Understanding Neural Network Batch Training: A Tutorial
There are two different
techniques for training a neural network: batch and online.
Understanding their similarities and differences is important in order
to be able to create accurate prediction systems.
using System;
namespace BatchTrain
{
class NeuralBatchProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin batch training neural network demo");
Console.WriteLine("\nData is the famous Iris flower set.");
Console.WriteLine("Data is sepal length, sepal width, petal length, petal width -> iris species");
Console.WriteLine("Iris setosa = 0 0 1, Iris versicolor = 0 1 0, Iris virginica = 1 0 0 ");
Console.WriteLine("The goal is to predict species from sepal length, width, petal length, width\n");
Console.WriteLine("Raw data resembles:\n");
Console.WriteLine(" 5.1, 3.5, 1.4, 0.2, Iris setosa");
Console.WriteLine(" 7.0, 3.2, 4.7, 1.4, Iris versicolor");
Console.WriteLine(" 6.3, 3.3, 6.0, 2.5, Iris virginica");
Console.WriteLine(" ......\n");
double[][] allData = new double[150][];
allData[0] = new double[] { 5.1, 3.5, 1.4, 0.2, 0, 0, 1 }; // sepal length, width, petal length, width
allData[1] = new double[] { 4.9, 3.0, 1.4, 0.2, 0, 0, 1 }; // Iris setosa = 0 0 1
allData[2] = new double[] { 4.7, 3.2, 1.3, 0.2, 0, 0, 1 }; // Iris versicolor = 0 1 0
allData[3] = new double[] { 4.6, 3.1, 1.5, 0.2, 0, 0, 1 }; // Iris virginica = 1 0 0
allData[4] = new double[] { 5.0, 3.6, 1.4, 0.2, 0, 0, 1 };
allData[5] = new double[] { 5.4, 3.9, 1.7, 0.4, 0, 0, 1 };
allData[6] = new double[] { 4.6, 3.4, 1.4, 0.3, 0, 0, 1 };
allData[7] = new double[] { 5.0, 3.4, 1.5, 0.2, 0, 0, 1 };
allData[8] = new double[] { 4.4, 2.9, 1.4, 0.2, 0, 0, 1 };
allData[9] = new double[] { 4.9, 3.1, 1.5, 0.1, 0, 0, 1 };
allData[10] = new double[] { 5.4, 3.7, 1.5, 0.2, 0, 0, 1 };
allData[11] = new double[] { 4.8, 3.4, 1.6, 0.2, 0, 0, 1 };
allData[12] = new double[] { 4.8, 3.0, 1.4, 0.1, 0, 0, 1 };
allData[13] = new double[] { 4.3, 3.0, 1.1, 0.1, 0, 0, 1 };
allData[14] = new double[] { 5.8, 4.0, 1.2, 0.2, 0, 0, 1 };
allData[15] = new double[] { 5.7, 4.4, 1.5, 0.4, 0, 0, 1 };
allData[16] = new double[] { 5.4, 3.9, 1.3, 0.4, 0, 0, 1 };
allData[17] = new double[] { 5.1, 3.5, 1.4, 0.3, 0, 0, 1 };
allData[18] = new double[] { 5.7, 3.8, 1.7, 0.3, 0, 0, 1 };
allData[19] = new double[] { 5.1, 3.8, 1.5, 0.3, 0, 0, 1 };
allData[20] = new double[] { 5.4, 3.4, 1.7, 0.2, 0, 0, 1 };
allData[21] = new double[] { 5.1, 3.7, 1.5, 0.4, 0, 0, 1 };
allData[22] = new double[] { 4.6, 3.6, 1.0, 0.2, 0, 0, 1 };
allData[23] = new double[] { 5.1, 3.3, 1.7, 0.5, 0, 0, 1 };
allData[24] = new double[] { 4.8, 3.4, 1.9, 0.2, 0, 0, 1 };
allData[25] = new double[] { 5.0, 3.0, 1.6, 0.2, 0, 0, 1 };
allData[26] = new double[] { 5.0, 3.4, 1.6, 0.4, 0, 0, 1 };
allData[27] = new double[] { 5.2, 3.5, 1.5, 0.2, 0, 0, 1 };
allData[28] = new double[] { 5.2, 3.4, 1.4, 0.2, 0, 0, 1 };
allData[29] = new double[] { 4.7, 3.2, 1.6, 0.2, 0, 0, 1 };
allData[30] = new double[] { 4.8, 3.1, 1.6, 0.2, 0, 0, 1 };
allData[31] = new double[] { 5.4, 3.4, 1.5, 0.4, 0, 0, 1 };
allData[32] = new double[] { 5.2, 4.1, 1.5, 0.1, 0, 0, 1 };
allData[33] = new double[] { 5.5, 4.2, 1.4, 0.2, 0, 0, 1 };
allData[34] = new double[] { 4.9, 3.1, 1.5, 0.1, 0, 0, 1 };
allData[35] = new double[] { 5.0, 3.2, 1.2, 0.2, 0, 0, 1 };
allData[36] = new double[] { 5.5, 3.5, 1.3, 0.2, 0, 0, 1 };
allData[37] = new double[] { 4.9, 3.1, 1.5, 0.1, 0, 0, 1 };
allData[38] = new double[] { 4.4, 3.0, 1.3, 0.2, 0, 0, 1 };
allData[39] = new double[] { 5.1, 3.4, 1.5, 0.2, 0, 0, 1 };
allData[40] = new double[] { 5.0, 3.5, 1.3, 0.3, 0, 0, 1 };
allData[41] = new double[] { 4.5, 2.3, 1.3, 0.3, 0, 0, 1 };
allData[42] = new double[] { 4.4, 3.2, 1.3, 0.2, 0, 0, 1 };
allData[43] = new double[] { 5.0, 3.5, 1.6, 0.6, 0, 0, 1 };
allData[44] = new double[] { 5.1, 3.8, 1.9, 0.4, 0, 0, 1 };
allData[45] = new double[] { 4.8, 3.0, 1.4, 0.3, 0, 0, 1 };
allData[46] = new double[] { 5.1, 3.8, 1.6, 0.2, 0, 0, 1 };
allData[47] = new double[] { 4.6, 3.2, 1.4, 0.2, 0, 0, 1 };
allData[48] = new double[] { 5.3, 3.7, 1.5, 0.2, 0, 0, 1 };
allData[49] = new double[] { 5.0, 3.3, 1.4, 0.2, 0, 0, 1 };
allData[50] = new double[] { 7.0, 3.2, 4.7, 1.4, 0, 1, 0 };
allData[51] = new double[] { 6.4, 3.2, 4.5, 1.5, 0, 1, 0 };
allData[52] = new double[] { 6.9, 3.1, 4.9, 1.5, 0, 1, 0 };
allData[53] = new double[] { 5.5, 2.3, 4.0, 1.3, 0, 1, 0 };
allData[54] = new double[] { 6.5, 2.8, 4.6, 1.5, 0, 1, 0 };
allData[55] = new double[] { 5.7, 2.8, 4.5, 1.3, 0, 1, 0 };
allData[56] = new double[] { 6.3, 3.3, 4.7, 1.6, 0, 1, 0 };
allData[57] = new double[] { 4.9, 2.4, 3.3, 1.0, 0, 1, 0 };
allData[58] = new double[] { 6.6, 2.9, 4.6, 1.3, 0, 1, 0 };
allData[59] = new double[] { 5.2, 2.7, 3.9, 1.4, 0, 1, 0 };
allData[60] = new double[] { 5.0, 2.0, 3.5, 1.0, 0, 1, 0 };
allData[61] = new double[] { 5.9, 3.0, 4.2, 1.5, 0, 1, 0 };
allData[62] = new double[] { 6.0, 2.2, 4.0, 1.0, 0, 1, 0 };
allData[63] = new double[] { 6.1, 2.9, 4.7, 1.4, 0, 1, 0 };
allData[64] = new double[] { 5.6, 2.9, 3.6, 1.3, 0, 1, 0 };
allData[65] = new double[] { 6.7, 3.1, 4.4, 1.4, 0, 1, 0 };
allData[66] = new double[] { 5.6, 3.0, 4.5, 1.5, 0, 1, 0 };
allData[67] = new double[] { 5.8, 2.7, 4.1, 1.0, 0, 1, 0 };
allData[68] = new double[] { 6.2, 2.2, 4.5, 1.5, 0, 1, 0 };
allData[69] = new double[] { 5.6, 2.5, 3.9, 1.1, 0, 1, 0 };
allData[70] = new double[] { 5.9, 3.2, 4.8, 1.8, 0, 1, 0 };
allData[71] = new double[] { 6.1, 2.8, 4.0, 1.3, 0, 1, 0 };
allData[72] = new double[] { 6.3, 2.5, 4.9, 1.5, 0, 1, 0 };
allData[73] = new double[] { 6.1, 2.8, 4.7, 1.2, 0, 1, 0 };
allData[74] = new double[] { 6.4, 2.9, 4.3, 1.3, 0, 1, 0 };
allData[75] = new double[] { 6.6, 3.0, 4.4, 1.4, 0, 1, 0 };
allData[76] = new double[] { 6.8, 2.8, 4.8, 1.4, 0, 1, 0 };
allData[77] = new double[] { 6.7, 3.0, 5.0, 1.7, 0, 1, 0 };
allData[78] = new double[] { 6.0, 2.9, 4.5, 1.5, 0, 1, 0 };
allData[79] = new double[] { 5.7, 2.6, 3.5, 1.0, 0, 1, 0 };
allData[80] = new double[] { 5.5, 2.4, 3.8, 1.1, 0, 1, 0 };
allData[81] = new double[] { 5.5, 2.4, 3.7, 1.0, 0, 1, 0 };
allData[82] = new double[] { 5.8, 2.7, 3.9, 1.2, 0, 1, 0 };
allData[83] = new double[] { 6.0, 2.7, 5.1, 1.6, 0, 1, 0 };
allData[84] = new double[] { 5.4, 3.0, 4.5, 1.5, 0, 1, 0 };
allData[85] = new double[] { 6.0, 3.4, 4.5, 1.6, 0, 1, 0 };
allData[86] = new double[] { 6.7, 3.1, 4.7, 1.5, 0, 1, 0 };
allData[87] = new double[] { 6.3, 2.3, 4.4, 1.3, 0, 1, 0 };
allData[88] = new double[] { 5.6, 3.0, 4.1, 1.3, 0, 1, 0 };
allData[89] = new double[] { 5.5, 2.5, 4.0, 1.3, 0, 1, 0 };
allData[90] = new double[] { 5.5, 2.6, 4.4, 1.2, 0, 1, 0 };
allData[91] = new double[] { 6.1, 3.0, 4.6, 1.4, 0, 1, 0 };
allData[92] = new double[] { 5.8, 2.6, 4.0, 1.2, 0, 1, 0 };
allData[93] = new double[] { 5.0, 2.3, 3.3, 1.0, 0, 1, 0 };
allData[94] = new double[] { 5.6, 2.7, 4.2, 1.3, 0, 1, 0 };
allData[95] = new double[] { 5.7, 3.0, 4.2, 1.2, 0, 1, 0 };
allData[96] = new double[] { 5.7, 2.9, 4.2, 1.3, 0, 1, 0 };
allData[97] = new double[] { 6.2, 2.9, 4.3, 1.3, 0, 1, 0 };
allData[98] = new double[] { 5.1, 2.5, 3.0, 1.1, 0, 1, 0 };
allData[99] = new double[] { 5.7, 2.8, 4.1, 1.3, 0, 1, 0 };
allData[100] = new double[] { 6.3, 3.3, 6.0, 2.5, 1, 0, 0 };
allData[101] = new double[] { 5.8, 2.7, 5.1, 1.9, 1, 0, 0 };
allData[102] = new double[] { 7.1, 3.0, 5.9, 2.1, 1, 0, 0 };
allData[103] = new double[] { 6.3, 2.9, 5.6, 1.8, 1, 0, 0 };
allData[104] = new double[] { 6.5, 3.0, 5.8, 2.2, 1, 0, 0 };
allData[105] = new double[] { 7.6, 3.0, 6.6, 2.1, 1, 0, 0 };
allData[106] = new double[] { 4.9, 2.5, 4.5, 1.7, 1, 0, 0 };
allData[107] = new double[] { 7.3, 2.9, 6.3, 1.8, 1, 0, 0 };
allData[108] = new double[] { 6.7, 2.5, 5.8, 1.8, 1, 0, 0 };
allData[109] = new double[] { 7.2, 3.6, 6.1, 2.5, 1, 0, 0 };
allData[110] = new double[] { 6.5, 3.2, 5.1, 2.0, 1, 0, 0 };
allData[111] = new double[] { 6.4, 2.7, 5.3, 1.9, 1, 0, 0 };
allData[112] = new double[] { 6.8, 3.0, 5.5, 2.1, 1, 0, 0 };
allData[113] = new double[] { 5.7, 2.5, 5.0, 2.0, 1, 0, 0 };
allData[114] = new double[] { 5.8, 2.8, 5.1, 2.4, 1, 0, 0 };
allData[115] = new double[] { 6.4, 3.2, 5.3, 2.3, 1, 0, 0 };
allData[116] = new double[] { 6.5, 3.0, 5.5, 1.8, 1, 0, 0 };
allData[117] = new double[] { 7.7, 3.8, 6.7, 2.2, 1, 0, 0 };
allData[118] = new double[] { 7.7, 2.6, 6.9, 2.3, 1, 0, 0 };
allData[119] = new double[] { 6.0, 2.2, 5.0, 1.5, 1, 0, 0 };
allData[120] = new double[] { 6.9, 3.2, 5.7, 2.3, 1, 0, 0 };
allData[121] = new double[] { 5.6, 2.8, 4.9, 2.0, 1, 0, 0 };
allData[122] = new double[] { 7.7, 2.8, 6.7, 2.0, 1, 0, 0 };
allData[123] = new double[] { 6.3, 2.7, 4.9, 1.8, 1, 0, 0 };
allData[124] = new double[] { 6.7, 3.3, 5.7, 2.1, 1, 0, 0 };
allData[125] = new double[] { 7.2, 3.2, 6.0, 1.8, 1, 0, 0 };
allData[126] = new double[] { 6.2, 2.8, 4.8, 1.8, 1, 0, 0 };
allData[127] = new double[] { 6.1, 3.0, 4.9, 1.8, 1, 0, 0 };
allData[128] = new double[] { 6.4, 2.8, 5.6, 2.1, 1, 0, 0 };
allData[129] = new double[] { 7.2, 3.0, 5.8, 1.6, 1, 0, 0 };
allData[130] = new double[] { 7.4, 2.8, 6.1, 1.9, 1, 0, 0 };
allData[131] = new double[] { 7.9, 3.8, 6.4, 2.0, 1, 0, 0 };
allData[132] = new double[] { 6.4, 2.8, 5.6, 2.2, 1, 0, 0 };
allData[133] = new double[] { 6.3, 2.8, 5.1, 1.5, 1, 0, 0 };
allData[134] = new double[] { 6.1, 2.6, 5.6, 1.4, 1, 0, 0 };
allData[135] = new double[] { 7.7, 3.0, 6.1, 2.3, 1, 0, 0 };
allData[136] = new double[] { 6.3, 3.4, 5.6, 2.4, 1, 0, 0 };
allData[137] = new double[] { 6.4, 3.1, 5.5, 1.8, 1, 0, 0 };
allData[138] = new double[] { 6.0, 3.0, 4.8, 1.8, 1, 0, 0 };
allData[139] = new double[] { 6.9, 3.1, 5.4, 2.1, 1, 0, 0 };
allData[140] = new double[] { 6.7, 3.1, 5.6, 2.4, 1, 0, 0 };
allData[141] = new double[] { 6.9, 3.1, 5.1, 2.3, 1, 0, 0 };
allData[142] = new double[] { 5.8, 2.7, 5.1, 1.9, 1, 0, 0 };
allData[143] = new double[] { 6.8, 3.2, 5.9, 2.3, 1, 0, 0 };
allData[144] = new double[] { 6.7, 3.3, 5.7, 2.5, 1, 0, 0 };
allData[145] = new double[] { 6.7, 3.0, 5.2, 2.3, 1, 0, 0 };
allData[146] = new double[] { 6.3, 2.5, 5.0, 1.9, 1, 0, 0 };
allData[147] = new double[] { 6.5, 3.0, 5.2, 2.0, 1, 0, 0 };
allData[148] = new double[] { 6.2, 3.4, 5.4, 2.3, 1, 0, 0 };
allData[149] = new double[] { 5.9, 3.0, 5.1, 1.8, 1, 0, 0 };
Console.WriteLine("\nFirst 3 rows of entire 150-item data set:");
ShowMatrix(allData, 3, 1, true);
Console.WriteLine("Creating 80% training and 20% test data matrices");
double[][] trainData = null;
double[][] testData = null;
MakeTrainTest(allData, out trainData, out testData);
Console.WriteLine("\nFirst 5 rows of non-normalized training data:");
ShowMatrix(trainData, 5, 1, true);
Console.WriteLine("First 3 rows of non-normalized test data:");
ShowMatrix(testData, 3, 1, true);
Console.WriteLine("\nCreating a 4-input, 7-hidden, 3-output neural network");
Console.Write("Hard-coded tanh function for input-to-hidden and softmax for ");
Console.WriteLine("hidden-to-output activations");
const int numInput = 4;
const int numHidden = 7;
const int numOutput = 3;
NeuralNetwork nn = new NeuralNetwork(numInput, numHidden, numOutput);
int maxEpochs = 2000;
double learnRate = 0.01;
Console.WriteLine("Setting maxEpochs = 2000, learnRate = 0.01");
Console.WriteLine("Training has hard-coded mean squared error < 0.020 stopping condition");
Console.WriteLine("\nBeginning training using batch back-propagation\n");
nn.Train(trainData, maxEpochs, learnRate);
Console.WriteLine("Training complete");
double[] weights = nn.GetWeights();
Console.WriteLine("Final neural network weights and bias values:");
ShowVector(weights, 10, 3, true);
double trainAcc = nn.Accuracy(trainData);
Console.WriteLine("\nAccuracy on training data = " + trainAcc.ToString("F4"));
double testAcc = nn.Accuracy(testData);
Console.WriteLine("\nAccuracy on test data = " + testAcc.ToString("F4"));
Console.WriteLine("\nEnd batch training neural network demo\n");
Console.ReadLine();
} // Main
static void MakeTrainTest(double[][] allData, out double[][] trainData, out double[][] testData)
{
// split allData into 80% trainData and 20% testData
Random rnd = new Random(0);
int totRows = allData.Length;
int numCols = allData[0].Length;
int trainRows = (int)(totRows * 0.80); // hard-coded 80-20 split
int testRows = totRows - trainRows;
trainData = new double[trainRows][];
testData = new double[testRows][];
int[] sequence = new int[totRows]; // create a random sequence of indexes
for (int i = 0; i < sequence.Length; ++i)
sequence[i] = i;
for (int i = 0; i < sequence.Length; ++i)
{
int r = rnd.Next(i, sequence.Length);
int tmp = sequence[r];
sequence[r] = sequence[i];
sequence[i] = tmp;
}
int si = 0; // index into sequence[]
int j = 0; // index into trainData or testData
for (; si < trainRows; ++si) // first rows to train data
{
trainData[j] = new double[numCols];
int idx = sequence[si];
Array.Copy(allData[idx], trainData[j], numCols);
++j;
}
j = 0; // reset to start of test data
for (; si < totRows; ++si) // remainder to test data
{
testData[j] = new double[numCols];
int idx = sequence[si];
Array.Copy(allData[idx], testData[j], numCols);
++j;
}
} // MakeTrainTest
public static void ShowVector(double[] vector, int valsPerRow, int decimals, bool newLine)
{
for (int i = 0; i < vector.Length; ++i)
{
if (i % valsPerRow == 0) Console.WriteLine("");
Console.Write(vector[i].ToString("F" + decimals).PadLeft(decimals + 4) + " ");
}
if (newLine == true) Console.WriteLine("");
}
public static void ShowMatrix(double[][] matrix, int numRows, int decimals, bool newLine)
{
for (int i = 0; i < numRows; ++i)
{
Console.Write(i.ToString().PadLeft(3) + ": ");
for (int j = 0; j < matrix[i].Length; ++j)
{
if (matrix[i][j] >= 0.0) Console.Write(" "); else Console.Write("-");
Console.Write(Math.Abs(matrix[i][j]).ToString("F" + decimals) + " ");
}
Console.WriteLine("");
}
if (newLine == true) Console.WriteLine("");
}
} // class Program
public class NeuralNetwork
{
private static Random rnd;
private int numInput;
private int numHidden;
private int numOutput;
private double[] inputs;
private double[][] ihWeights; // input-hidden
private double[] hBiases;
private double[] hOutputs;
private double[][] hoWeights; // hidden-output
private double[] oBiases;
private double[] outputs;
private double[] oGrads; // output gradients for back-propagation
private double[] hGrads; // hidden gradients for back-propagation
// batch training accumulated deltas
private double[][] ihAccDeltas;
private double[] hBiasesAccDeltas;
private double[][] hoAccDeltas;
private double[] oBiasesAccDeltas;
public NeuralNetwork(int numInput, int numHidden, int numOutput)
{
rnd = new Random(0); // for InitializeWeights()
this.numInput = numInput;
this.numHidden = numHidden;
this.numOutput = numOutput;
this.inputs = new double[numInput];
this.ihWeights = MakeMatrix(numInput, numHidden);
this.hBiases = new double[numHidden];
this.hOutputs = new double[numHidden];
this.hoWeights = MakeMatrix(numHidden, numOutput);
this.oBiases = new double[numOutput];
this.outputs = new double[numOutput];
this.hGrads = new double[numHidden];
this.oGrads = new double[numOutput];
this.ihAccDeltas = MakeMatrix(numInput, numHidden);
this.hBiasesAccDeltas = new double[numHidden];
this.hoAccDeltas = MakeMatrix(numHidden, numOutput);
this.oBiasesAccDeltas = new double[numOutput];
this.InitializeWeights();
} // ctor
private static double[][] MakeMatrix(int rows, int cols) // helper for ctor
{
double[][] result = new double[rows][];
for (int r = 0; r < result.Length; ++r)
result[r] = new double[cols];
return result;
}
// ----------------------------------------------------------------------------------------
private void SetWeights(double[] weights)
{
// copy weights and biases in weights[] array to i-h weights, i-h biases, h-o weights, h-o biases
int numWeights = (numInput * numHidden) + (numHidden * numOutput) + numHidden + numOutput;
if (weights.Length != numWeights)
throw new Exception("Bad weights array length: ");
int k = 0; // points into weights param
for (int i = 0; i < numInput; ++i)
for (int j = 0; j < numHidden; ++j)
ihWeights[i][j] = weights[k++];
for (int i = 0; i < numHidden; ++i)
hBiases[i] = weights[k++];
for (int i = 0; i < numHidden; ++i)
for (int j = 0; j < numOutput; ++j)
hoWeights[i][j] = weights[k++];
for (int i = 0; i < numOutput; ++i)
oBiases[i] = weights[k++];
}
private void InitializeWeights()
{
// initialize weights and biases to small random values
int numWeights = (numInput * numHidden) + (numHidden * numOutput) + numHidden + numOutput;
double[] initialWeights = new double[numWeights];
double lo = -0.01;
double hi = 0.01;
for (int i = 0; i < initialWeights.Length; ++i)
initialWeights[i] = (hi - lo) * rnd.NextDouble() + lo;
this.SetWeights(initialWeights);
}
public double[] GetWeights()
{
// returns the current set of wweights, presumably after training
int numWeights = (numInput * numHidden) + (numHidden * numOutput) + numHidden + numOutput;
double[] result = new double[numWeights];
int k = 0;
for (int i = 0; i < ihWeights.Length; ++i)
for (int j = 0; j < ihWeights[0].Length; ++j)
result[k++] = ihWeights[i][j];
for (int i = 0; i < hBiases.Length; ++i)
result[k++] = hBiases[i];
for (int i = 0; i < hoWeights.Length; ++i)
for (int j = 0; j < hoWeights[0].Length; ++j)
result[k++] = hoWeights[i][j];
for (int i = 0; i < oBiases.Length; ++i)
result[k++] = oBiases[i];
return result;
}
// ----------------------------------------------------------------------------------------
private double[] ComputeOutputs(double[] xValues)
{
double[] hSums = new double[numHidden]; // hidden nodes sums scratch array
double[] oSums = new double[numOutput]; // output nodes sums
for (int i = 0; i < xValues.Length; ++i) // copy x-values to inputs
this.inputs[i] = xValues[i];
for (int j = 0; j < numHidden; ++j) // compute i-h sum of weights * inputs
for (int i = 0; i < numInput; ++i)
hSums[j] += this.inputs[i] * this.ihWeights[i][j]; // note +=
for (int i = 0; i < numHidden; ++i) // add biases to input-to-hidden sums
hSums[i] += this.hBiases[i];
for (int i = 0; i < numHidden; ++i) // apply activation
this.hOutputs[i] = HyperTanFunction(hSums[i]); // hard-coded
for (int j = 0; j < numOutput; ++j) // compute h-o sum of weights * hOutputs
for (int i = 0; i < numHidden; ++i)
oSums[j] += hOutputs[i] * hoWeights[i][j];
for (int i = 0; i < numOutput; ++i) // add biases to input-to-hidden sums
oSums[i] += oBiases[i];
double[] softOut = Softmax(oSums); // softmax activation does all outputs at once for efficiency
Array.Copy(softOut, outputs, softOut.Length);
double[] retResult = new double[numOutput]; // could define a GetOutputs method instead
Array.Copy(this.outputs, retResult, retResult.Length);
return retResult;
} // ComputeOutputs
private static double HyperTanFunction(double x)
{
if (x < -20.0) return -1.0; // approximation is correct to 30 decimals
else if (x > 20.0) return 1.0;
else return Math.Tanh(x);
}
private static double[] Softmax(double[] oSums)
{
// determine max output sum
// does all output nodes at once so scale doesn't have to be re-computed each time
double max = oSums[0];
for (int i = 0; i < oSums.Length; ++i)
if (oSums[i] > max) max = oSums[i];
// determine scaling factor -- sum of exp(each val - max)
double scale = 0.0;
for (int i = 0; i < oSums.Length; ++i)
scale += Math.Exp(oSums[i] - max);
double[] result = new double[oSums.Length];
for (int i = 0; i < oSums.Length; ++i)
result[i] = Math.Exp(oSums[i] - max) / scale;
return result; // now scaled so that xi sum to 1.0
}
// ----------------------------------------------------------------------------------------
private void ComputeAndAccumulateDeltas(double[] tValues, double learnRate) // for curr outputs
{
// 1. compute output gradients
for (int i = 0; i < numOutput; ++i)
{
// derivative of softmax = (1 - y) * y (same as log-sigmoid)
double derivative = (1 - outputs[i]) * outputs[i];
oGrads[i] = derivative * (tValues[i] - outputs[i]); // assumes MSE
}
// 2. compute hidden gradients
for (int i = 0; i < numHidden; ++i)
{
// derivative of tanh = (1 - y) * (1 + y)
double derivative = (1 - hOutputs[i]) * (1 + hOutputs[i]);
double sum = 0.0;
for (int j = 0; j < numOutput; ++j) // each hidden delta is the sum of numOutput terms
{
double x = oGrads[j] * hoWeights[i][j];
sum += x;
}
hGrads[i] = derivative * sum;
}
// 3a. compute and accumulate input-hidden weight deltas
for (int i = 0; i < numInput; ++i)
{
for (int j = 0; j < numHidden; ++j)
{
double delta = learnRate * hGrads[j] * inputs[i]; // compute the new delta
this.ihAccDeltas[i][j] += delta; // accumulate
}
}
// 3b. compute hidden biases deltas
for (int i = 0; i < numHidden; ++i)
{
double delta = learnRate * hGrads[i] * 1.0; // 1.0 is dummy input
this.hBiasesAccDeltas[i] += delta;
}
// 4a. compute hidden-output weights deltas
for (int i = 0; i < numHidden; ++i)
{
for (int j = 0; j < numOutput; ++j)
{
double delta = learnRate * oGrads[j] * hOutputs[i];
this.hoAccDeltas[i][j] += delta;
}
}
// 4b. compute output biases deltas
for (int i = 0; i < numOutput; ++i)
{
double delta = learnRate * oGrads[i] * 1.0;
this.oBiasesAccDeltas[i] += delta;
}
} // ComputeAndAccumulateDeltas
// ----------------------------------------------------------------------------------------
public void Train(double[][] trainData, int maxEpochs, double learnRate)
{
// train a back-prop style NN using learning rate with batch training
int epoch = 0;
double[] xValues = new double[numInput]; // inputs
double[] tValues = new double[numOutput]; // target values
while (epoch < maxEpochs)
{
double mse = MeanSquaredError(trainData);
if (mse < 0.020) break; // consider passing value in as parameter
//if (epoch < 100)
// Console.WriteLine(epoch + "\t" + mse.ToString("F4"));
// zero-out accumulated weight deltas
for (int i = 0; i < numInput; ++i)
for (int j = 0; j < numHidden; ++j)
ihAccDeltas[i][j] = 0.0;
for (int i = 0; i < numHidden; ++i)
hBiasesAccDeltas[i] = 0.0;
for (int i = 0; i < numHidden; ++i)
for (int j = 0; j < numOutput; ++j)
hoAccDeltas[i][j] = 0.0;
for (int i = 0; i < numOutput; ++i)
oBiasesAccDeltas[i] = 0.0;
for (int i = 0; i < trainData.Length; ++i) // for each training item
{
Array.Copy(trainData[i], xValues, numInput); // get curr x-values
Array.Copy(trainData[i], numInput, tValues, 0, numOutput); // get curr t-values
ComputeOutputs(xValues); // compute outputs (store them internally)
ComputeAndAccumulateDeltas(tValues, learnRate);
}
// update all weights using the accumulated deltas
for (int i = 0; i < numInput; ++i)
for (int j = 0; j < numHidden; ++j)
ihWeights[i][j] += ihAccDeltas[i][j];
for (int i = 0; i < numHidden; ++i)
hBiases[i] += hBiasesAccDeltas[i];
for (int i = 0; i < numHidden; ++i)
for (int j = 0; j < numOutput; ++j)
hoWeights[i][j] += hoAccDeltas[i][j];
for (int i = 0; i < numOutput; ++i)
oBiases[i] += oBiasesAccDeltas[i];
++epoch;
}
} // Train
private double MeanSquaredError(double[][] trainData) // used as a training stopping condition
{
// average squared error per training tuple
double sumSquaredError = 0.0;
double[] xValues = new double[numInput]; // first numInput values in trainData
double[] tValues = new double[numOutput]; // last numOutput values
// walk thru each training case. looks like (6.9 3.2 5.7 2.3) (0 0 1)
for (int i = 0; i < trainData.Length; ++i)
{
Array.Copy(trainData[i], xValues, numInput);
Array.Copy(trainData[i], numInput, tValues, 0, numOutput); // get target values
double[] yValues = this.ComputeOutputs(xValues); // compute output using current weights
for (int j = 0; j < numOutput; ++j)
{
double err = tValues[j] - yValues[j];
sumSquaredError += err * err;
}
}
return sumSquaredError / trainData.Length;
}
// ----------------------------------------------------------------------------------------
public double Accuracy(double[][] testData)
{
// percentage correct using winner-takes all
int numCorrect = 0;
int numWrong = 0;
double[] xValues = new double[numInput]; // inputs
double[] tValues = new double[numOutput]; // targets
double[] yValues; // computed Y
for (int i = 0; i < testData.Length; ++i)
{
Array.Copy(testData[i], xValues, numInput); // parse test data into x-values and t-values
Array.Copy(testData[i], numInput, tValues, 0, numOutput);
yValues = this.ComputeOutputs(xValues);
int maxIndex = MaxIndex(yValues); // which cell in yValues has largest value?
if (tValues[maxIndex] == 1.0) // ugly. consider AreEqual(double x, double y)
++numCorrect;
else
++numWrong;
}
return (numCorrect * 1.0) / (numCorrect + numWrong); // ugly 2 - check for divide by zero
}
private static int MaxIndex(double[] vector) // helper for Accuracy()
{
// index of largest value
int bigIndex = 0;
double biggestVal = vector[0];
for (int i = 0; i < vector.Length; ++i)
{
if (vector[i] > biggestVal)
{
biggestVal = vector[i]; bigIndex = i;
}
}
return bigIndex;
}
} // NeuralNetwork
} // ns
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