/// <summary>
/// Spatial Bivariate Moran I using
/// I=Sigma_i(Sigma_j(Yi*Wij*Xj))/(S0*Sqrt(Variance(Y)*Variance(X)))
/// where S0 is the sum of all the elements in W
/// NOTE: X[i], Y[i] and Centroids[i] MUST all reference the same spatial area i.e. all three arrays are in step
/// </summary>
/// <param name="X">Data values of first table</param>
/// <param name="Y">Data values of second table (must match X spatially)</param>
/// <param name="Centroids">Centroid points of polygon areas to calculate distance weights (must match X and Y spatially)
/// first point is ([0,0], [0,1]), second point is ([1,0],[1,1]). The reason for using the 2d double array in preference to
/// an array of Point is the big increase in speed.</param>
/// <returns></returns>
public static double [] SpatialBivariateMoranI(double [] X, double [] Y, double [,] Centroids)
{
System.Diagnostics.Debug.WriteLine("SpatialBivariateMoranI start");
//Assert X.Length==Y.Length?
//compute some stats on the X and Y sequences that we're going to need
RunningStat rsx = new RunningStat();
foreach (double value in X)
{
rsx.Push(value);
}
RunningStat rsy = new RunningStat();
foreach (double value in Y)
{
rsy.Push(value);
}
double MeanX = rsx.Mean, SDX = rsx.StandardDeviation;
double MeanY = rsy.Mean, SDY = rsy.StandardDeviation;
double Sum1 = 0, Sum2 = 0;
double S0 = 0;
System.Diagnostics.Stopwatch timer = System.Diagnostics.Stopwatch.StartNew();
//Parallel.For(0, Y.Length, i =>
for (int i = 0; i < Y.Length; i++)
{
double CiX = Centroids[i, 0];
double CiY = Centroids[i, 1];
//Parallel.For(0, X.Length, j =>
for (int j = 0; j < X.Length; j++)
{
double dx = CiX - Centroids[j, 0];
double dy = CiY - Centroids[j, 1];
double D = Math.Sqrt(dx * dx + dy * dy); //SURELY 1/W !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
double W = 0;
if (D < 1)
{
W = 1; //autocorrelation weight=1
}
else
{
W = 1 / D; //otherwise the correlation weight is 1/D
}
Sum1 += Y[i] * W * X[j]; //version 1
Sum2 += ((Y[i] - MeanY) / SDY) * W * ((X[i] - MeanX) / SDX); //version 2
S0 += W; //sum of all weights
}/*);*/
}/*);*/
double I1 = Sum1 / (S0 * Math.Sqrt(rsy.Variance * rsx.Variance));
double I2 = Sum2 / S0;
System.Diagnostics.Debug.WriteLine("SpatialBivariateMoranI finished: " + timer.ElapsedMilliseconds + " ms");
return(new double [] { I1, I2 });
}
/// <summary>
/// Correlate two tables using K nearest neighbours.
/// NOTE: the X value is the base location, so the neighbours are looked up in Y.
/// TODO: do you need to weight the neighbours differently to the central value?
/// There are various ways of doing this. Here I'm using neighbours =0.5 but you could use centroid distances.
/// </summary>
/// <param name="areas">Area keys for the X and Y data arrays</param>
/// <param name="X"></param>
/// <param name="Y"></param>
public double Correlate(string[] areas, double[] X, double[] Y)
{
//go through each value of X, lookup the K nearest neighbours in Y and correlate
//Basically, this is a copy of Correlation.SpatialBivariateMoranI but with the K bit added
//compute some stats on the X and Y sequences that we're going to need
RunningStat rsx = new RunningStat();
foreach (double value in X)
{
rsx.Push(value);
}
RunningStat rsy = new RunningStat();
foreach (double value in Y)
{
rsy.Push(value);
}
double MeanX = rsx.Mean, SDX = rsx.StandardDeviation;
double MeanY = rsy.Mean, SDY = rsy.StandardDeviation;
double Sum = 0;
double S0 = 0; //sum of all weights
//System.Diagnostics.Stopwatch timer = System.Diagnostics.Stopwatch.StartNew();
for (int i = 0; i < X.Length; i++)
{
//do the central locations first
double W;
W = 1.0;
Sum += ((Y[i] - MeanY) / SDY) * W * ((X[i] - MeanX) / SDX);
S0 += W;
//now the K neighbours;
W = 0.5;
string[] KNs = Neighbours[areas[i]]; //K neighbours around area j
for (int j = 0; j < K; j++)
{
Sum +=
((Y[i] - MeanY) / SDY) * W * ((X[i] - MeanX) / SDX);
S0 += W;
}
}
double I = Sum / S0;
return(I);
}
//private void ZeroDeltaWeights()
//{
// for (int y = 0; y < OutputDimension; y++)
// {
// for (int x = 0; x < OutputDimension; x++)
// {
// for (int j = 0; j < InputNeurons; j++)
// {
// deltaW[x, y, j] = 0;
// }
// }
// }
//}
/// <summary>
/// Add all delta weights on to weights at the end of a training epoch
/// </summary>
//private double UpdateDeltaWeights()
//{
// double Sum = 0;
// for (int y = 0; y < OutputDimension; y++)
// {
// for (int x = 0; x < OutputDimension; x++)
// {
// for (int j = 0; j < InputNeurons; j++)
// {
// Sum += Math.Abs(deltaW[x, y, j]);
// W[x,y,j]+=deltaW[x, y, j];
// }
// }
// }
// return Sum;
//}
/// <summary>
/// Go through the whole training set and sum the mean square errors for every presented pattern.
/// This number is likely to be very big if there are 2558 datasets times 7201 areas = 18420158;
/// As an alternative, you could look at the stats of the worst and best case.
/// Divide this answer datasets*areas to get average error, which is more useful.
/// POST: places errors into eAll (RMS over all datasets), eMin (RMS best dataset) and eMax (RMS worst dataset)
/// </summary>
/// <param name="Matrix"></param>
/// <returns></returns>
public double CalculateError(List <double[]> Matrix)
{
double e = 0;
eMin = double.MaxValue; eMax = 0;
for (int i = 0; i < Matrix.Count; i++)
{
RunningStat rsx = new RunningStat();
foreach (double value in Matrix[i])
{
rsx.Push(value);
}
double MeanX = rsx.Mean, SDX = rsx.StandardDeviation;
if (double.IsNaN(MeanX) || double.IsNaN(SDX) || (SDX == 0))
{
//System.Diagnostics.Debug.WriteLine("Skipping "+VariableNamesIndex[i]);
continue;
}
double[] X = new double[InputNeurons];
for (int j = 0; j < InputNeurons; j++)
{
X[j] = (Matrix[i][j] - MeanX) / SDX;
}
Forward(X);
double Sum = 0;
for (int j = 0; j < InputNeurons; j++)
{
Sum += (W[WinX, WinY, j] - X[j]) * (W[WinX, WinY, j] - X[j]);
}
Sum = Math.Sqrt(Sum);
e += Sum;
if (Sum < eMin)
{
eMin = Sum;
}
if (Sum > eMax)
{
eMax = Sum;
}
}
eAll = e / (Matrix.Count * InputNeurons);
eMin /= InputNeurons;
eMax /= InputNeurons;
return(e); //this is the raw error sum
}
//Train on all the data and get the result out. Takes in all the data as a matrix of input values
public void Process(string ImageDirectory)
{
//NOTE: need geographic lookup between areas and rows in Matrix is only passed to the output function after
//the weights have been created - geography not needed for training
List <double[]> Matrix;
List <string> VariableNamesIndex;
BinaryFormatter formatter = new BinaryFormatter();
//load existing matrix (for speed), copied fron Datastore.ProcessKNearestNeighbourCorrelate
using (FileStream reader = new FileStream(Path.Combine(ImageDirectory, "matrix.bin"), FileMode.Open))
{
Matrix = (List <double[]>)formatter.Deserialize(reader);
}
using (FileStream reader = new FileStream(Path.Combine(ImageDirectory, "varnamesindex.bin"), FileMode.Open))
{
VariableNamesIndex = (List <string>)formatter.Deserialize(reader);
}
//TODO: several times through training set with modification in learning rate and neighbourhood
//now do the training
Epoch = 0;
double e = 0;
double DatasetsAreas = Matrix.Count * InputNeurons;
do
{
double LearnRate = 0.001, Distance = 0.5;
//if (Epoch < 2) { LearnRate = 0.85; Distance = 4.0; }
//else if (Epoch < 4) { LearnRate = 0.5; Distance = 3.0; }
//else if (Epoch < 6) { LearnRate=0.1; Distance=2.0; }
//else if (Epoch < 8) { LearnRate = 0.1; Distance = 1.0; }
//else { LearnRate = 10.0 / (float)Epoch; Distance = 0.5; }
LearnRate = 1.0 - (((double)Epoch + 1.0) / 10000.0);
if (LearnRate < 0.1)
{
LearnRate = 0.1;
}
Distance = 4.0 - (((double)Epoch + 1.0) / 1000.0);
if (Distance < 0.5)
{
Distance = 0.5;
}
//ZeroDeltaWeights();
//for (int i = 0; i <Matrix.Count; i++)
//{
int i = trainingRnd.Next(0, Matrix.Count); //pick a random pattern to apply
//System.Diagnostics.Debug.WriteLine("Applying: " + VariableNamesIndex[i]);
//Normalise input here - sd and mean, same method as correlation and KNN
RunningStat rsx = new RunningStat();
foreach (double value in Matrix[i])
{
rsx.Push(value);
}
double MeanX = rsx.Mean, SDX = rsx.StandardDeviation;
if (double.IsNaN(MeanX) || double.IsNaN(SDX) || (SDX == 0))
{
//System.Diagnostics.Debug.WriteLine("Skipping "+VariableNamesIndex[i]);
continue;
}
double[] X = new double[InputNeurons];
for (int j = 0; j < InputNeurons; j++)
{
X[j] = (Matrix[i][j] - MeanX) / SDX;
}
//back propagate, sum errors across whole of training set (NOTE: not using this error value)
double deltaE = Backward(LearnRate, Distance, X); //LearnRate and Distance here
//System.Diagnostics.Debug.WriteLine("e=" + e + " Mean="+MeanX+" SDX="+SDX);
//}
//now all the patterns have been presented, add the delta weights onto the weights and calculate the change
//double deltaSum = UpdateDeltaWeights();
//periodically present all the patterns and recalculate the error
if (Epoch % 100 == 0)
{
e = CalculateError(Matrix); //e=total error over all datasets and areas
}
if (Epoch % 100 == 0)
{
System.Diagnostics.Debug.WriteLine("Epoch: " + Epoch + " LearnRate=" + LearnRate + " Dist=" + Distance + " Error: " + e
+ " eAll: " + eAll + " eMin: " + eMin + " eMax: " + eMax);
}
if (Epoch % 1000 == 0)
{
SaveWeights(Path.Combine(ImageDirectory, "kohonen_weights.bin"));
}
++Epoch;
} while (eAll > 0.001);
SaveWeights(Path.Combine(ImageDirectory, "kohonen_weights.bin"));
//now output the results (the weights are maps) - need area keys
//currently doing this outside function due to areakey problem
}