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Neural Network Demo with C# by James McCaffrey, MSR and Build 2013 versions
// http://channel9.msdn.com/Events/Build/2013/2-401
// http://www.quaetrix.com/Build2013.html
using System;
// For 2013 Microsoft Build Conference attendees
// June 25-28, 2013
// San Francisco, CA
//
// This is source for a C# console application.
// To compile you can 1.) create a new Visual Studio
// C# console app project named BuildNeuralNetworkDemo
// then zap away the template code and replace with this code,
// or 2.) copy this code into notepad, save as NeuralNetworkProgram.cs
// on your local machine, launch the special VS command shell
// (it knows where the csc.exe compiler is), cd-navigate to
// the directory containing the .cs file, type 'csc.exe
// NeuralNetworkProgram.cs' and hit enter, and then after
// the compiler creates NeuralNetworkProgram.exe, you can
// run from the command line.
//
// This is an enhanced neural network. It is fully-connected
// and feed-forward. The training algorithm is back-propagation
// with momentum and weight decay. The inpput data is normalized
// so training is quite fast.
//
// You can use this code however you wish subject to the usual disclaimers
// (use at your own risk, etc.)
namespace BuildNeuralNetworkDemo
{
class NeuralNetworkProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin Build 2013 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 6 rows of entire 150-item data set:");
ShowMatrix(allData, 6, 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 training data:");
ShowMatrix(trainData, 5, 1, true);
Console.WriteLine("First 3 rows of test data:");
ShowMatrix(testData, 3, 1, true);
Normalize(trainData, new int[] { 0, 1, 2, 3 });
Normalize(testData, new int[] { 0, 1, 2, 3 });
Console.WriteLine("\nFirst 5 rows of normalized training data:");
ShowMatrix(trainData, 5, 1, true);
Console.WriteLine("First 3 rows of 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);
Console.WriteLine("\nInitializing weights and bias to small random values");
nn.InitializeWeights();
int maxEpochs = 2000;
double learnRate = 0.05;
double momentum = 0.01;
double weightDecay = 0.0001;
Console.WriteLine("Setting maxEpochs = 2000, learnRate = 0.05, momentum = 0.01, weightDecay = 0.0001");
Console.WriteLine("Training has hard-coded mean squared error < 0.020 stopping condition");
Console.WriteLine("\nBeginning training using incremental back-propagation\n");
nn.Train(trainData, maxEpochs, learnRate, momentum, weightDecay);
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 Build 2013 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
static void Normalize(double[][] dataMatrix, int[] cols)
{
// normalize specified cols by computing (x - mean) / sd for each value
foreach (int col in cols)
{
double sum = 0.0;
for (int i = 0; i < dataMatrix.Length; ++i)
sum += dataMatrix[i][col];
double mean = sum / dataMatrix.Length;
sum = 0.0;
for (int i = 0; i < dataMatrix.Length; ++i)
sum += (dataMatrix[i][col] - mean) * (dataMatrix[i][col] - mean);
// thanks to Dr. W. Winfrey, Concord Univ., for catching bug in original code
double sd = Math.Sqrt(sum / (dataMatrix.Length - 1));
for (int i = 0; i < dataMatrix.Length; ++i)
dataMatrix[i][col] = (dataMatrix[i][col] - mean) / sd;
}
}
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("");
}
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;
// back-prop specific arrays (these could be local to method UpdateWeights)
private double[] oGrads; // output gradients for back-propagation
private double[] hGrads; // hidden gradients for back-propagation
// back-prop momentum specific arrays (could be local to method Train)
private double[][] ihPrevWeightsDelta; // for momentum with back-propagation
private double[] hPrevBiasesDelta;
private double[][] hoPrevWeightsDelta;
private double[] oPrevBiasesDelta;
public NeuralNetwork(int numInput, int numHidden, int numOutput)
{
rnd = new Random(0); // for InitializeWeights() and Shuffle()
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];
// back-prop related arrays below
this.hGrads = new double[numHidden];
this.oGrads = new double[numOutput];
this.ihPrevWeightsDelta = MakeMatrix(numInput, numHidden);
this.hPrevBiasesDelta = new double[numHidden];
this.hoPrevWeightsDelta = MakeMatrix(numHidden, numOutput);
this.oPrevBiasesDelta = new double[numOutput];
} // 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;
}
public override string ToString() // yikes
{
string s = "";
s += "===============================\n";
s += "numInput = " + numInput + " numHidden = " + numHidden + " numOutput = " + numOutput + "\n\n";
s += "inputs: \n";
for (int i = 0; i < inputs.Length; ++i)
s += inputs[i].ToString("F2") + " ";
s += "\n\n";
s += "ihWeights: \n";
for (int i = 0; i < ihWeights.Length; ++i)
{
for (int j = 0; j < ihWeights[i].Length; ++j)
{
s += ihWeights[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "hBiases: \n";
for (int i = 0; i < hBiases.Length; ++i)
s += hBiases[i].ToString("F4") + " ";
s += "\n\n";
s += "hOutputs: \n";
for (int i = 0; i < hOutputs.Length; ++i)
s += hOutputs[i].ToString("F4") + " ";
s += "\n\n";
s += "hoWeights: \n";
for (int i = 0; i < hoWeights.Length; ++i)
{
for (int j = 0; j < hoWeights[i].Length; ++j)
{
s += hoWeights[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "oBiases: \n";
for (int i = 0; i < oBiases.Length; ++i)
s += oBiases[i].ToString("F4") + " ";
s += "\n\n";
s += "hGrads: \n";
for (int i = 0; i < hGrads.Length; ++i)
s += hGrads[i].ToString("F4") + " ";
s += "\n\n";
s += "oGrads: \n";
for (int i = 0; i < oGrads.Length; ++i)
s += oGrads[i].ToString("F4") + " ";
s += "\n\n";
s += "ihPrevWeightsDelta: \n";
for (int i = 0; i < ihPrevWeightsDelta.Length; ++i)
{
for (int j = 0; j < ihPrevWeightsDelta[i].Length; ++j)
{
s += ihPrevWeightsDelta[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "hPrevBiasesDelta: \n";
for (int i = 0; i < hPrevBiasesDelta.Length; ++i)
s += hPrevBiasesDelta[i].ToString("F4") + " ";
s += "\n\n";
s += "hoPrevWeightsDelta: \n";
for (int i = 0; i < hoPrevWeightsDelta.Length; ++i)
{
for (int j = 0; j < hoPrevWeightsDelta[i].Length; ++j)
{
s += hoPrevWeightsDelta[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "oPrevBiasesDelta: \n";
for (int i = 0; i < oPrevBiasesDelta.Length; ++i)
s += oPrevBiasesDelta[i].ToString("F4") + " ";
s += "\n\n";
s += "outputs: \n";
for (int i = 0; i < outputs.Length; ++i)
s += outputs[i].ToString("F2") + " ";
s += "\n\n";
s += "===============================\n";
return s;
}
// ----------------------------------------------------------------------------------------
public 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++];
}
public 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)
{
if (xValues.Length != numInput)
throw new Exception("Bad xValues array length");
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 UpdateWeights(double[] tValues, double learnRate, double momentum, double weightDecay)
{
// update the weights and biases using back-propagation, with target values, eta (learning rate),
// alpha (momentum).
// assumes that SetWeights and ComputeOutputs have been called and so all the internal arrays
// and matrices have values (other than 0.0)
if (tValues.Length != numOutput)
throw new Exception("target values not same Length as output in UpdateWeights");
// 1. compute output gradients
for (int i = 0; i < oGrads.Length; ++i)
{
// derivative of softmax = (1 - y) * y (same as log-sigmoid)
double derivative = (1 - outputs[i]) * outputs[i];
// 'mean squared error version' includes (1-y)(y) derivative
oGrads[i] = derivative * (tValues[i] - outputs[i]);
}
// 2. compute hidden gradients
for (int i = 0; i < hGrads.Length; ++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. update hidden weights (gradients must be computed right-to-left but weights
// can be updated in any order)
for (int i = 0; i < ihWeights.Length; ++i) // 0..2 (3)
{
for (int j = 0; j < ihWeights[0].Length; ++j) // 0..3 (4)
{
double delta = learnRate * hGrads[j] * inputs[i]; // compute the new delta
ihWeights[i][j] += delta; // update. note we use '+' instead of '-'. this can be very tricky.
// now add momentum using previous delta. on first pass old value will be 0.0 but that's OK.
ihWeights[i][j] += momentum * ihPrevWeightsDelta[i][j];
ihWeights[i][j] -= (weightDecay * ihWeights[i][j]); // weight decay
ihPrevWeightsDelta[i][j] = delta; // don't forget to save the delta for momentum
}
}
// 3b. update hidden biases
for (int i = 0; i < hBiases.Length; ++i)
{
double delta = learnRate * hGrads[i] * 1.0; // t1.0 is constant input for bias; could leave out
hBiases[i] += delta;
hBiases[i] += momentum * hPrevBiasesDelta[i]; // momentum
hBiases[i] -= (weightDecay * hBiases[i]); // weight decay
hPrevBiasesDelta[i] = delta; // don't forget to save the delta
}
// 4. update hidden-output weights
for (int i = 0; i < hoWeights.Length; ++i)
{
for (int j = 0; j < hoWeights[0].Length; ++j)
{
// see above: hOutputs are inputs to the nn outputs
double delta = learnRate * oGrads[j] * hOutputs[i];
hoWeights[i][j] += delta;
hoWeights[i][j] += momentum * hoPrevWeightsDelta[i][j]; // momentum
hoWeights[i][j] -= (weightDecay * hoWeights[i][j]); // weight decay
hoPrevWeightsDelta[i][j] = delta; // save
}
}
// 4b. update output biases
for (int i = 0; i < oBiases.Length; ++i)
{
double delta = learnRate * oGrads[i] * 1.0;
oBiases[i] += delta;
oBiases[i] += momentum * oPrevBiasesDelta[i]; // momentum
oBiases[i] -= (weightDecay * oBiases[i]); // weight decay
oPrevBiasesDelta[i] = delta; // save
}
} // UpdateWeights
// ----------------------------------------------------------------------------------------
public void Train(double[][] trainData, int maxEprochs, double learnRate, double momentum,
double weightDecay)
{
// train a back-prop style NN classifier using learning rate and momentum
// weight decay reduces the magnitude of a weight value over time unless that value
// is constantly increased
int epoch = 0;
double[] xValues = new double[numInput]; // inputs
double[] tValues = new double[numOutput]; // target values
int[] sequence = new int[trainData.Length];
for (int i = 0; i < sequence.Length; ++i)
sequence[i] = i;
while (epoch < maxEprochs)
{
double mse = MeanSquaredError(trainData);
if (mse < 0.020) break; // consider passing value in as parameter
//if (mse < 0.001) break; // consider passing value in as parameter
Shuffle(sequence); // visit each training data in random order
for (int i = 0; i < trainData.Length; ++i)
{
int idx = sequence[i];
Array.Copy(trainData[idx], xValues, numInput);
Array.Copy(trainData[idx], numInput, tValues, 0, numOutput);
ComputeOutputs(xValues); // copy xValues in, compute outputs (store them internally)
UpdateWeights(tValues, learnRate, momentum, weightDecay); // find better weights
} // each training tuple
++epoch;
}
} // Train
private static void Shuffle(int[] sequence)
{
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;
}
}
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
// http://channel9.msdn.com/Events/Build/2013/2-401
// http://research.microsoft.com/en-us/projects/neuralnetworks/BackPropDemo.aspx
// http://www.quaetrix.com/NeuralNetworkDemo.html
using System;
// C# console application demo of a neural network classification program using Visual Studio.
// Assumes you have Visual Studio (you can get a free 'Visual Studio Express' version).
// To build from command line, copy this code into notepad or similar editor and then save on
// your local machine as file MSRNeuralProgram.cs. Next, launch the special Visual Studio
// command shell (it knows where the C# compiler is) and then cd-navigate to the directory
// where you saved this file. Then type 'csc.exe MSRNeuralProgram.cs' and hit (Enter).
// The program will compile and create file MSRNeuralProgram.exe which you can run from the
// command line.
//
// The demo problem is to classify some dummy data. The 4 predictor values are just arbitrary
// numbers between 0 and 40. The value-to-predict is color, which can be either 'red',
// 'yellow', or 'blue'. The data is based on the famous Fisher's Iris data set.
//
// The neural network in this demo is 'normal' - it fully-connected and feed-forward.
// Training uses the back-propagation algorithm with momentum but no weight-decay, and
// the behind-the-scenes error term is sum of squared errors (even though research suggests
// that cross-entropy is superior). The program does not perform input data normalization
// and so training is slower than it could be.
namespace ResearchNeuralNetworkDemo
{
class MSRNeuralProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin neural network classification and prediction demo");
Console.WriteLine("\nData is dummy, artificial data.");
Console.WriteLine("X-data is x0, x1, x2, x3");
Console.WriteLine("Y-data is Red = 0 0 1, Yellow = 0 1 0, Blue = 1 0 0 "); // 1-of-N encoded
Console.WriteLine("The goal is to predict color from x0, x1, x2, x3\n");
Console.WriteLine("Raw data resembles:\n");
Console.WriteLine(" 25.6, 17.6, 7.1, 1.1, Red");
Console.WriteLine(" 35.1, 16.1, 23.6, 7.1, Yellow");
Console.WriteLine(" 31.6, 16.6, 30.1, 12.6, Blue");
Console.WriteLine(" ......\n");
double[][] allData = new double[150][];
allData[0] = new double[] { 25.6, 17.6, 7.1, 1.1, 0, 0, 1 };
allData[1] = new double[] { 24.6, 15.1, 7.1, 1.1, 0, 0, 1 };
allData[2] = new double[] { 23.6, 16.1, 6.6, 1.1, 0, 0, 1 };
allData[3] = new double[] { 23.1, 15.6, 7.6, 1.1, 0, 0, 1 };
allData[4] = new double[] { 25.1, 18.1, 7.1, 1.1, 0, 0, 1 };
allData[5] = new double[] { 27.1, 19.6, 8.6, 2.1, 0, 0, 1 };
allData[6] = new double[] { 23.1, 17.1, 7.1, 1.6, 0, 0, 1 };
allData[7] = new double[] { 25.1, 17.1, 7.6, 1.1, 0, 0, 1 };
allData[8] = new double[] { 22.1, 14.6, 7.1, 1.1, 0, 0, 1 };
allData[9] = new double[] { 24.6, 15.6, 7.6, 0.6, 0, 0, 1 };
allData[10] = new double[] { 27.1, 18.6, 7.6, 1.1, 0, 0, 1 };
allData[11] = new double[] { 24.1, 17.1, 8.1, 1.1, 0, 0, 1 };
allData[12] = new double[] { 24.1, 15.1, 7.1, 0.6, 0, 0, 1 };
allData[13] = new double[] { 21.6, 15.1, 5.6, 0.6, 0, 0, 1 };
allData[14] = new double[] { 29.1, 20.1, 6.1, 1.1, 0, 0, 1 };
allData[15] = new double[] { 28.6, 22.1, 7.6, 2.1, 0, 0, 1 };
allData[16] = new double[] { 27.1, 19.6, 6.6, 2.1, 0, 0, 1 };
allData[17] = new double[] { 25.6, 17.6, 7.1, 1.6, 0, 0, 1 };
allData[18] = new double[] { 28.6, 19.1, 8.6, 1.6, 0, 0, 1 };
allData[19] = new double[] { 25.6, 19.1, 7.6, 1.6, 0, 0, 1 };
allData[20] = new double[] { 27.1, 17.1, 8.6, 1.1, 0, 0, 1 };
allData[21] = new double[] { 25.6, 18.6, 7.6, 2.1, 0, 0, 1 };
allData[22] = new double[] { 23.1, 18.1, 5.1, 1.1, 0, 0, 1 };
allData[23] = new double[] { 25.6, 16.6, 8.6, 2.6, 0, 0, 1 };
allData[24] = new double[] { 24.1, 17.1, 9.6, 1.1, 0, 0, 1 };
allData[25] = new double[] { 25.1, 15.1, 8.1, 1.1, 0, 0, 1 };
allData[26] = new double[] { 25.1, 17.1, 8.1, 2.1, 0, 0, 1 };
allData[27] = new double[] { 26.1, 17.6, 7.6, 1.1, 0, 0, 1 };
allData[28] = new double[] { 26.1, 17.1, 7.1, 1.1, 0, 0, 1 };
allData[29] = new double[] { 23.6, 16.1, 8.1, 1.1, 0, 0, 1 };
allData[30] = new double[] { 24.1, 15.6, 8.1, 1.1, 0, 0, 1 };
allData[31] = new double[] { 27.1, 17.1, 7.6, 2.1, 0, 0, 1 };
allData[32] = new double[] { 26.1, 20.6, 7.6, 0.6, 0, 0, 1 };
allData[33] = new double[] { 27.6, 21.1, 7.1, 1.1, 0, 0, 1 };
allData[34] = new double[] { 24.6, 15.6, 7.6, 0.6, 0, 0, 1 };
allData[35] = new double[] { 25.1, 16.1, 6.1, 1.1, 0, 0, 1 };
allData[36] = new double[] { 27.6, 17.6, 6.6, 1.1, 0, 0, 1 };
allData[37] = new double[] { 24.6, 15.6, 7.6, 0.6, 0, 0, 1 };
allData[38] = new double[] { 22.1, 15.1, 6.6, 1.1, 0, 0, 1 };
allData[39] = new double[] { 25.6, 17.1, 7.6, 1.1, 0, 0, 1 };
allData[40] = new double[] { 25.1, 17.6, 6.6, 1.6, 0, 0, 1 };
allData[41] = new double[] { 22.6, 11.6, 6.6, 1.6, 0, 0, 1 };
allData[42] = new double[] { 22.1, 16.1, 6.6, 1.1, 0, 0, 1 };
allData[43] = new double[] { 25.1, 17.6, 8.1, 3.1, 0, 0, 1 };
allData[44] = new double[] { 25.6, 19.1, 9.6, 2.1, 0, 0, 1 };
allData[45] = new double[] { 24.1, 15.1, 7.1, 1.6, 0, 0, 1 };
allData[46] = new double[] { 25.6, 19.1, 8.1, 1.1, 0, 0, 1 };
allData[47] = new double[] { 23.1, 16.1, 7.1, 1.1, 0, 0, 1 };
allData[48] = new double[] { 26.6, 18.6, 7.6, 1.1, 0, 0, 1 };
allData[49] = new double[] { 25.1, 16.6, 7.1, 1.1, 0, 0, 1 };
allData[50] = new double[] { 35.1, 16.1, 23.6, 7.1, 0, 1, 0 };
allData[51] = new double[] { 32.1, 16.1, 22.6, 7.6, 0, 1, 0 };
allData[52] = new double[] { 34.6, 15.6, 24.6, 7.6, 0, 1, 0 };
allData[53] = new double[] { 27.6, 11.6, 20.1, 6.6, 0, 1, 0 };
allData[54] = new double[] { 32.6, 14.1, 23.1, 7.6, 0, 1, 0 };
allData[55] = new double[] { 28.6, 14.1, 22.6, 6.6, 0, 1, 0 };
allData[56] = new double[] { 31.6, 16.6, 23.6, 8.1, 0, 1, 0 };
allData[57] = new double[] { 24.6, 12.1, 16.6, 5.1, 0, 1, 0 };
allData[58] = new double[] { 33.1, 14.6, 23.1, 6.6, 0, 1, 0 };
allData[59] = new double[] { 26.1, 13.6, 19.6, 7.1, 0, 1, 0 };
allData[60] = new double[] { 25.1, 10.1, 17.6, 5.1, 0, 1, 0 };
allData[61] = new double[] { 29.6, 15.1, 21.1, 7.6, 0, 1, 0 };
allData[62] = new double[] { 30.1, 11.1, 20.1, 5.1, 0, 1, 0 };
allData[63] = new double[] { 30.6, 14.6, 23.6, 7.1, 0, 1, 0 };
allData[64] = new double[] { 28.1, 14.6, 18.1, 6.6, 0, 1, 0 };
allData[65] = new double[] { 33.6, 15.6, 22.1, 7.1, 0, 1, 0 };
allData[66] = new double[] { 28.1, 15.1, 22.6, 7.6, 0, 1, 0 };
allData[67] = new double[] { 29.1, 13.6, 20.6, 5.1, 0, 1, 0 };
allData[68] = new double[] { 31.1, 11.1, 22.6, 7.6, 0, 1, 0 };
allData[69] = new double[] { 28.1, 12.6, 19.6, 5.6, 0, 1, 0 };
allData[70] = new double[] { 29.6, 16.1, 24.1, 9.1, 0, 1, 0 };
allData[71] = new double[] { 30.6, 14.1, 20.1, 6.6, 0, 1, 0 };
allData[72] = new double[] { 31.6, 12.6, 24.6, 7.6, 0, 1, 0 };
allData[73] = new double[] { 30.6, 14.1, 23.6, 6.1, 0, 1, 0 };
allData[74] = new double[] { 32.1, 14.6, 21.6, 6.6, 0, 1, 0 };
allData[75] = new double[] { 33.1, 15.1, 22.1, 7.1, 0, 1, 0 };
allData[76] = new double[] { 34.1, 14.1, 24.1, 7.1, 0, 1, 0 };
allData[77] = new double[] { 33.6, 15.1, 25.1, 8.6, 0, 1, 0 };
allData[78] = new double[] { 30.1, 14.6, 22.6, 7.6, 0, 1, 0 };
allData[79] = new double[] { 28.6, 13.1, 17.6, 5.1, 0, 1, 0 };
allData[80] = new double[] { 27.6, 12.1, 19.1, 5.6, 0, 1, 0 };
allData[81] = new double[] { 27.6, 12.1, 18.6, 5.1, 0, 1, 0 };
allData[82] = new double[] { 29.1, 13.6, 19.6, 6.1, 0, 1, 0 };
allData[83] = new double[] { 30.1, 13.6, 25.6, 8.1, 0, 1, 0 };
allData[84] = new double[] { 27.1, 15.1, 22.6, 7.6, 0, 1, 0 };
allData[85] = new double[] { 30.1, 17.1, 22.6, 8.1, 0, 1, 0 };
allData[86] = new double[] { 33.6, 15.6, 23.6, 7.6, 0, 1, 0 };
allData[87] = new double[] { 31.6, 11.6, 22.1, 6.6, 0, 1, 0 };
allData[88] = new double[] { 28.1, 15.1, 20.6, 6.6, 0, 1, 0 };
allData[89] = new double[] { 27.6, 12.6, 20.1, 6.6, 0, 1, 0 };
allData[90] = new double[] { 27.6, 13.1, 22.1, 6.1, 0, 1, 0 };
allData[91] = new double[] { 30.6, 15.1, 23.1, 7.1, 0, 1, 0 };
allData[92] = new double[] { 29.1, 13.1, 20.1, 6.1, 0, 1, 0 };
allData[93] = new double[] { 25.1, 11.6, 16.6, 5.1, 0, 1, 0 };
allData[94] = new double[] { 28.1, 13.6, 21.1, 6.6, 0, 1, 0 };
allData[95] = new double[] { 28.6, 15.1, 21.1, 6.1, 0, 1, 0 };
allData[96] = new double[] { 28.6, 14.6, 21.1, 6.6, 0, 1, 0 };
allData[97] = new double[] { 31.1, 14.6, 21.6, 6.6, 0, 1, 0 };
allData[98] = new double[] { 25.6, 12.6, 15.1, 5.6, 0, 1, 0 };
allData[99] = new double[] { 28.6, 14.1, 20.6, 6.6, 0, 1, 0 };
allData[100] = new double[] { 31.6, 16.6, 30.1, 12.6, 1, 0, 0 };
allData[101] = new double[] { 29.1, 13.6, 25.6, 9.6, 1, 0, 0 };
allData[102] = new double[] { 35.6, 15.1, 29.6, 10.6, 1, 0, 0 };
allData[103] = new double[] { 31.6, 14.6, 28.1, 9.1, 1, 0, 0 };
allData[104] = new double[] { 32.6, 15.1, 29.1, 11.1, 1, 0, 0 };
allData[105] = new double[] { 38.1, 15.1, 33.1, 10.6, 1, 0, 0 };
allData[106] = new double[] { 24.6, 12.6, 22.6, 8.6, 1, 0, 0 };
allData[107] = new double[] { 36.6, 14.6, 31.6, 9.1, 1, 0, 0 };
allData[108] = new double[] { 33.6, 12.6, 29.1, 9.1, 1, 0, 0 };
allData[109] = new double[] { 36.1, 18.1, 30.6, 12.6, 1, 0, 0 };
allData[110] = new double[] { 32.6, 16.1, 25.6, 10.1, 1, 0, 0 };
allData[111] = new double[] { 32.1, 13.6, 26.6, 9.6, 1, 0, 0 };
allData[112] = new double[] { 34.1, 15.1, 27.6, 10.6, 1, 0, 0 };
allData[113] = new double[] { 28.6, 12.6, 25.1, 10.1, 1, 0, 0 };
allData[114] = new double[] { 29.1, 14.1, 25.6, 12.1, 1, 0, 0 };
allData[115] = new double[] { 32.1, 16.1, 26.6, 11.6, 1, 0, 0 };
allData[116] = new double[] { 32.6, 15.1, 27.6, 9.1, 1, 0, 0 };
allData[117] = new double[] { 38.6, 19.1, 33.6, 11.1, 1, 0, 0 };
allData[118] = new double[] { 38.6, 13.1, 34.6, 11.6, 1, 0, 0 };
allData[119] = new double[] { 30.1, 11.1, 25.1, 7.6, 1, 0, 0 };
allData[120] = new double[] { 34.6, 16.1, 28.6, 11.6, 1, 0, 0 };
allData[121] = new double[] { 28.1, 14.1, 24.6, 10.1, 1, 0, 0 };
allData[122] = new double[] { 38.6, 14.1, 33.6, 10.1, 1, 0, 0 };
allData[123] = new double[] { 31.6, 13.6, 24.6, 9.1, 1, 0, 0 };
allData[124] = new double[] { 33.6, 16.6, 28.6, 10.6, 1, 0, 0 };
allData[125] = new double[] { 36.1, 16.1, 30.1, 9.1, 1, 0, 0 };
allData[126] = new double[] { 31.1, 14.1, 24.1, 9.1, 1, 0, 0 };
allData[127] = new double[] { 30.6, 15.1, 24.6, 9.1, 1, 0, 0 };
allData[128] = new double[] { 32.1, 14.1, 28.1, 10.6, 1, 0, 0 };
allData[129] = new double[] { 36.1, 15.1, 29.1, 8.1, 1, 0, 0 };
allData[130] = new double[] { 37.1, 14.1, 30.6, 9.6, 1, 0, 0 };
allData[131] = new double[] { 39.6, 19.1, 32.1, 10.1, 1, 0, 0 };
allData[132] = new double[] { 32.1, 14.1, 28.1, 11.1, 1, 0, 0 };
allData[133] = new double[] { 31.6, 14.1, 25.6, 7.6, 1, 0, 0 };
allData[134] = new double[] { 30.6, 13.1, 28.1, 7.1, 1, 0, 0 };
allData[135] = new double[] { 38.6, 15.1, 30.6, 11.6, 1, 0, 0 };
allData[136] = new double[] { 31.6, 17.1, 28.1, 12.1, 1, 0, 0 };
allData[137] = new double[] { 32.1, 15.6, 27.6, 9.1, 1, 0, 0 };
allData[138] = new double[] { 30.1, 15.1, 24.1, 9.1, 1, 0, 0 };
allData[139] = new double[] { 34.6, 15.6, 27.1, 10.6, 1, 0, 0 };
allData[140] = new double[] { 33.6, 15.6, 28.1, 12.1, 1, 0, 0 };
allData[141] = new double[] { 34.6, 15.6, 25.6, 11.6, 1, 0, 0 };
allData[142] = new double[] { 29.1, 13.6, 25.6, 9.6, 1, 0, 0 };
allData[143] = new double[] { 34.1, 16.1, 29.6, 11.6, 1, 0, 0 };
allData[144] = new double[] { 33.6, 16.6, 28.6, 12.6, 1, 0, 0 };
allData[145] = new double[] { 33.6, 15.1, 26.1, 11.6, 1, 0, 0 };
allData[146] = new double[] { 31.6, 12.6, 25.1, 9.6, 1, 0, 0 };
allData[147] = new double[] { 32.6, 15.1, 26.1, 10.1, 1, 0, 0 };
allData[148] = new double[] { 31.1, 17.1, 27.1, 11.6, 1, 0, 0 };
allData[149] = new double[] { 29.6, 15.1, 25.6, 9.1, 1, 0, 0 };
Console.WriteLine("\nFirst 6 rows of entire 150-item data set:");
ShowMatrix(allData, 6, 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 training data:");
ShowMatrix(trainData, 5, 1, true);
Console.WriteLine("First 3 rows of test data:");
ShowMatrix(testData, 3, 1, true);
// Data really should be normalized here!
Console.WriteLine("\nCreating a 4-input, 7-hidden, 3-output neural network");
Console.WriteLine("Hard-coded tanh for input-to-hidden and softmax for hidden-to-output activations");
const int numInput = 4;
const int numHidden = 7;
const int numOutput = 3;
NeuralNetwork nn = new NeuralNetwork(numInput, numHidden, numOutput);
Console.WriteLine("\nInitializing weights and bias to small random values");
nn.InitializeWeights();
int maxEpochs = 4000;
double learnRate = 0.01;
double momentum = 0.001;
Console.WriteLine("Setting maxEpochs = 4000, learnRate = 0.01, momentum = 0.001");
Console.WriteLine("Training has hard-coded mean squared error < 0.020 stopping condition");
Console.WriteLine("\nBeginning training using incremental back-propagation\n");
nn.Train(trainData, maxEpochs, learnRate, momentum);
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 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
static void Normalize(double[][] dataMatrix, int[] cols)
{
// in most cases you want to normalize the x-data
}
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("");
}
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).PadRight(5) + " ");
}
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;
// back-prop specific arrays (these could be local to method UpdateWeights)
private double[] oGrads; // output gradients for back-propagation
private double[] hGrads; // hidden gradients for back-propagation
// back-prop momentum specific arrays (these could be local to method Train)
private double[][] ihPrevWeightsDelta; // for momentum with back-propagation
private double[] hPrevBiasesDelta;
private double[][] hoPrevWeightsDelta;
private double[] oPrevBiasesDelta;
public NeuralNetwork(int numInput, int numHidden, int numOutput)
{
rnd = new Random(0); // for InitializeWeights() and Shuffle()
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];
// back-prop related arrays below
this.hGrads = new double[numHidden];
this.oGrads = new double[numOutput];
this.ihPrevWeightsDelta = MakeMatrix(numInput, numHidden);
this.hPrevBiasesDelta = new double[numHidden];
this.hoPrevWeightsDelta = MakeMatrix(numHidden, numOutput);
this.oPrevBiasesDelta = new double[numOutput];
} // 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;
}
public override string ToString() // yikes
{
string s = "";
s += "===============================\n";
s += "numInput = " + numInput + " numHidden = " + numHidden + " numOutput = " + numOutput + "\n\n";
s += "inputs: \n";
for (int i = 0; i < inputs.Length; ++i)
s += inputs[i].ToString("F2") + " ";
s += "\n\n";
s += "ihWeights: \n";
for (int i = 0; i < ihWeights.Length; ++i)
{
for (int j = 0; j < ihWeights[i].Length; ++j)
{
s += ihWeights[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "hBiases: \n";
for (int i = 0; i < hBiases.Length; ++i)
s += hBiases[i].ToString("F4") + " ";
s += "\n\n";
s += "hOutputs: \n";
for (int i = 0; i < hOutputs.Length; ++i)
s += hOutputs[i].ToString("F4") + " ";
s += "\n\n";
s += "hoWeights: \n";
for (int i = 0; i < hoWeights.Length; ++i)
{
for (int j = 0; j < hoWeights[i].Length; ++j)
{
s += hoWeights[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "oBiases: \n";
for (int i = 0; i < oBiases.Length; ++i)
s += oBiases[i].ToString("F4") + " ";
s += "\n\n";
s += "hGrads: \n";
for (int i = 0; i < hGrads.Length; ++i)
s += hGrads[i].ToString("F4") + " ";
s += "\n\n";
s += "oGrads: \n";
for (int i = 0; i < oGrads.Length; ++i)
s += oGrads[i].ToString("F4") + " ";
s += "\n\n";
s += "ihPrevWeightsDelta: \n";
for (int i = 0; i < ihPrevWeightsDelta.Length; ++i)
{
for (int j = 0; j < ihPrevWeightsDelta[i].Length; ++j)
{
s += ihPrevWeightsDelta[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "hPrevBiasesDelta: \n";
for (int i = 0; i < hPrevBiasesDelta.Length; ++i)
s += hPrevBiasesDelta[i].ToString("F4") + " ";
s += "\n\n";
s += "hoPrevWeightsDelta: \n";
for (int i = 0; i < hoPrevWeightsDelta.Length; ++i)
{
for (int j = 0; j < hoPrevWeightsDelta[i].Length; ++j)
{
s += hoPrevWeightsDelta[i][j].ToString("F4") + " ";
}
s += "\n";
}
s += "\n";
s += "oPrevBiasesDelta: \n";
for (int i = 0; i < oPrevBiasesDelta.Length; ++i)
s += oPrevBiasesDelta[i].ToString("F4") + " ";
s += "\n\n";
s += "outputs: \n";
for (int i = 0; i < outputs.Length; ++i)
s += outputs[i].ToString("F2") + " ";
s += "\n\n";
s += "===============================\n";
return s;
}
// ----------------------------------------------------------------------------------------
public 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++];
}
public 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)
{
if (xValues.Length != numInput)
throw new Exception("Bad xValues array length");
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)
{
// does all output nodes at once so scale doesn't have to be re-computed each time
// 1. determine max output sum
double max = oSums[0];
for (int i = 0; i < oSums.Length; ++i)
if (oSums[i] > max) max = oSums[i];
// 2. 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 UpdateWeights(double[] tValues, double learnRate, double momentum)
{
// update the weights and biases using back-propagation, with target values, eta (learning rate),
// alpha (momentum)
// assumes that SetWeights and ComputeOutputs have been called and so all the internal arrays and
// matrices have values (other than 0.0)
if (tValues.Length != numOutput)
throw new Exception("target values not same Length as output in UpdateWeights");
// 1. compute output gradients
for (int i = 0; i < oGrads.Length; ++i)
{
// derivative of softmax = (1 - y) * y (same as log-sigmoid)
double derivative = (1 - outputs[i]) * outputs[i];
// 'mean squared error version'. research suggests cross-entropy is better here . . .
oGrads[i] = derivative * (tValues[i] - outputs[i]);
}
// 2. compute hidden gradients
for (int i = 0; i < hGrads.Length; ++i)
{
double derivative = (1 - hOutputs[i]) * (1 + hOutputs[i]); // derivative of tanh = (1 - y) * (1 + y)
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. update hidden weights (gradients must be computed right-to-left but weights
// can be updated in any order)
for (int i = 0; i < ihWeights.Length; ++i) // 0..2 (3)
{
for (int j = 0; j < ihWeights[0].Length; ++j) // 0..3 (4)
{
double delta = learnRate * hGrads[j] * inputs[i]; // compute the new delta
ihWeights[i][j] += delta; // update. note we use '+' instead of '-'. this can be very tricky.
// add momentum using previous delta. on first pass old value will be 0.0 but that's OK.
ihWeights[i][j] += momentum * ihPrevWeightsDelta[i][j];
// weight decay would go here
ihPrevWeightsDelta[i][j] = delta; // don't forget to save the delta for momentum
}
}
// 3b. update hidden biases
for (int i = 0; i < hBiases.Length; ++i)
{
// the 1.0 below is the constant input for any bias; could leave out
double delta = learnRate * hGrads[i] * 1.0;
hBiases[i] += delta;
hBiases[i] += momentum * hPrevBiasesDelta[i]; // momentum
// weight decay here
hPrevBiasesDelta[i] = delta; // don't forget to save the delta
}
// 4. update hidden-output weights
for (int i = 0; i < hoWeights.Length; ++i)
{
for (int j = 0; j < hoWeights[0].Length; ++j)
{
// see above: hOutputs are inputs to the nn outputs
double delta = learnRate * oGrads[j] * hOutputs[i];
hoWeights[i][j] += delta;
hoWeights[i][j] += momentum * hoPrevWeightsDelta[i][j]; // momentum
// weight decay here
hoPrevWeightsDelta[i][j] = delta; // save
}
}
// 4b. update output biases
for (int i = 0; i < oBiases.Length; ++i)
{
double delta = learnRate * oGrads[i] * 1.0;
oBiases[i] += delta;
oBiases[i] += momentum * oPrevBiasesDelta[i]; // momentum
// weight decay here
oPrevBiasesDelta[i] = delta; // save
}
} // UpdateWeights
// ----------------------------------------------------------------------------------------
public void Train(double[][] trainData, int maxEprochs, double learnRate, double momentum)
{
// train a back-prop style NN classifier using learning rate and momentum
// no weight decay
int epoch = 0;
double[] xValues = new double[numInput]; // inputs
double[] tValues = new double[numOutput]; // target values
int[] sequence = new int[trainData.Length];
for (int i = 0; i < sequence.Length; ++i)
sequence[i] = i;
while (epoch < maxEprochs)
{
double mse = MeanSquaredError(trainData);
if (mse < 0.020) break; // consider passing value in as parameter
//if (mse < 0.001) break; // consider passing value in as parameter
Shuffle(sequence); // visit each training data in random order
for (int i = 0; i < trainData.Length; ++i)
{
int idx = sequence[i];
Array.Copy(trainData[idx], xValues, numInput); // extract x's and y's.
Array.Copy(trainData[idx], numInput, tValues, 0, numOutput);
ComputeOutputs(xValues); // copy xValues in, compute outputs (and store them internally)
UpdateWeights(tValues, learnRate, momentum); // use back-prop to find better weights
} // each training tuple
++epoch;
}
} // Train
private static void Shuffle(int[] sequence)
{
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;
}
}
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
for (int i = 0; i < trainData.Length; ++i)
{
// walk thru each training case. looks like (6.9 3.2 5.7 2.3) (0 0 1)
// where the parens are not really there
Array.Copy(trainData[i], xValues, numInput); // get xValues.
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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