// *** Layout utils ***
// *** experimental
public static Bitmap __DrawElevation__(IEnumerable <Vector2D> layout, LayoutSettings layoutSettings, int matrixRows, int matrixCols)
{
double[,] elevData = ComputeLayoutElevation(layout, layoutSettings, matrixRows, matrixCols);
Bitmap bmp = new Bitmap((int)Math.Ceiling(layoutSettings.Width), (int)Math.Ceiling(layoutSettings.Height));
Graphics gfx = Graphics.FromImage(bmp);
Vector2D pixSz = new Vector2D(layoutSettings.Width / (double)matrixCols, layoutSettings.Height / (double)matrixRows);
int row = 0;
int oldY = 0;
for (double y = pixSz.Y; row < elevData.GetLength(0); row++, y += pixSz.Y)
{
int _y = (int)Math.Round(y);
int col = 0;
int oldX = 0;
for (double x = pixSz.X; col < elevData.GetLength(1); col++, x += pixSz.X)
{
int _x = (int)Math.Round(x);
Brush brush = new SolidBrush(Color.FromArgb(255, 0, 0, (int)Math.Round(255.0 * elevData[row, col])));
gfx.FillRectangle(brush, oldX, oldY, _x - oldX, _y - oldY);
brush.Dispose();
oldX = _x;
}
oldY = _y;
}
return(bmp);
}
public static double[,] ComputeLayoutElevation(IEnumerable <Vector2D> layout, LayoutSettings layoutSettings, int matrixRows, int matrixCols,
double sigma, double r, bool normalize, bool cut, double cutStdevMult)
{
Utils.ThrowException(layout == null ? new ArgumentNullException("layout") : null);
Utils.ThrowException(layoutSettings == null ? new ArgumentNullException("layoutSettings") : null);
Utils.ThrowException(matrixRows < 1 ? new ArgumentOutOfRangeException("matrixRows") : null);
Utils.ThrowException(matrixCols < 1 ? new ArgumentOutOfRangeException("matrixCols") : null);
Utils.ThrowException(sigma <= 0 ? new ArgumentOutOfRangeException("sigma") : null);
LayoutSettings nrmLayoutSettings = layoutSettings.Clone();
double fX = 1.0 / (layoutSettings.Width - 2.0 * layoutSettings.MarginHoriz);
double fY = 1.0 / (layoutSettings.Height - 2.0 * layoutSettings.MarginVert);
nrmLayoutSettings.Width *= fX;
nrmLayoutSettings.MarginHoriz *= fX;
nrmLayoutSettings.Height *= fY;
nrmLayoutSettings.MarginVert *= fY;
Vector2D[] nrmLayout = nrmLayoutSettings.AdjustLayout(layout);
LayoutIndex layoutIndex = new LayoutIndex();
layoutIndex.MaxPointsPerLeaf = 100; // *** hardcoded max points per leaf
if (r > 0)
{
layoutIndex.BuildIndex(nrmLayout);
}
double[,] zMtx = new double[matrixRows, matrixCols];
Vector2D pixSz = new Vector2D(nrmLayoutSettings.Width / (double)matrixCols, nrmLayoutSettings.Height / (double)matrixRows);
double maxZ = 0;
double avgZ = 0;
int row = 0;
for (double y = pixSz.Y / 2.0; y < nrmLayoutSettings.Height; y += pixSz.Y, row++)
{
int col = 0;
for (double x = pixSz.X / 2.0; x < nrmLayoutSettings.Width; x += pixSz.X, col++)
{
Vector2D pt0 = new Vector2D(x, y);
double z = 0;
if (r <= 0)
{
foreach (Vector2D pt in nrmLayout)
{
double dist = (pt - pt0).GetLength();
z += Math.Exp(-sigma * dist * dist);
}
}
else
{
foreach (IdxDat <Vector2D> pt in layoutIndex.GetPoints(pt0, r))
{
double dist = (pt.Dat - pt0).GetLength();
z += Math.Exp(-sigma * dist * dist);
}
}
zMtx[row, col] = z;
if (z > maxZ)
{
maxZ = z;
}
avgZ += z;
}
}
avgZ /= (double)(matrixRows * matrixCols);
if (avgZ > 0)
{
if (cut)
{
double stdev = 0;
for (row = 0; row < zMtx.GetLength(0); row++)
{
for (int col = 0; col < zMtx.GetLength(1); col++)
{
stdev += (zMtx[row, col] - avgZ) * (zMtx[row, col] - avgZ);
}
}
stdev = Math.Sqrt(stdev / (double)(matrixRows * matrixCols));
maxZ = avgZ + stdev * cutStdevMult;
for (row = 0; row < zMtx.GetLength(0); row++)
{
for (int col = 0; col < zMtx.GetLength(1); col++)
{
if (zMtx[row, col] > maxZ)
{
zMtx[row, col] = maxZ;
}
}
}
}
if (normalize && maxZ > 0)
{
for (row = 0; row < zMtx.GetLength(0); row++)
{
for (int col = 0; col < zMtx.GetLength(1); col++)
{
zMtx[row, col] /= maxZ;
}
}
}
}
return(zMtx);
}
public static double[,] ComputeLayoutElevation(IEnumerable <Vector2D> layout, LayoutSettings layoutSettings, int matrixRows, int matrixCols)
{
return(ComputeLayoutElevation(layout, layoutSettings, matrixRows, matrixCols, /*sigma=*/ 500, /*r=*/ 0.1, /*normalize=*/ true, /*cut=*/ false, 2));
}
public Vector2D[] ComputeLayout(LayoutSettings settings)
{
UnlabeledDataset <SparseVector <double> > dataset = new UnlabeledDataset <SparseVector <double> >(mDataset);
// clustering
mLogger.Info("ComputeLayout", "Clustering ...");
KMeansFast kMeans = new KMeansFast(mKClust);
kMeans.Eps = mKMeansEps;
kMeans.Random = mRandom;
kMeans.Trials = 1;
ClusteringResult clustering = kMeans.Cluster(mDataset); // throws ArgumentValueException
// determine reference instances
UnlabeledDataset <SparseVector <double> > dsRefInst = new UnlabeledDataset <SparseVector <double> >();
foreach (Cluster cluster in clustering.Roots)
{
SparseVector <double> centroid
= cluster.Items.Count > 0 ? cluster.ComputeCentroid(mDataset, CentroidType.NrmL2) : new SparseVector <double>();
dsRefInst.Add(centroid); // dataset of reference instances
dataset.Add(centroid); // add centroids to the main dataset
}
// position reference instances
mLogger.Info("ComputeLayout", "Positioning reference instances ...");
SparseMatrix <double> simMtx = ModelUtils.GetDotProductSimilarity(dsRefInst, mSimThresh, /*fullMatrix=*/ false);
StressMajorizationLayout sm = new StressMajorizationLayout(dsRefInst.Count, new DistFunc(simMtx));
sm.Random = mRandom;
Vector2D[] centrPos = sm.ComputeLayout();
// k-NN
mLogger.Info("ComputeLayout", "Computing similarities ...");
simMtx = ModelUtils.GetDotProductSimilarity(dataset, mSimThresh, /*fullMatrix=*/ true);
mLogger.Info("ComputeLayout", "Constructing system of linear equations ...");
LabeledDataset <double, SparseVector <double> > lsqrDs = new LabeledDataset <double, SparseVector <double> >();
foreach (IdxDat <SparseVector <double> > simMtxRow in simMtx)
{
if (simMtxRow.Dat.Count <= 1)
{
mLogger.Warn("ComputeLayout", "Instance #{0} has no neighborhood.", simMtxRow.Idx);
}
ArrayList <KeyDat <double, int> > knn = new ArrayList <KeyDat <double, int> >(simMtxRow.Dat.Count);
foreach (IdxDat <double> item in simMtxRow.Dat)
{
if (item.Idx != simMtxRow.Idx)
{
knn.Add(new KeyDat <double, int>(item.Dat, item.Idx));
}
}
knn.Sort(DescSort <KeyDat <double, int> > .Instance);
int count = Math.Min(knn.Count, mKNN);
SparseVector <double> eq = new SparseVector <double>();
double wgt = 1.0 / (double)count;
for (int i = 0; i < count; i++)
{
eq.InnerIdx.Add(knn[i].Dat);
eq.InnerDat.Add(-wgt);
}
eq.InnerIdx.Sort(); // *** sort only indices
eq[simMtxRow.Idx] = 1;
lsqrDs.Add(0, eq);
}
Vector2D[] layout = new Vector2D[dataset.Count - mKClust];
for (int i = dataset.Count - mKClust, j = 0; i < dataset.Count; i++, j++)
{
SparseVector <double> eq = new SparseVector <double>(new IdxDat <double>[] { new IdxDat <double>(i, 1) });
lsqrDs.Add(centrPos[j].X, eq);
}
LSqrModel lsqr = new LSqrModel();
lsqr.Train(lsqrDs);
for (int i = 0; i < layout.Length; i++)
{
layout[i].X = lsqr.Solution[i];
}
for (int i = lsqrDs.Count - mKClust, j = 0; i < lsqrDs.Count; i++, j++)
{
lsqrDs[i].Label = centrPos[j].Y;
}
lsqr.Train(lsqrDs);
for (int i = 0; i < layout.Length; i++)
{
layout[i].Y = lsqr.Solution[i];
}
return(settings == null ? layout : settings.AdjustLayout(layout));
}
public Vector2D[] ComputeLayout(LayoutSettings settings, Vector2D[] initLayout)
{
if (settings == null)
{
settings = new LayoutSettings();
}
if (mNumPoints == 1)
{
return(settings.AdjustLayout(new Vector2D[] { new Vector2D() }));
} // trivial case
const double eps = 0.00001;
Vector2D[] layout = new Vector2D[mNumPoints];
// initialize layout
if (initLayout != null)
{
int initLen = Math.Min(mNumPoints, initLayout.Length);
Array.Copy(initLayout, layout, initLen);
for (int i = initLayout.Length; i < mNumPoints; i++)
{
layout[i] = new Vector2D(mRnd.NextDouble(), mRnd.NextDouble());
}
}
else
{
for (int i = 0; i < mNumPoints; i++)
{
layout[i] = new Vector2D(mRnd.NextDouble(), mRnd.NextDouble());
}
}
// main optimization loop
double globalStress = 0, stressDiff = 0;
double oldGlobalStress = double.MaxValue;
for (int step = 0; step < mMaxSteps; step++)
{
globalStress = 0;
for (int i = 0; i < mNumPoints; i++)
{
double div = 0;
Vector2D newPos = new Vector2D(0, 0);
for (int j = 0; j < mNumPoints; j++)
{
if (i != j)
{
double dIj = mDistFunc.GetDistance(i, j);
if (dIj < eps)
{
dIj = eps;
}
double wIj = 1.0 / Math.Pow(dIj, 2);
double xIMinusXJ = layout[i].X - layout[j].X;
double yIMinusYJ = layout[i].Y - layout[j].Y;
double denom = Math.Sqrt(Math.Pow(xIMinusXJ, 2) + Math.Pow(yIMinusYJ, 2));
if (denom < eps)
{
denom = eps;
} // avoid dividing by zero
div += wIj;
newPos.X += wIj * (layout[j].X + dIj * (xIMinusXJ / denom));
newPos.Y += wIj * (layout[j].Y + dIj * (yIMinusYJ / denom));
if (i < j)
{
Vector2D diff = layout[i] - layout[j];
globalStress += wIj * Math.Pow(diff.GetLength() - dIj, 2);
}
}
}
layout[i].X = newPos.X / div;
layout[i].Y = newPos.Y / div;
}
stressDiff = oldGlobalStress - globalStress;
if ((step - 1) % 100 == 0)
{
mLogger.Info("ComputeLayout", "Global stress: {0:0.00} Diff: {1:0.0000}", globalStress, stressDiff);
}
oldGlobalStress = globalStress;
if (stressDiff <= mMinDiff)
{
break;
}
}
mLogger.Info("ComputeLayout", "Final global stress: {0:0.00} Diff: {1:0.0000}", globalStress, stressDiff);
return(settings.AdjustLayout(layout));
}
public Vector2D[] ComputeLayout(LayoutSettings settings)
{
return(ComputeLayout(settings, /*initLayout=*/ null));
}
