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Showing content from http://accord-framework.net/docs/html/T_Accord_Statistics_Analysis_PrincipalComponentAnalysis.htm below:

double[][] data =
{
    new[] { 2.5,  2.4 },
    new[] { 0.5,  0.7 },
    new[] { 2.2,  2.9 },
    new[] { 1.9,  2.2 },
    new[] { 3.1,  3.0 },
    new[] { 2.3,  2.7 },
    new[] { 2.0,  1.6 },
    new[] { 1.0,  1.1 },
    new[] { 1.5,  1.6 },
    new[] { 1.1,  0.9 }
};










var method = PrincipalComponentMethod.Center;












var pca = new PrincipalComponentAnalysis(method);


pca.Learn(data);









double[] eigenvalues = { 1.28402771, 0.0490833989 };


double[] proportion = eigenvalues.Divide(eigenvalues.Sum());



double[,] eigenvectors =
{
    { -0.677873399, -0.735178656 },
    { -0.735178656,  0.677873399 }
};













double[] v = eigenvectors.GetColumn(0);


eigenvectors.SetColumn(0, v.Multiply(-1));


Assert.IsTrue(eigenvectors.IsEqual(pca.ComponentMatrix, rtol: 1e-9));
Assert.IsTrue(proportion.IsEqual(pca.ComponentProportions, rtol: 1e-9));
Assert.IsTrue(eigenvalues.IsEqual(pca.Eigenvalues, rtol: 1e-5));




double[][] actual = pca.Transform(data);


double[,] expected = new double[,]
{
    {  0.827970186, -0.175115307 },
    { -1.77758033,   0.142857227 },
    {  0.992197494,  0.384374989 },
    {  0.274210416,  0.130417207 },
    {  1.67580142,  -0.209498461 },
    {  0.912949103,  0.175282444 },
    { -0.099109437, -0.349824698 },
    { -1.14457216,   0.046417258 },
    { -0.438046137,  0.017764629 },
    { -1.22382056,  -0.162675287 },
};


Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));



pca.NumberOfOutputs = 1;


actual = pca.Transform(data);


expected = new double[,]
{
    {  0.827970186 },
    { -1.77758033, },
    {  0.992197494 },
    {  0.274210416 },
    {  1.67580142, },
    {  0.912949103 },
    { -0.099109437 },
    { -1.14457216, },
    { -0.438046137 },
    { -1.22382056, },
};


Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));

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