/// <summary>
/// Procustes statistics which gives a (di)similiarity measure of two set of points, by removing translation, rotation and dilation(stretching) degrees of freedom.
/// Zero as result means the two sets of points are basically the same after translation, rotation and dilation with the corresponding matrices.
/// Reference: Modern Multidimensional Scaling, Theory and Applications, page 436, Procrustes Analysis
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
public static Tuple <String, double> ProcrustesStatistics(List <Point> A, List <Point> B)
{
int n = A.Count;
//make A to be unitlength
double minX = A.Min(p => p.X);
double maxX = A.Max(p => p.X);
double minY = A.Min(p => p.Y);
double maxY = A.Max(p => p.Y);
double deltaX = maxX - minX;
double deltaY = maxY - minY;
double scale = Math.Max(deltaX, deltaY);
A = A.Select(p => new Point(p.X / scale, p.Y / scale)).ToList();
var centerA = new Point(A.Average(a => a.X), A.Average(a => a.Y));
var centerB = new Point(B.Average(b => b.X), B.Average(b => b.Y));
Matrix X = DenseMatrix.Create(n, 2, (i, j) => j == 0 ? A[i].X:A[i].Y);
Matrix Y = DenseMatrix.Create(n, 2, (i, j) => j == 0 ? B[i].X:B[i].Y);
Matrix Xc = DenseMatrix.Create(n, 2, (i, j) => j == 0 ? A[i].X - centerA.X : A[i].Y - centerA.Y);
Matrix Yc = DenseMatrix.Create(n, 2, (i, j) => j == 0 ? B[i].X - centerB.X : B[i].Y - centerB.Y);
//Reference: Modern Multidimensional Scaling, Theory and Applications, page 436, Procrustes Analysis
DenseMatrix C = (DenseMatrix)(Xc.Transpose() * Y);
Svd svd = new DenseSvd(C, true);
//rotation
Matrix <double> T = (svd.VT().Transpose()) * (svd.U().Transpose());
//dilation
double s = ((C * T).Trace()) / ((Yc.Transpose() * Y).Trace());
//column Vector with n times 1
Vector <double> vector1 = DenseVector.Create(n, i => 1);
//translation vector
Vector <double> t = (1.0 / n) * (X - s * Y * T).Transpose() * vector1;
Matrix translationMatrix = DenseMatrix.Create(n, 2, (i, j) => t.At(j));
Matrix <double> YPrime = s * Y * T + translationMatrix;
Matrix <double> delta = X - YPrime;
double rSquare = 0;
for (int i = 0; i < n; i++)
{
rSquare += delta.Row(i) * delta.Row(i);
}
return(Tuple.Create("ProcrustesStatistics", Math.Sqrt(rSquare)));
}
public void GenerateMatrix(List <UniqueWords> UniqueWordList)
{
double sum = 0;
tfidfDocMatrix = new DenseMatrix(UniqueWordList.Count, DocumentInfo.TotalPages);
//builds tf-idf document matrix
for (int i = 0; i < UniqueWordList.Count; i++)
{
for (int j = 0; j < DocumentInfo.TotalPages; j++)
{
if (UniqueWordList[i].PagenoWithFrequency.ContainsKey(j + 1)) //insert into matrix only if the key is present in the dictionary or else 0 is already initialised
{
int tf = UniqueWordList[i].PagenoWithFrequency[j + 1];
//calculating IDF
double idf = Math.Log10(Convert.ToDouble(DocumentInfo.TotalPages) / UniqueWordList[i].DocFrequency);
tfidfDocMatrix[i, j] = tf * idf;
//tfidfDocMatrix[i, j] = tfidfDocMatrix[i, j]/_eachPageWordCount[j]; //normalised TF.IDF matrix
tfidfDocMatrix[i, j] = Math.Round(tfidfDocMatrix[i, j], 2);
}
}
}
// WordnFrequencyTxtBox.AppendText(tfidfDocMatrix.ToMatrixString(UniqueWordList.Count, DocumentInfo.TotalPages));
//for(int i=0;i<UniqueWordList.Count;i++)
//{
// for (int j = 3; j < 4; j++)
// {
// sum += tfidfDocMatrix[i, j];
// }
//}
//WordnFrequencyTxtBox.AppendText(sum.ToString());
// DenseMatrix dm=new DenseMatrix(tfidfDocMatrix);
// Svd svd=new DenseSvd(dm,true);
Svd svd = new DenseSvd(tfidfDocMatrix, true);
//Matrix<double> s = svd.W();
//Matrix<double> t = svd.U();
//Matrix<double> d = svd.VT();
//Matrix<double> tsd = t*s*d;
//WordnFrequencyTxtBox.AppendText("\n" + "\n" + tfidfDocMatrix.ToString());
//WordnFrequencyTxtBox.AppendText("\n"+"\n"+tsd.ToString());
// WordnFrequencyTxtBox.AppendText("\n" + "\n" +s.ToString());
Matrix <double> f = svd.U();
Matrix <double> s = svd.W();
Matrix <double> t = svd.VT();
Matrix <double> tc1 = t.Column(0).ToColumnMatrix();
Matrix <double> tc2 = t.Column(1).ToColumnMatrix();
//tc1.SetSubMatrix();
Matrix <double> rorigi = f * s * t;
// WordnFrequencyTxtBox.Clear();
for (int i = 0; i < rorigi.RowCount; i++)
{
for (int j = 0; j < rorigi.ColumnCount; j++)
{
int r;
if (rorigi[i, j].ToString().Contains("E")) //insert into matrix only if the key is present in the dictionary or else 0 is already initialised
{
rorigi[i, j] = 0;
}
}
}
// WordnFrequencyTxtBox.AppendText("\n" + rorigi.ToString());
// WordnFrequencyTxtBox.AppendText("\n" + tfidfDocMatrix.ToString());
}