Y, X);
IMathAdaptor math = MultivariateAnalysisPlugin.App.GetMathAdaptor();
double[][] rCxx = math.InvertMatrix(Covariance(X, X));
double[][] rCyy = math.InvertMatrix(Covariance(Y, Y));
MakeSymmetric(rCxx);
MakeSymmetric(rCyy);
double[][] A = MatrixProduct(rCxx, Cxy);
double[][] B = MatrixProduct(rCyy, Cyx);
double[][] Cx = MatrixProduct(A, B);
double[][] Cy = MatrixProduct(B, A);
double[][] Wx, Wy;
double[] Rx, Ry;
math.EigenDecomposition(Cx, out Wx, out Rx);
math.EigenDecomposition(Cy, out Wy, out Ry);
//
// Rx and Ry should be the equal upto permutation and dimension.
// Wy can be calculated from Wx by Ry = sqrt(1/Rx) * B * Rx
//
/*
* double x0 = Math.Sqrt(Rx[0]);
* double x1 = Math.Sqrt(Rx[1]);
* double x2 = Math.Sqrt(Rx[2]);
*
* double y0 = Math.Sqrt(Ry[0]);
* double y1 = Math.Sqrt(Ry[1]);
* double y2 = Math.Sqrt(Ry[2]);
*
* 0.7165 0.4906 0.2668
*/
SortEigenVectors(Wx, Rx);
SortEigenVectors(Wy, Ry);
//ValidateMatrix(Wx);
//ValidateMatrix(Wy);
PlsResult ret = new PlsResult();
ret.ProjectionX = EigenProjection(tableX, Wx);
ret.ProjectionY = EigenProjection(tableY, Wy);
ret.EigenVectorsX = Wx;
ret.EigenVectorsY = Wy;
ret.EigenValuesX = Rx;
ret.EigenValuesY = Ry;
return(ret);
}
/// <summary>
/// Perform PLS analysis on columns of two number tables.
/// </summary>
/// <param name="tableX">A number table.</param>
/// <param name="tableY">A number table.</param>
/// <returns>A PlsResult structure.</returns>
/// <remarks>This method finds directions for tableX and tableY; so that these two tables will
/// have maximal covariance in those directions.</remarks>
public PlsResult DoPLS(INumberTable tableX, INumberTable tableY)
{
double[][] Cxy = Covariance((double[][])tableX.Matrix, (double[][])tableY.Matrix);
double[][] Cyx = Covariance((double[][])tableY.Matrix, (double[][])tableX.Matrix);
double[][] CxyCyx = MatrixProduct(Cxy, Cyx);
double[][] CyxCxy = MatrixProduct(Cyx, Cxy);
IMathAdaptor math = MultivariateAnalysisPlugin.App.GetMathAdaptor();
double[][] Wx, Wy;
double[] Rx, Ry;
// These two matrix might be slightly asymmetric due to calculation errors.
MakeSymmetric(CxyCyx);
MakeSymmetric(CyxCxy);
math.EigenDecomposition(CxyCyx, out Wx, out Rx);
math.EigenDecomposition(CyxCxy, out Wy, out Ry);
SortEigenVectors(Wx, Rx);
SortEigenVectors(Wy, Ry);
PlsResult ret = new PlsResult();
ret.ProjectionX = EigenProjection(tableX, Wx);
ret.ProjectionY = EigenProjection(tableY, Wy);
ret.EigenVectorsX = Wx;
ret.EigenVectorsY = Wy;
ret.EigenValuesX = Rx;
ret.EigenValuesY = Ry;
return(ret);
}