/// <summary>
/// Classical Multidimensional Scaling
/// </summary>
public MDS()
{
// creates distance matrix
int size = CityDistance.GetLength(0);
CvMat t = new CvMat(size, size, MatrixType.F64C1, CityDistance);
// adds Torgerson's additive constant to t
t += Torgerson(t);
// squares all elements of t
t.Mul(t, t);
// centering matrix G
CvMat g = CenteringMatrix(size);
// calculates inner product matrix B
CvMat b = g * t * g.T() * -0.5;
// calculates eigenvalues and eigenvectors of B
CvMat vectors = new CvMat(size, size, MatrixType.F64C1);
CvMat values = new CvMat(size, 1, MatrixType.F64C1);
Cv.EigenVV(b, vectors, values);
for (int r = 0; r < values.Rows; r++)
{
if (values[r] < 0)
values[r] = 0;
}
// multiplies sqrt(eigenvalue) by eigenvector
CvMat result = vectors.GetRows(0, 2);
for (int r = 0; r < result.Rows; r++)
{
for (int c = 0; c < result.Cols; c++)
{
result[r, c] *= Math.Sqrt(values[r]);
}
}
// scaling
Cv.Normalize(result, result, 0, 800, NormType.MinMax);
//Console.WriteLine(vectors);
//Console.WriteLine(values);
//Console.WriteLine(result);
// opens a window
using (IplImage img = new IplImage(800, 600, BitDepth.U8, 3))
using (CvFont font = new CvFont(FontFace.HersheySimplex, 0.5f, 0.5f))
using (CvWindow window = new CvWindow("City Location Estimation"))
{
img.Zero();
for (int c = 0; c < size; c++)
{
double x = result[0, c];
double y = result[1, c];
x = x * 0.7 + img.Width * 0.1;
y = y * 0.7 + img.Height * 0.1;
img.Circle((int)x, (int)y, 5, CvColor.Red, -1);
img.PutText(CityNames[c], new CvPoint((int)x+5, (int)y+10), font, CvColor.White);
}
window.Image = img;
Cv.WaitKey();
}
}
/// <summary>
/// Classical Multidimensional Scaling
/// </summary>
public MDS()
{
// creates distance matrix
int size = CityDistance.GetLength(0);
CvMat t = new CvMat(size, size, MatrixType.F64C1, CityDistance);
// adds Torgerson's additive constant to t
t += Torgerson(t);
// squares all elements of t
t.Mul(t, t);
// centering matrix G
CvMat g = CenteringMatrix(size);
// calculates inner product matrix B
CvMat b = g * t * g.T() * -0.5;
// calculates eigenvalues and eigenvectors of B
CvMat vectors = new CvMat(size, size, MatrixType.F64C1);
CvMat values = new CvMat(size, 1, MatrixType.F64C1);
Cv.EigenVV(b, vectors, values);
for (int r = 0; r < values.Rows; r++)
{
if (values[r] < 0)
{
values[r] = 0;
}
}
// multiplies sqrt(eigenvalue) by eigenvector
CvMat result = vectors.GetRows(0, 2);
for (int r = 0; r < result.Rows; r++)
{
for (int c = 0; c < result.Cols; c++)
{
result[r, c] *= Math.Sqrt(values[r]);
}
}
// scaling
Cv.Normalize(result, result, 0, 800, NormType.MinMax);
//Console.WriteLine(vectors);
//Console.WriteLine(values);
//Console.WriteLine(result);
// opens a window
using (IplImage img = new IplImage(800, 600, BitDepth.U8, 3))
using (CvFont font = new CvFont(FontFace.HersheySimplex, 0.5f, 0.5f))
using (CvWindow window = new CvWindow("City Location Estimation"))
{
img.Zero();
for (int c = 0; c < size; c++)
{
double x = result[0, c];
double y = result[1, c];
x = x * 0.7 + img.Width * 0.1;
y = y * 0.7 + img.Height * 0.1;
img.Circle((int)x, (int)y, 5, CvColor.Red, -1);
img.PutText(CityNames[c], new CvPoint((int)x + 5, (int)y + 10), font, CvColor.White);
}
window.Image = img;
Cv.WaitKey();
}
}
