private static void ComputeApproximateGradient(int[] rowP, int[] colP, double[] valP, double[,] y, int n, int d, double[,] dC, double theta)
{
var tree = new SpacePartitioningTree(y);
var sumQ = 0.0;
var posF = new double[n, d];
var negF = new double[n, d];
SpacePartitioningTree.ComputeEdgeForces(rowP, colP, valP, n, posF, y, d);
var row = new double[d];
for (var n1 = 0; n1 < n; n1++)
{
Array.Clear(row, 0, row.Length);
tree.ComputeNonEdgeForces(n1, theta, row, ref sumQ);
Buffer.BlockCopy(row, 0, negF, (sizeof(double) * n1 * d), d * sizeof(double));
}
// Compute final t-SNE gradient
for (var i = 0; i < n; i++)
{
for (var j = 0; j < d; j++)
{
dC[i, j] = posF[i, j] - negF[i, j] / sumQ;
}
}
}
private void Subdivide()
{
// Create new children
var newCorner = new double[dimension];
var newWidth = new double[dimension];
for (var i = 0; i < noChildren; i++)
{
var div = 1;
for (var d = 0; d < dimension; d++)
{
newWidth[d] = .5 * boundary.GetWidth(d);
if (i / div % 2 == 1)
{
newCorner[d] = boundary.GetCorner(d) - .5 * boundary.GetWidth(d);
}
else
{
newCorner[d] = boundary.GetCorner(d) + .5 * boundary.GetWidth(d);
}
div *= 2;
}
children[i] = new SpacePartitioningTree(data, newCorner, newWidth);
}
// Move existing points to correct children
for (var i = 0; i < size; i++)
{
var success = false;
for (var j = 0; j < noChildren; j++)
{
if (!success)
{
success = children[j].Insert(index[i]);
}
}
index[i] = -1; // as in tSNE implementation by van der Maaten
}
// Empty parent node
size = 0;
isLeaf = false;
}
private static double EvaluateErrorApproximate(IReadOnlyList <int> rowP, IReadOnlyList <int> colP, IReadOnlyList <double> valP, double[,] y, double theta)
{
// Get estimate of normalization term
var n = y.GetLength(0);
var d = y.GetLength(1);
var tree = new SpacePartitioningTree(y);
var buff = new double[d];
var sumQ = 0.0;
for (var i = 0; i < n; i++)
{
tree.ComputeNonEdgeForces(i, theta, buff, ref sumQ);
}
// Loop over all edges to compute t-SNE error
var c = .0;
for (var k = 0; k < n; k++)
{
for (var i = rowP[k]; i < rowP[k + 1]; i++)
{
var q = .0;
for (var j = 0; j < d; j++)
{
buff[j] = y[k, j];
}
for (var j = 0; j < d; j++)
{
buff[j] -= y[colP[i], j];
}
for (var j = 0; j < d; j++)
{
q += buff[j] * buff[j];
}
q = (1.0 / (1.0 + q)) / sumQ;
c += valP[i] * Math.Log((valP[i] + float.Epsilon) / (q + float.Epsilon));
}
}
return(c);
}
