/// <summary>
/// Layouts a connected graph with Multidimensional Scaling, using
/// shortest-path distances as Euclidean target distances.
/// </summary>
/// <param name="geometryGraph">A graph.</param>
/// <param name="settings">The settings for the algorithm.</param>
/// <param name="x">Coordinate vector.</param>
/// <param name="y">Coordinate vector.</param>
internal static void LayoutGraphWithMds(GeometryGraph geometryGraph, MdsLayoutSettings settings, out double[] x, out double[] y)
{
x = new double[geometryGraph.Nodes.Count];
y = new double[geometryGraph.Nodes.Count];
if (geometryGraph.Nodes.Count == 0)
{
return;
}
if (geometryGraph.Nodes.Count == 1)
{
x[0] = y[0] = 0;
return;
}
int k = Math.Min(settings.PivotNumber, geometryGraph.Nodes.Count);
int iter = settings.GetNumberOfIterationsWithMajorization(geometryGraph.Nodes.Count);
double exponent = settings.Exponent;
var pivotArray = new int[k];
PivotDistances pivotDistances = new PivotDistances(geometryGraph, false, pivotArray);
pivotDistances.Run();
double[][] c = pivotDistances.Result;
MultidimensionalScaling.LandmarkClassicalScaling(c, out x, out y, pivotArray);
ScaleToAverageEdgeLength(geometryGraph, x, y);
if (iter > 0)
{
AllPairsDistances apd = new AllPairsDistances(geometryGraph, false);
apd.Run();
double[][] d = apd.Result;
double[][] w = MultidimensionalScaling.ExponentialWeightMatrix(d, exponent);
// MultidimensionalScaling.DistanceScaling(d, x, y, w, iter);
MultidimensionalScaling.DistanceScalingSubset(d, x, y, w, iter);
}
}
void SetNodePositionsAndMovedBoundaries() {
int pivotNumber = Math.Min(graph.Nodes.Count,settings.PivotNumber);
double scaleX = settings.ScaleX;
double scaleY = settings.ScaleY;
int[] pivotArray = new int[pivotNumber];
PivotDistances pivotDistances = new PivotDistances(graph, false, pivotArray);
pivotDistances.Run();
double[][] c = pivotDistances.Result;
double[] x, y;
MultidimensionalScaling.LandmarkClassicalScaling(c, out x, out y, pivotArray);
Standardize(x);
double[] p = Centrality.PageRank(graph, .85, false);
// double[] q = Centrality.PageRank(graph, .85, true);
Standardize(p);
// Standardize(q);
int index = 0;
foreach (Node node in graph.Nodes) {
node.Center = new Point((int) (x[index]*scaleX), (int) (Math.Sqrt(p[index])*scaleY));
index++;
}
OverlapRemoval.RemoveOverlaps(graph.Nodes.ToArray(), settings.NodeSeparation);
}
public static void Main() {
modshogun.init_shogun_with_defaults();
double[,] data = Load.load_numbers("../data/fm_train_real.dat");
RealFeatures features = new RealFeatures(data);
MultidimensionalScaling mds = new MultidimensionalScaling();
mds.set_target_dim(1);
mds.set_landmark(false);
mds.apply(features);
}
public static void Main()
{
modshogun.init_shogun_with_defaults();
double[,] data = Load.load_numbers("../data/fm_train_real.dat");
RealFeatures features = new RealFeatures(data);
MultidimensionalScaling mds = new MultidimensionalScaling();
mds.set_target_dim(1);
mds.set_landmark(false);
mds.apply(features);
}
public void MdsReturnsCorrectResult()
{
ILArray <double> dist = ILMath.zeros(3, 3);
dist[1, 0] = 4.94760097137838;
dist[2, 0] = 3.48822665076897;
dist[0, 1] = 4.94760097137838;
dist[2, 1] = 5.07828347170446;
dist[0, 2] = 3.48822665076897;
dist[1, 2] = 5.07828347170446;
MultidimensionalScaling.Scale(dist);
Assert.IsTrue(false);
}
private static Point eigenSystem2(Point[] B, out Point[] Q)
{
double[][] b = new double[B.Length][];
for (int i = 0; i < B.Length; i++)
{
b[i] = new double[2];
b[i][0] = B[i].X;
b[i][1] = B[i].Y;
}
double lambda1;
double[] q1;
double lambda2;
double[] q2;
MultidimensionalScaling.SpectralDecomposition(b, out q1, out lambda1, out q2, out lambda2, 300, 1e-8);
Q = new Point[] { new Point(q1[0], q1[1]), new Point(q2[0], q2[1]) };
return(new Point(lambda1, lambda2));
}
public void TestGoodnessOfFit()
{
double stress;
DoubleMatrix distances3 = new DoubleMatrix(3, 3);
// Example 1: A right triangle
distances3[0, 1] = distances3[1, 0] = 3;
distances3[0, 2] = distances3[2, 0] = 4;
distances3[1, 2] = distances3[2, 1] = 5;
stress = MultidimensionalScaling.CalculateNormalizedStress(distances3,
MultidimensionalScaling.KruskalShepard(distances3));
Assert.IsTrue(stress < 0.1);
// Example 2: An arbitrary triangle
distances3[0, 1] = distances3[1, 0] = 8;
distances3[0, 2] = distances3[2, 0] = 6.4;
distances3[1, 2] = distances3[2, 1] = 5;
DoubleMatrix coords3 = MultidimensionalScaling.KruskalShepard(distances3);
Console.WriteLine("Coordinates: ");
Console.WriteLine("A = ({0}, {1}), B = ({2}, {3}), C = ({4}, {5})", coords3[0, 0], coords3[0, 1], coords3[1, 0], coords3[1, 1], coords3[2, 0], coords3[2, 1]);
stress = MultidimensionalScaling.CalculateNormalizedStress(distances3, coords3);
Console.WriteLine("Stress = " + stress.ToString(CultureInfo.InvariantCulture.NumberFormat));
Assert.IsTrue(stress < 0.1);
DoubleMatrix distances4 = new DoubleMatrix(4, 4);
// Example 3: A small square
distances4[0, 1] = distances4[1, 0] = 1;
distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2);
distances4[0, 3] = distances4[3, 0] = 1;
distances4[1, 2] = distances4[2, 1] = 1;
distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2);
distances4[2, 3] = distances4[3, 2] = 1;
stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
MultidimensionalScaling.KruskalShepard(distances4));
Assert.IsTrue(stress < 0.1);
// Example 4: A large square
distances4[0, 1] = distances4[1, 0] = 1000;
distances4[0, 2] = distances4[2, 0] = Math.Sqrt(2000000);
distances4[0, 3] = distances4[3, 0] = 1000;
distances4[1, 2] = distances4[2, 1] = 1000;
distances4[1, 3] = distances4[3, 1] = Math.Sqrt(2000000);
distances4[2, 3] = distances4[3, 2] = 1000;
stress = MultidimensionalScaling.CalculateNormalizedStress(distances4,
MultidimensionalScaling.KruskalShepard(distances4));
Assert.IsTrue(stress < 0.1);
// Example 5: An arbitrary cloud of 8 points in a plane
DoubleMatrix distancesK = GetDistances(new double[, ] {
{ 2, 1 }, { 5, 2 }, { 7, 1 }, { 4, 0 }, { 3, 3 }, { 4, 2 }, { 1, 8 }, { 6, 3 }
});
stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
MultidimensionalScaling.KruskalShepard(distancesK));
Assert.IsTrue(stress < 0.1);
// Example 6: A tetrahedron
distancesK = GetDistances(new double[, ] {
{ 0, 0, 0 }, { 4, 0, 0 }, { 2, 3.4641, 0 }, { 2, 1.1547, 3.2660 }
});
stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
MultidimensionalScaling.KruskalShepard(distancesK));
Assert.IsTrue(stress < 0.1);
// Example 7: A matrix of perceived dissimilarities between 14 colors, published in the literature
distancesK = new DoubleMatrix(new double[, ] {
{ 0.00, 0.14, 0.58, 0.58, 0.82, 0.94, 0.93, 0.96, 0.98, 0.93, 0.91, 0.88, 0.87, 0.84 },
{ 0.14, 0.00, 0.50, 0.56, 0.78, 0.91, 0.93, 0.93, 0.98, 0.96, 0.93, 0.89, 0.87, 0.86 },
{ 0.58, 0.50, 0.00, 0.19, 0.53, 0.83, 0.90, 0.92, 0.98, 0.99, 0.98, 0.99, 0.95, 0.97 },
{ 0.58, 0.56, 0.19, 0.00, 0.46, 0.75, 0.90, 0.91, 0.98, 0.99, 1.00, 0.99, 0.98, 0.96 },
{ 0.82, 0.78, 0.53, 0.46, 0.00, 0.39, 0.69, 0.74, 0.93, 0.98, 0.98, 0.99, 0.98, 1.00 },
{ 0.94, 0.91, 0.83, 0.75, 0.39, 0.00, 0.38, 0.55, 0.86, 0.92, 0.98, 0.98, 0.98, 0.99 },
{ 0.93, 0.93, 0.90, 0.90, 0.69, 0.38, 0.00, 0.27, 0.78, 0.86, 0.95, 0.98, 0.98, 1.00 },
{ 0.96, 0.93, 0.92, 0.91, 0.74, 0.55, 0.27, 0.00, 0.67, 0.81, 0.96, 0.97, 0.98, 0.98 },
{ 0.98, 0.98, 0.98, 0.98, 0.93, 0.86, 0.78, 0.67, 0.00, 0.42, 0.63, 0.73, 0.80, 0.77 },
{ 0.93, 0.96, 0.99, 0.99, 0.98, 0.92, 0.86, 0.81, 0.42, 0.00, 0.26, 0.50, 0.59, 0.72 },
{ 0.91, 0.93, 0.98, 1.00, 0.98, 0.98, 0.95, 0.96, 0.63, 0.26, 0.00, 0.24, 0.38, 0.45 },
{ 0.88, 0.89, 0.99, 0.99, 0.99, 0.98, 0.98, 0.97, 0.73, 0.50, 0.24, 0.00, 0.15, 0.32 },
{ 0.87, 0.87, 0.95, 0.98, 0.98, 0.98, 0.98, 0.98, 0.80, 0.59, 0.38, 0.15, 0.00, 0.24 },
{ 0.84, 0.86, 0.97, 0.96, 1.00, 0.99, 1.00, 0.98, 0.77, 0.72, 0.45, 0.32, 0.24, 0.00 }
});
stress = MultidimensionalScaling.CalculateNormalizedStress(distancesK,
MultidimensionalScaling.KruskalShepard(distancesK));
Assert.IsTrue(stress < 0.1);
}