public void CalculateGraphTest()
{
var testData = MatlabReader.ReadAll <double>("data.mat")["Data"];
var testResult = MatlabReader.ReadAll <double>("testResult.mat")["SecPathKJ"];
Algorithm algorithm = new Algorithm();
Vector <double> result = Vector <double> .Build.Dense(512, 0);
//for (int i = 0; i < testData.RowCount; i = i + 512)
//{
for (int j = 0; j < 1; j++)
{
//var chanData = testData.Column(j, i, 512);
//var outData = testData.Column(16, i, 512);
var chanData = testData.Column(j);
var outData = testData.Column(16);
result = algorithm.Nlms(outData, chanData, 512, 0.1);
}
//}
for (int i = 0; i < testResult.RowCount; i++)
{
if (Math.Abs(testResult[i, 0] - result[i]) > 1e-10)
{
Assert.Fail();
}
}
}
public void CanReadNamedMatrices()
{
var matrices = MatlabReader.ReadAll <double>("./data/Matlab/collection.mat", "Ad", "Au64");
Assert.AreEqual(2, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Double.DenseMatrix), matrix.Value.GetType());
}
}
public void CanReadFloatAllMatrices()
{
var matrices = MatlabReader.ReadAll <float>("./data/Matlab/collection.mat");
Assert.AreEqual(30, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Single.DenseMatrix), matrix.Value.GetType());
}
}
/// <summary>
/// Lee una matriz con una matriz de entrada de filas como numero de muestras y columnas como cararateristicas
/// </summary>
/// <param name="path">Ruta al archivo .mat</param>
/// <param name="InputKey"> nombre de la matriz de caracteristicas en matlab</param>
/// <param name="TargetKey">nombre de la matriz (n x 1) de targets en Matlab</param>
/// <returns>entrega una lista con los registros de eentradas y objetivo</returns>
public static List <NetEvaluation.InputAndTarget> ReadDataMatlabMatrix(string path, string InputKey, string TargetKey)
{
Dictionary <string, Matrix <float> > ms = MatlabReader.ReadAll <float>(path);
List <NetEvaluation.InputAndTarget> list = new List <NetEvaluation.InputAndTarget>();
for (int i = 0; i < ms.Values.First().RowCount; i++)
{
list.Add(new NetEvaluation.InputAndTarget(ms[InputKey].Row(i).ToArray(), ms[TargetKey].At(i, 0)));
}
return(list);
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
System.Console.WriteLine("Principal Component Analysis ex.7_pca");
System.Console.WriteLine("=====================================\n");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
//// ================== Part 1: Load Example Dataset ===================
// We start this exercise by using a small dataset that is easily to
// visualize
//
// read all matrices of a file by name into a dictionary
Dictionary <string, Matrix <double> > mr = MatlabReader.ReadAll <double>("data\\ex7data1.mat");
// loads dataset
System.Console.WriteLine("Loading dataset....\n");
Matrix <double> X = mr["X"];
System.Console.WriteLine(X);
//// =============== Part 2: Principal Component Analysis ===============
// You should now implement PCA, a dimension reduction technique. You
// should complete the code in pca.m
//
System.Console.WriteLine("\nRunning PCA on example dataset.\n\n");
// Before running PCA, it is important to first normalize X
System.Console.WriteLine("Features normalization...");
(Matrix <double> X_norm, Matrix <double> mu, Matrix <double> sigma)norm_res;
norm_res = FeatureNormalize(X);
System.Console.WriteLine(norm_res.X_norm);
// Run PCA
(Matrix <double> U, Vector <double> S)pca_res;
pca_res = pca(norm_res.X_norm);
System.Console.WriteLine("Top eigenvector: \n");
System.Console.WriteLine(" U(:,1) = {0:f6} {1:f6} \n", pca_res.U[0, 0], pca_res.U[1, 0]);
System.Console.WriteLine("\n(you should expect to see -0.707107 -0.707107)\n");
Pause();
}
public void CanReadFloatAllMatrices()
{
using (var stream = TestData.Data.ReadStream("Matlab.collection.mat"))
{
var matrices = MatlabReader.ReadAll <float>(stream);
Assert.AreEqual(30, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Single.DenseMatrix), matrix.Value.GetType());
}
}
}
public void CanWriteDoubleMatrices()
{
Matrix <double> mat1 = Matrix <double> .Build.Dense(5, 5);
for (var i = 0; i < mat1.ColumnCount; i++)
{
mat1[i, i] = i + .1;
}
Matrix <double> mat2 = Matrix <double> .Build.Dense(4, 5);
for (var i = 0; i < mat2.RowCount; i++)
{
mat2[i, i] = i + .1;
}
Matrix <double> mat3 = Matrix <double> .Build.Sparse(5, 4);
mat3[0, 0] = 1.1;
mat3[0, 2] = 2.2;
mat3[4, 3] = 3.3;
Matrix <double> mat4 = Matrix <double> .Build.Sparse(3, 5);
mat4[0, 0] = 1.1;
mat4[0, 2] = 2.2;
mat4[2, 4] = 3.3;
Matrix <double>[] write = { mat1, mat2, mat3, mat4 };
string[] names = { "mat1", "dense_matrix_2", "s1", "sparse2" };
if (File.Exists("testd.mat"))
{
File.Delete("testd.mat");
}
MatlabWriter.Write("testd.mat", write, names);
var read = MatlabReader.ReadAll <double>("testd.mat", names);
Assert.AreEqual(write.Length, read.Count);
for (var i = 0; i < write.Length; i++)
{
var w = write[i];
var r = read[names[i]];
Assert.AreEqual(w.RowCount, r.RowCount);
Assert.AreEqual(w.ColumnCount, r.ColumnCount);
Assert.IsTrue(w.Equals(r));
}
File.Delete("testd.mat");
}
public void CanReadNamedMatrices()
{
using (var stream = TestData.Data.ReadStream("Matlab.collection.mat"))
{
var matrices = MatlabReader.ReadAll <double>(stream, "Ad", "Au64");
Assert.AreEqual(2, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Double.DenseMatrix), matrix.Value.GetType());
}
}
}
public void CanWriteComplexMatrices()
{
var mat1 = Matrix <Complex> .Build.Dense(5, 3);
for (var i = 0; i < mat1.ColumnCount; i++)
{
mat1[i, i] = new Complex(i + .1, i + .1);
}
var mat2 = Matrix <Complex> .Build.Dense(4, 5);
for (var i = 0; i < mat2.RowCount; i++)
{
mat2[i, i] = new Complex(i + .1, i + .1);
}
var mat3 = Matrix <Complex> .Build.Sparse(5, 4);
mat3[0, 0] = new Complex(1.1, 1.1);
mat3[0, 2] = new Complex(2.2, 2.2);
mat3[4, 3] = new Complex(3.3, 3.3);
var mat4 = Matrix <Complex> .Build.Sparse(3, 5);
mat4[0, 0] = new Complex(1.1, 1.1);
mat4[0, 2] = new Complex(2.2, 2.2);
mat4[2, 4] = new Complex(3.3, 3.3);
Matrix <Complex>[] write = { mat1, mat2, mat3, mat4 };
string[] names = { "mat1", "dense_matrix_2", "s1", "sparse2" };
if (File.Exists("testz.mat"))
{
File.Delete("testz.mat");
}
MatlabWriter.Write("testz.mat", write, names);
var read = MatlabReader.ReadAll <Complex>("testz.mat", names);
Assert.AreEqual(write.Length, read.Count);
for (var i = 0; i < write.Length; i++)
{
var w = write[i];
var r = read[names[i]];
Assert.AreEqual(w.RowCount, r.RowCount);
Assert.AreEqual(w.ColumnCount, r.ColumnCount);
Assert.IsTrue(w.Equals(r));
}
File.Delete("testz.mat");
}
public void CanReadNamedMatrix()
{
var matrices = MatlabReader.ReadAll <double>("./data/Matlab/collection.mat", "Ad");
Assert.AreEqual(1, matrices.Count);
var ad = matrices["Ad"];
Assert.AreEqual(100, ad.RowCount);
Assert.AreEqual(100, ad.ColumnCount);
AssertHelpers.AlmostEqual(100.431635988639, ad.FrobeniusNorm(), 5);
Assert.AreEqual(typeof(LinearAlgebra.Double.DenseMatrix), ad.GetType());
}
public void CanReadFloatNamedMatrix()
{
using (var stream = TestData.Data.ReadStream("Matlab.collection.mat"))
{
var matrices = MatlabReader.ReadAll <float>(stream, "Ad");
Assert.AreEqual(1, matrices.Count);
var ad = matrices["Ad"];
Assert.AreEqual(100, ad.RowCount);
Assert.AreEqual(100, ad.ColumnCount);
AssertHelpers.AlmostEqual(100.431635988639f, ad.FrobeniusNorm(), 6);
Assert.AreEqual(typeof(LinearAlgebra.Single.DenseMatrix), ad.GetType());
}
}
public void CanReadComplex32AllMatrices()
{
var matrices = MatlabReader.ReadAll <Complex32>("./data/Matlab/complex.mat");
Assert.AreEqual(3, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Complex32.DenseMatrix), matrix.Value.GetType());
}
var a = matrices["a"];
Assert.AreEqual(100, a.RowCount);
Assert.AreEqual(100, a.ColumnCount);
AssertHelpers.AlmostEqual(27.232498979698409, a.L2Norm(), 5);
}
public void CanReadSparseComplex32AllMatrices()
{
var matrices = MatlabReader.ReadAll <Complex32>("./data/Matlab/sparse_complex.mat");
Assert.AreEqual(3, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Complex32.SparseMatrix), matrix.Value.GetType());
}
var a = matrices["sa"];
Assert.AreEqual(100, a.RowCount);
Assert.AreEqual(100, a.ColumnCount);
AssertHelpers.AlmostEqual(13.223654390985379, a.L2Norm(), 5);
}
public void CanReadSparseComplexAllMatrices()
{
using (var stream = TestData.Data.ReadStream("Matlab.sparse_complex.mat"))
{
var matrices = MatlabReader.ReadAll <Complex>(stream);
Assert.AreEqual(3, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Complex.SparseMatrix), matrix.Value.GetType());
}
var a = matrices["sa"];
Assert.AreEqual(100, a.RowCount);
Assert.AreEqual(100, a.ColumnCount);
AssertHelpers.AlmostEqual(13.223654390985379, a.L2Norm(), 13);
}
}
public void CanReadComplexAllMatrices()
{
using (var stream = TestData.Data.ReadStream("Matlab.complex.mat"))
{
var matrices = MatlabReader.ReadAll <Complex>(stream);
Assert.AreEqual(3, matrices.Count);
foreach (var matrix in matrices)
{
Assert.AreEqual(typeof(LinearAlgebra.Complex.DenseMatrix), matrix.Value.GetType());
}
var a = matrices["a"];
Assert.AreEqual(100, a.RowCount);
Assert.AreEqual(100, a.ColumnCount);
AssertHelpers.AlmostEqual(27.232498979698409, a.L2Norm(), 13);
}
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
//// =============== Part 1: Loading and Visualizing Data ================
// We start the exercise by first loading and visualizing the dataset.
// The following code will load the dataset into your environment and plot
// the data.
//
System.Console.WriteLine("Loading and Visualizing Data ...\n");
// Load from ex6data1:
// You will have X, y in your environment
Dictionary <string, Matrix <double> > ms = MatlabReader.ReadAll <double>("data\\ex6data1.mat");
Matrix <double> X = ms["X"]; // 51 X 2
Vector <double> y = ms["y"].Column(0); // 51 X 1
// Plot training data
GnuPlot.HoldOn();
PlotData(X, y);
Pause();
//// ==================== Part 2: Training Linear SVM ====================
// The following code will train a linear SVM on the dataset and plot the
// decision boundary learned.
//
System.Console.WriteLine("\nTraining Linear SVM ...\n");
// You should try to change the C value below and see how the decision
// boundary varies (e.g., try C = 1000)
double C = 1.0;
var linearKernel = KernelHelper.LinearKernel();
List <List <double> > libSvmData = ConvertToLibSvmFormat(X, y);
svm_problem prob = ProblemHelper.ReadProblem(libSvmData);
var svc = new C_SVC(prob, linearKernel, C);
PlotBoundary(X, svc);
GnuPlot.HoldOff();
System.Console.WriteLine();
Pause();
//// =============== Part 3: Implementing Gaussian Kernel ===============
// You will now implement the Gaussian kernel to use
// with the SVM. You should complete the code in gaussianKernel.m
//
System.Console.WriteLine("\nEvaluating the Gaussian Kernel ...\n");
double sigma = 2.0;
double sim = GaussianKernel(
V.DenseOfArray(new [] { 1.0, 2, 1 }),
V.DenseOfArray(new [] { 0.0, 4, -1 }),
sigma
);
System.Console.WriteLine("Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = {0:f6} :\n\t{1:f6}\n(for sigma = 2, this value should be about 0.324652)\n", sigma, sim);
Pause();
//// =============== Part 4: Visualizing Dataset 2 ================
// The following code will load the next dataset into your environment and
// plot the data.
//
System.Console.WriteLine("Loading and Visualizing Data ...\n");
// Load from ex6data2:
// You will have X, y in your environment
ms = MatlabReader.ReadAll <double>("data\\ex6data2.mat");
X = ms["X"]; // 863 X 2
y = ms["y"].Column(0); // 863 X 1
// Plot training data
GnuPlot.HoldOn();
PlotData(X, y);
Pause();
//// ========== Part 5: Training SVM with RBF Kernel (Dataset 2) ==========
// After you have implemented the kernel, we can now use it to train the
// SVM classifier.
//
System.Console.WriteLine("\nTraining SVM with RBF Kernel (this may take 1 to 2 minutes) ...\n");
// SVM Parameters
C = 1;
sigma = 0.1;
double gamma = 1 / (2 * sigma * sigma);
var rbfKernel = KernelHelper.RadialBasisFunctionKernel(gamma);
libSvmData = ConvertToLibSvmFormat(X, y);
prob = ProblemHelper.ReadProblem(libSvmData);
svc = new C_SVC(prob, rbfKernel, C);
PlotBoundary(X, svc);
GnuPlot.HoldOff();
Pause();
double acc = svc.GetCrossValidationAccuracy(10);
System.Console.WriteLine("\nCross Validation Accuracy: {0:f6}\n", acc);
Pause();
//// =============== Part 6: Visualizing Dataset 3 ================
// The following code will load the next dataset into your environment and
// plot the data.
//
System.Console.WriteLine("Loading and Visualizing Data ...\n");
// Load from ex6data2:
// You will have X, y in your environment
ms = MatlabReader.ReadAll <double>("data\\ex6data3.mat");
Matrix <double> Xval;
Vector <double> yval;
X = ms["X"]; // 211 X 2
y = ms["y"].Column(0); // 211 X 1
Xval = ms["Xval"]; // 200 X 2
yval = ms["yval"].Column(0); // 200 X 1
// Plot training data
GnuPlot.HoldOn();
PlotData(X, y);
//// ========== Part 7: Training SVM with RBF Kernel (Dataset 3) ==========
// This is a different dataset that you can use to experiment with. Try
// different values of C and sigma here.
//
(C, sigma) = Dataset3Params(X, y, Xval, yval);
gamma = 1 / (2 * sigma * sigma);
rbfKernel = KernelHelper.RadialBasisFunctionKernel(gamma);
libSvmData = ConvertToLibSvmFormat(X, y);
prob = ProblemHelper.ReadProblem(libSvmData);
svc = new C_SVC(prob, rbfKernel, C);
PlotBoundary(X, svc);
GnuPlot.HoldOff();
Pause();
}
public void KalmanFilteringTest()
{
var vectorBuilder = Vector <double> .Build;
var matrixBuild = Matrix <double> .Build;
var resultPositon = vectorBuilder.Dense(6, 0);
resultPositon[0] = -0.11712893894299961;
resultPositon[1] = -0.0085413873210193024;
resultPositon[2] = -0.00034048259997198428;
resultPositon[3] = 0.47421163145835582;
resultPositon[4] = -0.00690331375794314;
resultPositon[5] = -0.00027109000134432605;
double[,] prevariance =
{
{
0.242766594755489, 0.0523105449659795, 0.00101097341848172, 7.62628147622445e-09,
1.83912407997933e-06, 0.000104585919975806
},
{
0.0523105449659795, 7.99334660284189, 0.220587578642543, 1.83912407997933e-06, 0.000460038020961047,
0.0287783990337413
},
{
0.00101097341848172, 0.220587578642543, 10.3999959410456, 0.000104585919975806, 0.0287783990337413,
2.39999917381918
},
{
7.62628147622445e-09, 1.83912407997933e-06, 0.000104585919975806, 0.242766594755489,
0.0523105449659795, 0.00101097341848172
},
{
1.83912407997933e-06, 0.000460038020961047, 0.0287783990337413, 0.0523105449659795,
7.99334660284189, 0.220587578642543
},
{
0.000104585919975806, 0.0287783990337413, 2.39999917381918, 0.00101097341848172, 0.220587578642543,
10.3999959410456
}
};
var varianceTemp = matrixBuild.DenseOfArray(prevariance);
var m1 = MatlabReader.ReadAll <double>("testData.mat");
KalmanFiltering kalmanFiltering = new KalmanFiltering();
foreach (Matrix <double> testData in m1.Values)
{
var result = kalmanFiltering.TraceTableEstablishment(testData);
kalmanFiltering.PrePosition[0] = -0.0950698731643758;
kalmanFiltering.PrePosition[1] = 0.00483652853477623;
kalmanFiltering.PrePosition[2] = 9.61518040733592e-05;
kalmanFiltering.PrePosition[3] = 0.487928863356650;
kalmanFiltering.PrePosition[4] = 0.00140521891949567;
kalmanFiltering.PrePosition[5] = 3.61578884580855e-05;
kalmanFiltering.PreVarience = varianceTemp;
kalmanFiltering.Tracking(result);
Assert.AreEqual(resultPositon, kalmanFiltering.CurrentPosition);
}
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
System.Console.WriteLine("Multi-class Classification and Neural Networks ex.3");
System.Console.WriteLine("================================================\n");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
// read all matrices of a file by name into a dictionary
Dictionary <string, Matrix <double> > ms = MatlabReader.ReadAll <double>("data\\ex3data1.mat");
Matrix <double> X = ms["X"];
Vector <double> y = ms["y"].Column(0);
// get a casual sequence of 100 int numbers
var srs = new MathNet.Numerics.Random.SystemRandomSource();
var seq = srs.NextInt32Sequence(0, 5000).Take(100).ToList();
// Randomly select 100 data points to display
Vector <double>[] sel = new Vector <double> [100];
int idx = 0;
Vector <double> v = V.Dense(400);
foreach (int i in seq)
{
sel[idx++] = X.Row(i);
}
// display
DisplayData(sel);
Pause();
//// ============ Part 2a: Vectorize Logistic Regression ============
// In this part of the exercise, you will reuse your logistic regression
// code from the last exercise. You task here is to make sure that your
// regularized logistic regression implementation is vectorized. After
// that, you will implement one-vs-all classification for the handwritten
// digit dataset.
//
// Test case for lrCostFunction
System.Console.WriteLine("\nTesting Cost Function with regularization");
Vector <double> theta_t = V.DenseOfArray(new[] { -2.0, -1, 1, 2 });
Matrix <double> X_t = M.DenseOfArray(new [, ] {
{ 1.0, 0.1, 0.6, 1.1 },
{ 1.0, 0.2, 0.7, 1.2 },
{ 1.0, 0.3, 0.8, 1.3 },
{ 1.0, 0.4, 0.9, 1.4 },
{ 1.0, 0.5, 1.0, 1.5 },
});
Vector <Double> y_t = V.DenseOfArray(new [] { 1.0, 0, 1, 0, 1 });
int lambda_t = 3;
LogisticRegression lr = new LogisticRegression(X_t, y_t);
lr.Lambda = lambda_t;
double J = lr.Cost(theta_t);
Vector <double> grad = lr.Gradient(theta_t);
System.Console.WriteLine("\nCost: {0:f5}\n", J);
System.Console.WriteLine("Expected cost: 2.534819\n");
System.Console.WriteLine("Gradients:\n");
System.Console.WriteLine(" {0:f5} \n", grad);
System.Console.WriteLine("Expected gradients:\n");
System.Console.WriteLine(" 0.146561\n -0.548558\n 0.724722\n 1.398003\n");
Pause();
//// ============ Part 2b: One-vs-All Training ============
System.Console.WriteLine("\nTraining One-vs-All Logistic Regression...\n");
double lambda = 0.1;
int num_labels = 10;
Matrix <double> all_theta = OneVsAll(X, y, num_labels, lambda);
Pause();
// ================ Part 3: Predict for One-Vs-All ================
Vector <double> pred = PredictOneVsAll(all_theta, X);
Vector <double> comp = V.Dense(y.Count);
for (int i = 0; i < y.Count; i++)
{
if (pred[i] == y[i])
{
comp[i] = 1;
}
else
{
comp[i] = 0;
}
}
double accuracy = comp.Mean() * 100;
System.Console.WriteLine("\nTraining Set Accuracy: {0:f5}\n", accuracy);
Pause();
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
System.Console.WriteLine("Regularized Linear Regression and Bias v.s. Variance ex.5");
System.Console.WriteLine("=========================================================\n");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
// =========== Part 1: Loading and Visualizing Data =============
// We start the exercise by first loading and visualizing the dataset.
// The following code will load the dataset into your environment and plot
// the data.
// Load Training Data
System.Console.WriteLine("Loading and Visualizing Data ...\n");
// Load from ex5data1:
// You will have X, y, Xval, yval, Xtest, ytest in your environment
Dictionary <string, Matrix <double> > ms = MatlabReader.ReadAll <double>("data\\ex5data1.mat");
Matrix <double> X = ms["X"];
Vector <double> y = ms["y"].Column(0);
Matrix <double> Xval = ms["Xval"];
Vector <double> yval = ms["yval"].Column(0);
Matrix <double> Xtest = ms["Xtest"];
Vector <double> ytest = ms["ytest"].Column(0);
// m = Number of examples
int m = X.RowCount;
GnuPlot.HoldOn();
PlotData(X.Column(0).ToArray(), y.ToArray());
Pause();
// =========== Part 2: Regularized Linear Regression Cost =============
// You should now implement the cost function for regularized linear
// regression.
Vector <double> theta = V.Dense(2, 1.0);
LinearRegression lr = new LinearRegression(X.InsertColumn(0, V.Dense(m, 1)), y, 1);
double J = lr.Cost(theta);
Vector <double> grad = lr.Gradient(theta);
System.Console.WriteLine("Cost at theta = [1 ; 1]: {0:f6} \n(this value should be about 303.993192)\n", J);
Pause();
// =========== Part 3: Regularized Linear Regression Gradient =============
// You should now implement the gradient for regularized linear
// regression.
System.Console.WriteLine("Gradient at theta = [1 ; 1]: [{0:f6}; {1:f6}] \n(this value should be about [-15.303016; 598.250744])\n", grad[0], grad[1]);
Pause();
// =========== Part 4: Train Linear Regression =============
// Once you have implemented the cost and gradient correctly, the
// trainLinearReg function will use your cost function to train
// regularized linear regression.
//
// Write Up Note: The data is non-linear, so this will not give a great
// fit.
//
// Train linear regression with lambda = 0
lr = new LinearRegression(X.InsertColumn(0, V.Dense(m, 1)), y, 0);
var result = lr.Train();
Vector <double> h = X.InsertColumn(0, V.Dense(m, 1)) * result.MinimizingPoint; // hypothesys
PlotLinearFit(X.Column(0).ToArray(), h.ToArray());
GnuPlot.HoldOff();
Pause();
// =========== Part 5: Learning Curve for Linear Regression =============
// Next, you should implement the learningCurve function.
//
// Write Up Note: Since the model is underfitting the data, we expect to
// see a graph with "high bias" -- Figure 3 in ex5.pdf
//
(Vector <double> error_train, Vector <double> error_val)res;
res = LearningCurve(X.InsertColumn(0, V.Dense(m, 1)), y, Xval.InsertColumn(0, V.Dense(Xval.RowCount, 1)), yval, 0);
PlotLinearLearningCurve(
Generate.LinearRange(1, 1, m),
res.error_train.ToArray(),
res.error_val.ToArray()
);
System.Console.WriteLine("# Training Examples\tTrain Error\tCross Validation Error\n");
for (int i = 0; i < m; i++)
{
System.Console.WriteLine("\t{0,2}\t\t{1:f6}\t{2:f6}", i, res.error_train[i], res.error_val[i]);
}
System.Console.WriteLine();
Pause();
// =========== Part 6: Feature Mapping for Polynomial Regression =============
// One solution to this is to use polynomial regression. You should now
// complete polyFeatures to map each example into its powers
//
int p = 8;
// Map X onto Polynomial Features and Normalize
Matrix <double> X_poly = MapPolyFeatures(X, p);
// normalize
var norm = FeatureNormalize(X_poly);
X_poly = norm.X_norm;
// add one's
X_poly = X_poly.InsertColumn(0, V.Dense(X_poly.RowCount, 1));
// Map X_poly_test and normalize (using mu and sigma)
Matrix <double> X_poly_test = MapPolyFeatures(Xtest, p);
for (int i = 0; i < X_poly_test.ColumnCount; i++)
{
Vector <double> v = X_poly_test.Column(i);
v = v - norm.mu[0, i];
v = v / norm.sigma[0, i];
X_poly_test.SetColumn(i, v);
}
// add one's
X_poly_test = X_poly_test.InsertColumn(0, V.Dense(X_poly_test.RowCount, 1));
// Map X_poly_val and normalize (using mu and sigma)
Matrix <double> X_poly_val = MapPolyFeatures(Xval, p);
for (int i = 0; i < X_poly_val.ColumnCount; i++)
{
Vector <double> v = X_poly_val.Column(i);
v = v - norm.mu[0, i];
v = v / norm.sigma[0, i];
X_poly_val.SetColumn(i, v);
}
// add one's
X_poly_val = X_poly_val.InsertColumn(0, V.Dense(X_poly_val.RowCount, 1));
System.Console.WriteLine("Normalized Training Example 1:\n");
System.Console.WriteLine(X_poly.Row(0));
Pause();
// =========== Part 7: Learning Curve for Polynomial Regression =============
// Now, you will get to experiment with polynomial regression with multiple
// values of lambda. The code below runs polynomial regression with
// lambda = 0. You should try running the code with different values of
// lambda to see how the fit and learning curve change.
//
double lambda = 0;
lr = new LinearRegression(X_poly, y, lambda);
var minRes = lr.Train();
GnuPlot.HoldOn();
GnuPlot.Set("terminal wxt 1");
PlotData(X.Column(0).ToArray(), y.ToArray());
PlotFit(X.Column(0).Minimum(), X.Column(0).Maximum(), norm.mu.Row(0), norm.sigma.Row(0), minRes.MinimizingPoint, p, lambda);
GnuPlot.HoldOff();
// learning curve
GnuPlot.Set("terminal wxt 2");
res = LearningCurve(X_poly, y, X_poly_val, yval, lambda);
PlotLinearLearningCurve(
Generate.LinearRange(1, 1, m),
res.error_train.ToArray(),
res.error_val.ToArray()
);
System.Console.WriteLine("# Training Examples\tTrain Error\tCross Validation Error\n");
for (int i = 0; i < m; i++)
{
System.Console.WriteLine("\t{0,2}\t\t{1:f6}\t{2:f6}", i, res.error_train[i], res.error_val[i]);
}
System.Console.WriteLine();
Pause();
// =========== Part 8: Validation for Selecting Lambda =============
// You will now implement validationCurve to test various values of
// lambda on a validation set. You will then use this to select the
// "best" lambda value.
//
var resVal = ValidationCurve(X_poly, y, X_poly_val, yval);
PlotValidationCurve(resVal.Lamda_vec.ToArray(), resVal.error_train.ToArray(), resVal.error_val.ToArray());
System.Console.WriteLine("# Lambda\tTrain Error\tCross Validation Error\n");
for (int i = 0; i < resVal.error_train.Count; i++)
{
System.Console.WriteLine("\t{0:f4}\t\t{1:f6}\t{2:f6}", resVal.Lamda_vec[i], resVal.error_train[i], resVal.error_val[i]);
}
System.Console.WriteLine();
Pause();
// =========== Part 9: Compute test set error =============
// Compute the test error using the best value of λ you
// found
lambda = 3.0;
lr = new LinearRegression(X_poly, y, lambda);
minRes = lr.Train();
theta = minRes.MinimizingPoint;
h = X_poly_test * theta;
m = X_poly.RowCount;
System.Console.WriteLine("Evaluating test-set:\n");
System.Console.WriteLine("# \tHypothesis\tExpected\tError\n");
for (int i = 0; i < m; i++)
{
System.Console.WriteLine("{0,3}\t{1:f6}\t{2:f6}\t{3:f6}", i + 1, h[i], ytest[i], h[i] - ytest[i]);
}
double mae = (h - ytest).L1Norm(); // Mean Absolute Error
double mse = (h - ytest).L2Norm(); // Mean Squared Error
double rmse = Math.Sqrt(mse); // Root Mean Squared Error
System.Console.WriteLine("\nMAE on test set: {0:F6}", mae);
System.Console.WriteLine("MSE on test set: {0:F6}", mse);
System.Console.WriteLine("RMSE on test set: {0:F6}\n", rmse);
Pause();
GnuPlot.HoldOn();
GnuPlot.Set("terminal wxt 3");
PlotData(Xtest.Column(0).ToArray(), ytest.ToArray());
PlotFit(Xtest.Column(0).Minimum(), Xtest.Column(0).Maximum(), norm.mu.Row(0), norm.sigma.Row(0), theta, p, lambda);
GnuPlot.HoldOff();
Pause();
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
System.Console.WriteLine("Multi-class Classification and Neural Networks ex.4");
System.Console.WriteLine("===================================================\n");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
// Setup the parameters you will use for this exercise
int input_layer_size = 400; // 20x20 Input Images of Digits
int hidden_layer_size = 25; // 25 hidden units
int num_labels = 10; // 10 labels, from 1 to 10
// (note that we have mapped "0" to label 10)
// =========== Part 1: Loading and Visualizing Data =============
// We start the exercise by first loading and visualizing the dataset.
// You will be working with a dataset that contains handwritten digits.
//
// read all matrices of a file by name into a dictionary
Dictionary <string, Matrix <double> > ms = MatlabReader.ReadAll <double>("data\\ex3data1.mat");
Matrix <double> X = ms["X"];
Vector <double> y = ms["y"].Column(0);
// get a casual sequence of 100 int numbers
var srs = new MathNet.Numerics.Random.SystemRandomSource();
var seq = srs.NextInt32Sequence(0, 5000).Take(100).ToList();
// Randomly select 100 data points to display
Vector <double>[] sel = new Vector <double> [100];
int idx = 0;
Vector <double> v = V.Dense(400);
foreach (int i in seq)
{
sel[idx++] = X.Row(i);
}
// display
DisplayData(sel);
Pause();
// ================ Part 2: Loading Parameters ================
// In this part of the exercise, we load some pre-initialized
// neural network parameters.
System.Console.WriteLine("\nLoading Saved Neural Network Parameters ...\n");
// read all matrices of a file by name into a dictionary
Dictionary <string, Matrix <double> > mr = MatlabReader.ReadAll <double>("data\\ex3weights.mat");
Matrix <double> theta1 = mr["Theta1"]; // 25 X 401
Matrix <double> theta2 = mr["Theta2"]; // 10 X 26
// Unroll parameters
Vector <double> nn_params = NeuralNetwork.UnrollParameters(theta1, theta2);
Pause();
// ================ Part 3: Compute Cost (Feedforward) ================
// To the neural network, you should first start by implementing the
// feedforward part of the neural network that returns the cost only. You
// should complete the code in nnCostFunction.m to return cost. After
// implementing the feedforward to compute the cost, you can verify that
// your implementation is correct by verifying that you get the same cost
// as us for the fixed debugging parameters.
//
// We suggest implementing the feedforward cost *without* regularization
// first so that it will be easier for you to debug. Later, in part 4, you
// will get to implement the regularized cost.
System.Console.WriteLine("\nFeedforward Using Neural Network ...\n");
// Weight regularization parameter (we set this to 0 here).
NeuralNetwork nn = new NeuralNetwork(X, y, input_layer_size, hidden_layer_size, num_labels);
nn.Lambda = 0.0;
double J = nn.Cost(nn_params);
System.Console.WriteLine("Cost at parameters (loaded from ex4weights): {0:f6}\n(this value should be about 0.287629)\n", J);
Pause();
// =============== Part 4: Implement Regularization ===============
// Once your cost function implementation is correct, you should now
// continue to implement the regularization with the cost.
//
System.Console.WriteLine("\nChecking Cost Function (w/ Regularization) ... \n");
// Weight regularization parameter (we set this to 1 here).
nn.Lambda = 1.0;
J = nn.Cost(nn_params);
System.Console.WriteLine("Cost at parameters (loaded from ex4weights): {0:f6} \n(this value should be about 0.383770)\n", J);
Pause();
// ================ Part 5: Sigmoid Gradient ================
// Before you start implementing the neural network, you will first
// implement the gradient for the sigmoid function. You should complete the
// code in the sigmoidGradient.m file.
System.Console.WriteLine("\nEvaluating sigmoid gradient...\n");
var g = nn.SigmoidGradient(V.DenseOfArray(new[] { -1.0, -0.5, 0, 0.5, 1 }));
System.Console.WriteLine("Sigmoid gradient evaluated at [-1 -0.5 0 0.5 1]:\n ");
System.Console.WriteLine("{0:f5} ", g);
System.Console.WriteLine("\n\n");
Pause();
// ================ Part 6: Initializing Pameters ================
// In this part of the exercise, you will be starting to implment a two
// layer neural network that classifies digits. You will start by
// implementing a function to initialize the weights of the neural network
// (randInitializeWeights.m)
System.Console.WriteLine("\nInitializing Neural Network Parameters ...\n");
Matrix <double> initial_Theta1 = RandInitializeWeights(input_layer_size + 1, hidden_layer_size);
Matrix <double> initial_Theta2 = RandInitializeWeights(hidden_layer_size + 1, num_labels);
// Unroll parameters
Vector <double> initial_nn_params = NeuralNetwork.UnrollParameters(initial_Theta1, initial_Theta2);
Pause();
// =============== Part 7: Implement Backpropagation ===============
// Once your cost matches up with ours, you should proceed to implement the
// backpropagation algorithm for the neural network. You should add to the
// code you've written in nnCostFunction.m to return the partial
// derivatives of the parameters.
System.Console.WriteLine("\nChecking Backpropagation... \n");
CheckGradient(0);
Pause();
// =============== Part 8: Implement Regularization ===============
// Once your backpropagation implementation is correct, you should now
// continue to implement the regularization with the cost and gradient.
System.Console.WriteLine("\nChecking Backpropagation (w/ Regularization) ... \n");
// Check gradients by running checkNNGradients
double lambda = 3;
CheckGradient(lambda);
// Also output the costFunction debugging values
nn.Lambda = lambda;
double debug_J = nn.Cost(nn_params);
System.Console.WriteLine("\n\nCost at (fixed) debugging parameters (w/ lambda = {0:f1}): {1:f6} " +
"\n(for lambda = 3, this value should be about 0.576051)\n\n", lambda, debug_J);
Pause();
// =================== Part 8: Training NN ===================
// You have now implemented all the code necessary to train a neural
// network. To train your neural network, we will now use "fmincg", which
// is a function which works similarly to "fminunc". Recall that these
// advanced optimizers are able to train our cost functions efficiently as
// long as we provide them with the gradient computations.
System.Console.WriteLine("\nTraining Neural Network... \n");
// After you have completed the assignment, change the MaxIter to a larger
// value to see how more training helps.
int maxIter = 40;
// You should also try different values of lambda
lambda = 1;
nn.Lambda = lambda;
var obj = ObjectiveFunction.Gradient(nn.Cost, nn.Gradient);
var solver = new LimitedMemoryBfgsMinimizer(1e-5, 1e-5, 1e-5, 5, maxIter);
var result = solver.FindMinimum(obj, initial_nn_params);
System.Console.WriteLine("Reason For Exit: {0}", result.ReasonForExit);
System.Console.WriteLine("Iterations: {0}", result.Iterations);
System.Console.WriteLine("Cost: {0:e}", result.FunctionInfoAtMinimum.Value);
Pause();
// ================= Part 10: Implement Predict =================
// After training the neural network, we would like to use it to predict
// the labels. You will now implement the "predict" function to use the
// neural network to predict the labels of the training set. This lets
// you compute the training set accuracy.
Vector <double> pred = nn.Predict(result.MinimizingPoint, X);
Vector <double> comp = V.Dense(y.Count);
for (int i = 0; i < y.Count; i++)
{
if (pred[i] == y[i])
{
comp[i] = 1;
}
else
{
comp[i] = 0;
}
}
double accuracy = comp.Mean() * 100;
System.Console.WriteLine("\nTraining Set Accuracy: {0:f5}\n", accuracy);
Pause();
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
System.Console.WriteLine("Neural Networks ex.3_nn");
System.Console.WriteLine("==================================================\n");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
//// =========== Part 1: Loading and Visualizing Data =============
// We start the exercise by first loading and visualizing the dataset.
// You will be working with a dataset that contains handwritten digits.
//
// Load Training Data
System.Console.WriteLine("Loading and Visualizing Data ...\n");
// read all matrices of a file by name into a dictionary
Dictionary <string, Matrix <double> > mr = MatlabReader.ReadAll <double>("data\\ex3data1.mat");
Matrix <double> X = mr["X"];
Vector <double> y = mr["y"].Column(0);
Double m = X.RowCount;
// get a casual sequence of 100 int numbers
var srs = new MathNet.Numerics.Random.SystemRandomSource();
var seq = srs.NextInt32Sequence(0, 5000).Take(100).ToList();
// Randomly select 100 data points to display
Vector <double>[] sel = new Vector <double> [100];
int idx = 0;
Vector <double> v = V.Dense(400);
foreach (int i in seq)
{
sel[idx++] = X.Row(i);
}
// display
DisplayData(sel);
Pause();
// ================ Part 2: Loading Pameters ================
// In this part of the exercise, we load some pre-initialized
// neural network parameters.
System.Console.WriteLine("\nLoading Saved Neural Network Parameters ...\n");
// read all matrices of a file by name into a dictionary
mr = MatlabReader.ReadAll <double>("data\\ex3weights.mat");
Matrix <double> theta1 = mr["Theta1"]; // 25 X 401
Matrix <double> theta2 = mr["Theta2"]; // 10 X 26
Pause();
//// ================= Part 3: Implement Predict =================
// After training the neural network, we would like to use it to predict
// the labels. You will now implement the "predict" function to use the
// neural network to predict the labels of the training set. This lets
// you compute the training set accuracy.
Vector <double> pred = Predict(theta1, theta2, X);
Vector <double> comp = V.Dense(y.Count);
for (int i = 0; i < y.Count; i++)
{
if (pred[i] == y[i])
{
comp[i] = 1;
}
else
{
comp[i] = 0;
}
}
double accuracy = comp.Mean() * 100;
System.Console.WriteLine("\nTraining Set Accuracy: {0:f5}\n", accuracy);
// Randomly permute examples
seq = srs.NextInt32Sequence(0, 5000).Take(5000).ToList();
for (int i = 0; i < m; i++)
{
// display
DisplayData(new[] { X.Row(seq[i]) });
Matrix <double> x = M.DenseOfRowVectors(new[] { X.Row(seq[i]) });
pred = Predict(theta1, theta2, x);
double p = pred[0];
System.Console.WriteLine("\nNeural Network Prediction: {0:N0} (digit {1:N0})\n", p, p % 10);
// Pause with quit option
System.Console.WriteLine("Paused - press enter to continue, q to exit:");
string s = Console.ReadLine();
if (s.ToLower() == "q")
{
break;
}
}
Pause();
}
static void Main(string[] args)
{
if (!System.Console.IsOutputRedirected)
{
System.Console.Clear();
}
CultureInfo.CurrentCulture = CultureInfo.CreateSpecificCulture("en-US");
var M = Matrix <double> .Build;
var V = Vector <double> .Build;
//// ================= Part 1: Find Closest Centroids ====================
// To help you implement K-Means, we have divided the learning algorithm
// into two functions -- findClosestCentroids and computeCentroids. In this
// part, you should complete the code in the findClosestCentroids function.
//
System.Console.WriteLine("Finding closest centroids.\n\n");
// Load an example dataset that we will be using
Dictionary <string, Matrix <double> > ms = MatlabReader.ReadAll <double>("data\\ex7data2.mat");
Matrix <double> X = ms["X"]; // 300 X 2
System.Console.WriteLine(X);
// Select an initial set of centroids
int K = 3; // 3 Centroids
Matrix <double> initial_centroids = M.DenseOfArray(new [, ] {
{ 3.0, 3.0 },
{ 6.0, 2.0 },
{ 8.0, 5.0 }
});
System.Console.Write("Initial centroids: ");
System.Console.WriteLine(initial_centroids);
Vector <double> idx = FindClosestCentroids(X, initial_centroids);
System.Console.WriteLine("Closest centroids for the first 3 examples: \n");
System.Console.WriteLine(idx.SubVector(0, 3));
System.Console.WriteLine("\n(the closest centroids should be 0, 2, 1 respectively)\n");
Pause();
//// ===================== Part 2: Compute Means =========================
// After implementing the closest centroids function, you should now
// complete the computeCentroids function.
//
System.Console.WriteLine("\nComputing centroids means.\n\n");
// Compute means based on the closest centroids found in the previous part.
Matrix <double> centroids;
centroids = ComputeCentroids(X, idx, K);
System.Console.WriteLine("Centroids computed after initial finding of closest centroids: \n");
System.Console.WriteLine(centroids);
System.Console.WriteLine("\nthe centroids should be");
System.Console.WriteLine(" [ 2.428301 3.157924 ]");
System.Console.WriteLine(" [ 5.813503 2.633656 ]");
System.Console.WriteLine(" [ 7.119387 3.616684 ]\n");
Pause();
//// =================== Part 3: K-Means Clustering ======================
// After you have completed the two functions computeCentroids and
// findClosestCentroids, you have all the necessary pieces to run the
// kMeans algorithm. In this part, you will run the K-Means algorithm on
// the example dataset we have provided.
//
System.Console.WriteLine("\nRunning K-Means clustering on example dataset.\n\n");
// Settings for running K-Means
K = 3;
int max_iters = 10;
// For consistency, here we set centroids to specific values
// but in practice you want to generate them automatically, such as by
// settings them to be random examples (as can be seen in
// kMeansInitCentroids).
initial_centroids = M.DenseOfArray(new [, ] {
{ 3.0, 3.0 },
{ 6.0, 2.0 },
{ 8.0, 5.0 }
});
// Run K-Means algorithm. The 'true' at the end tells our function to plot
// the progress of K-Means
(Matrix <double> centroids, Vector <double> idx)kMeans = RunkMeans(X, initial_centroids, max_iters, true);
System.Console.WriteLine("\nK-Means Done.\n\n");
Pause();
}