/// <summary>
/// Classical Multidimensional Scaling
/// </summary>
public void Run()
{
// creates distance matrix
int size = CityDistance.GetLength(0);
Mat t = new Mat(size, size, MatType.CV_64FC1, CityDistance);
// adds Torgerson's additive constant to t
double torgarson = Torgerson(t);
t += torgarson;
// squares all elements of t
t = t.Mul(t);
// centering matrix G
Mat g = CenteringMatrix(size);
// calculates inner product matrix B
Mat b = g * t * g.T() * -0.5;
// calculates eigenvalues and eigenvectors of B
Mat values = new Mat();
Mat vectors = new Mat();
Cv2.Eigen(b, values, vectors);
for (int r = 0; r < values.Rows; r++)
{
if (values.Get <double>(r) < 0)
{
values.Set <double>(r, 0);
}
}
//Console.WriteLine(values.Dump());
// multiplies sqrt(eigenvalue) by eigenvector
Mat result = vectors.RowRange(0, 2);
{
var at = result.GetGenericIndexer <double>();
for (int r = 0; r < result.Rows; r++)
{
for (int c = 0; c < result.Cols; c++)
{
at[r, c] *= Math.Sqrt(values.Get <double>(r));
}
}
}
// scaling
Cv2.Normalize(result, result, 0, 800, NormTypes.MinMax);
// opens a window
using (Mat img = Mat.Zeros(600, 800, MatType.CV_8UC3))
using (Window window = new Window("City Location Estimation"))
{
var at = result.GetGenericIndexer <double>();
for (int c = 0; c < size; c++)
{
double x = at[0, c];
double y = at[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, Scalar.Red, -1);
Point textPos = new Point(x + 5, y + 10);
img.PutText(CityNames[c], textPos, HersheyFonts.HersheySimplex, 0.5, Scalar.White);
}
window.Image = img;
Cv2.WaitKey();
}
}
