/// <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);
}
/// <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);
}
}