/// <summary>
/// Applies the rotation operator to the given dataset according to the reference dataset
/// </summary>
/// <param name="p">Procrusted dataset to rotate</param>
/// <param name="p_reference">Reference procrusted dataset</param>
/// <returns>The rotated dataset</returns>
double[,] Rotate(ProcrustedDataset p, ProcrustedDataset p_reference)
{
// Rotation calculus per Amy Ross, Procrustes Analysis : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.119.2686&rep=rep1&type=pdf
SingularValueDecomposition svd = new SingularValueDecomposition(p_reference.Dataset.TransposeAndDot(p.Dataset));
double[,] Q = svd.RightSingularVectors.TransposeAndDot(svd.LeftSingularVectors);
p.RotationMatrix = Q;
return(p.Dataset.Dot(Q));
}
/// <summary>
/// Apply Procrustes translation and scale to the given dataset
/// </summary>
///
/// <param name="p">Procrusted dataset to process and store the results to</param>
///
/// <param name="samples">The dataset itself</param>
///
private void ApplyTranslateScale(ProcrustedDataset p, double[,] samples)
{
// Save the original data
p.Source = samples;
// Save the original data center (i.e. mean)
p.Center = p.Source.Mean(dimension: 0);
// Translate the samples to zero
p.Dataset = Translate(samples);
// Save the original scale of the dataset
p.Scale = GetDatasetScale(p.Dataset);
// Scale the dataset to 1
p.Dataset = Scale(p.Dataset);
}
/// <summary>
/// Transforms the dataset to match the given reference original dataset
/// </summary>
/// <param name="p_reference">Dataset to match</param>
/// <returns>The transformed dataset matched to the reference</returns>
public double[,] Transform(ProcrustedDataset p_reference)
{
// Make a copy of the current Procrustes dataset
double[,] tData = (double[, ])Dataset.Clone();
// Rotate the dataset to match the reference dataset rotation
tData = tData.Dot(p_reference.RotationMatrix.Transpose());
// Scale the dataset to match the reference scale
tData = tData.Multiply(p_reference.Scale);
// Prepare a negative translation vector to...
double[] refCenter = p_reference.Center.Multiply(-1);
// ... move the dataset to the same center as the reference
tData = tData.Center(refCenter);
return(tData);
}
/// <summary>
/// Compute the Procrustes analysis to extract Procrustes distances and models by specifying the reference dataset
/// </summary>
///
/// <param name="reference_sample_index">Index of the reference dataset. If out of bounds of the sample array, the first dataset is used.</param>
/// <param name="samples">List of sample data sets to analyze</param>
///
/// <returns>Procrustes distances of the analyzed samples</returns>
///
public double[,] Compute(int reference_sample_index, params double[][,] samples)
{
// Check arguments in case of mistakes
CheckSampleDataArgument(samples);
// If reference index out of bounds...
if (reference_sample_index < 0 || reference_sample_index >= samples.Length)
{
// Use the first element of the array
reference_sample_index = 0;
}
// Allocate space for the computed results
ProcrustedDatasets = new ProcrustedDataset[samples.Length];
// Start with the reference dataset
ProcrustedDatasets[reference_sample_index] = new ProcrustedDataset();
// The rotation martrix of the reference is the identity matrix (i.e. no rotation since it's the reference itself)
ProcrustedDatasets[reference_sample_index].RotationMatrix = Matrix.Identity(samples[reference_sample_index].GetLength(1));
// Translate then scale the dataset to set it with scale = 1 and center position at zero
ApplyTranslateScale(ProcrustedDatasets[reference_sample_index], samples[reference_sample_index]);
// For each data set
for (int i = 0; i < samples.Length; i++)
{
// Except for the reference
if (i != reference_sample_index)
{
ProcrustedDatasets[i] = new ProcrustedDataset();
// Translate then scale the dataset
ApplyTranslateScale(ProcrustedDatasets[i], samples[i]);
// Finally, rotate the sample to fit the reference data rotation
ProcrustedDatasets[i].Dataset = Rotate(ProcrustedDatasets[i], ProcrustedDatasets[reference_sample_index]);
}
}
// Update the Procrustes distance matrix
UpdateProcrustesDistances(ProcrustedDatasets);
return(ProcrustesDistances);
}
/// <summary>
/// Transforms the dataset to match the given reference original dataset
/// </summary>
/// <param name="p_reference">Dataset to match</param>
/// <returns>The transformed dataset matched to the reference</returns>
public double[,] Transform(ProcrustedDataset p_reference)
{
// Make a copy of the current Procrustes dataset
double[,] tData = (double[,])Dataset.Clone();
// Rotate the dataset to match the reference dataset rotation
tData = tData.Dot(p_reference.RotationMatrix.Transpose());
// Scale the dataset to match the reference scale
tData = tData.Multiply(p_reference.Scale);
// Prepare a negative translation vector to...
double[] refCenter = p_reference.Center.Multiply(-1);
// ... move the dataset to the same center as the reference
tData = tData.Center(refCenter);
return tData;
}
/// <summary>
/// Compute the Procrustes analysis to extract Procrustes distances and models by specifying the reference dataset
/// </summary>
///
/// <param name="reference_sample_index">Index of the reference dataset. If out of bounds of the sample array, the first dataset is used.</param>
/// <param name="samples">List of sample data sets to analyze</param>
///
/// <returns>Procrustes distances of the analyzed samples</returns>
///
public double[,] Compute(int reference_sample_index, params double[][,] samples)
{
// Check arguments in case of mistakes
CheckSampleDataArgument(samples);
// If reference index out of bounds...
if (reference_sample_index < 0 || reference_sample_index >= samples.Length)
{
// Use the first element of the array
reference_sample_index = 0;
}
// Allocate space for the computed results
ProcrustedDatasets = new ProcrustedDataset[samples.Length];
// Start with the reference dataset
ProcrustedDatasets[reference_sample_index] = new ProcrustedDataset();
// The rotation martrix of the reference is the identity matrix (i.e. no rotation since it's the reference itself)
ProcrustedDatasets[reference_sample_index].RotationMatrix = Matrix.Identity(samples[reference_sample_index].GetLength(1));
// Translate then scale the dataset to set it with scale = 1 and center position at zero
ApplyTranslateScale(ProcrustedDatasets[reference_sample_index], samples[reference_sample_index]);
// For each data set
for (int i = 0; i < samples.Length; i++)
{
// Except for the reference
if (i != reference_sample_index)
{
ProcrustedDatasets[i] = new ProcrustedDataset();
// Translate then scale the dataset
ApplyTranslateScale(ProcrustedDatasets[i], samples[i]);
// Finally, rotate the sample to fit the reference data rotation
ProcrustedDatasets[i].Dataset = Rotate(ProcrustedDatasets[i], ProcrustedDatasets[reference_sample_index]);
}
}
// Update the Procrustes distance matrix
UpdateProcrustesDistances(ProcrustedDatasets);
return ProcrustesDistances;
}
/// <summary>
/// Apply Procrustes translation and scale to the given dataset
/// </summary>
///
/// <param name="p">Procrusted dataset to process and store the results to</param>
///
/// <param name="samples">The dataset itself</param>
///
private void ApplyTranslateScale(ProcrustedDataset p, double[,] samples)
{
// Save the original data
p.Source = samples;
// Save the original data center (i.e. mean)
p.Center = p.Source.Mean(dimension: 0);
// Translate the samples to zero
p.Dataset = Translate(samples);
// Save the original scale of the dataset
p.Scale = GetDatasetScale(p.Dataset);
// Scale the dataset to 1
p.Dataset = Scale(p.Dataset);
}
/// <summary>
/// Applies the rotation operator to the given dataset according to the reference dataset
/// </summary>
/// <param name="p">Procrusted dataset to rotate</param>
/// <param name="p_reference">Reference procrusted dataset</param>
/// <returns>The rotated dataset</returns>
double[,] Rotate(ProcrustedDataset p, ProcrustedDataset p_reference)
{
// Rotation calculus per Amy Ross, Procrustes Analysis : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.119.2686&rep=rep1&type=pdf
SingularValueDecomposition svd = new SingularValueDecomposition(p_reference.Dataset.TransposeAndDot(p.Dataset));
double[,] Q = svd.RightSingularVectors.TransposeAndDot(svd.LeftSingularVectors);
p.RotationMatrix = Q;
return p.Dataset.Dot(Q);
}