public void ComputeTest5()
{
var dataset = SequentialMinimalOptimizationTest.GetYingYang();
var inputs = dataset.Submatrix(null, 0, 1).ToJagged();
var labels = dataset.GetColumn(2).ToInt32();
var kernel = new Polynomial(2, 0);
{
var machine = new KernelSupportVectorMachine(kernel, inputs[0].Length);
var smo = new SequentialMinimalOptimization(machine, inputs, labels);
smo.UseComplexityHeuristic = true;
double error = smo.Run();
Assert.AreEqual(0.2, error);
Assert.AreEqual(0.11714451552090824, smo.Complexity);
int[] actual = new int[labels.Length];
for (int i = 0; i < actual.Length; i++)
{
actual[i] = Math.Sign(machine.Compute(inputs[i]));
}
ConfusionMatrix matrix = new ConfusionMatrix(actual, labels);
Assert.AreEqual(20, matrix.FalseNegatives);
Assert.AreEqual(0, matrix.FalsePositives);
Assert.AreEqual(30, matrix.TruePositives);
Assert.AreEqual(50, matrix.TrueNegatives);
}
{
Accord.Math.Tools.SetupGenerator(0);
var projection = inputs.Apply(kernel.Transform);
var machine = new SupportVectorMachine(projection[0].Length);
var smo = new LinearNewtonMethod(machine, projection, labels);
smo.UseComplexityHeuristic = true;
double error = smo.Run();
Assert.AreEqual(0.18, error);
Assert.AreEqual(0.11714451552090821, smo.Complexity, 1e-15);
int[] actual = new int[labels.Length];
for (int i = 0; i < actual.Length; i++)
{
actual[i] = Math.Sign(machine.Compute(projection[i]));
}
ConfusionMatrix matrix = new ConfusionMatrix(actual, labels);
Assert.AreEqual(17, matrix.FalseNegatives);
Assert.AreEqual(1, matrix.FalsePositives);
Assert.AreEqual(33, matrix.TruePositives);
Assert.AreEqual(49, matrix.TrueNegatives);
}
}
public void LearnTest()
{
double[][] inputs =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
int[] xor =
{
-1,
1,
1,
-1
};
var kernel = new Polynomial(2, 0.0);
double[][] augmented = new double[inputs.Length][];
for (int i = 0; i < inputs.Length; i++)
{
augmented[i] = kernel.Transform(inputs[i]);
}
SupportVectorMachine machine = new SupportVectorMachine(augmented[0].Length);
// Create the Least Squares Support Vector Machine teacher
var learn = new LinearNewtonMethod(machine, augmented, xor);
// Run the learning algorithm
double error = learn.Run();
Assert.AreEqual(0, error);
int[] output = augmented.Apply(p => Math.Sign(machine.Compute(p)));
for (int i = 0; i < output.Length; i++)
{
Assert.AreEqual(System.Math.Sign(xor[i]), System.Math.Sign(output[i]));
}
}
public void sparse_zero_vector_test()
{
// Create a linear-SVM learning method
var teacher = new LinearNewtonMethod <Linear, Sparse <double> >()
{
Tolerance = 1e-10,
Complexity = 1e+10, // learn a hard-margin model
};
// Now suppose you have some points
Sparse <double>[] inputs = Sparse.FromDense(new[]
{
new double[] { 1, 1, 2 },
new double[] { 0, 1, 6 },
new double[] { 1, 0, 8 },
new double[] { 0, 0, 0 },
});
int[] outputs = { 1, -1, 1, -1 };
// Learn the support vector machine
var svm = teacher.Learn(inputs, outputs);
// Compute the predicted points
bool[] predicted = svm.Decide(inputs);
// And the squared error loss using
double error = new ZeroOneLoss(outputs).Loss(predicted);
Assert.AreEqual(3, svm.NumberOfInputs);
Assert.AreEqual(1, svm.NumberOfOutputs);
Assert.AreEqual(2, svm.NumberOfClasses);
Assert.AreEqual(1, svm.Weights.Length);
Assert.AreEqual(1, svm.SupportVectors.Length);
Assert.AreEqual(1.0, svm.Weights[0], 1e-6);
Assert.AreEqual(2.0056922148257597, svm.SupportVectors[0][0], 1e-6);
Assert.AreEqual(-0.0085361347231909836, svm.SupportVectors[0][1], 1e-6);
Assert.AreEqual(0.0014225721169379331, svm.SupportVectors[0][2], 1e-6);
Assert.AreEqual(0.0, error);
}
public void linear_regression_test()
{
#region doc_linreg
// Declare some training data. This is exactly the same
// data used in the MultipleLinearRegression documentation page
// We will try to model a plane as an equation in the form
// "ax + by + c = z". We have two input variables (x and y)
// and we will be trying to find two parameters a and b and
// an intercept term c.
// Create a linear-SVM learning method
var teacher = new LinearNewtonMethod()
{
Tolerance = 1e-10,
Complexity = 1e+10, // learn a hard-margin model
};
// Now suppose you have some points
double[][] inputs =
{
new double[] { 1, 1 },
new double[] { 0, 1 },
new double[] { 1, 0 },
new double[] { 0, 0 },
};
// located in the same Z (z = 1)
double[] outputs = { 1, 1, 1, 1 };
// Learn the support vector machine
var svm = teacher.Learn(inputs, outputs);
// Convert the svm to logistic regression
var regression = (MultipleLinearRegression)svm;
// As result, we will be given the following:
double a = regression.Weights[0]; // a = 0
double b = regression.Weights[1]; // b = 0
double c = regression.Intercept; // c = 1
// This is the plane described by the equation
// ax + by + c = z => 0x + 0y + 1 = z => 1 = z.
// We can compute the predicted points using
double[] predicted = regression.Transform(inputs);
// And the squared error loss using
double error = new SquareLoss(outputs).Loss(predicted);
#endregion
Assert.AreEqual(2, regression.NumberOfInputs);
Assert.AreEqual(1, regression.NumberOfOutputs);
Assert.AreEqual(0.0, a, 1e-6);
Assert.AreEqual(0.0, b, 1e-6);
Assert.AreEqual(1.0, c, 1e-6);
Assert.AreEqual(0.0, error, 1e-6);
double[] expected = regression.Compute(inputs);
double[] actual = regression.Transform(inputs);
Assert.IsTrue(expected.IsEqual(actual, 1e-10));
double r = regression.CoefficientOfDetermination(inputs, outputs);
Assert.AreEqual(1.0, r);
}
public void learn_linear_sparse()
{
#region doc_xor_sparse
// As an example, we will try to learn a linear machine that can
// replicate the "exclusive-or" logical function. However, since we
// will be using a linear SVM, we will not be able to solve this
// problem perfectly as the XOR is a non-linear classification problem:
Sparse <double>[] inputs =
{
Sparse.FromDense(new double[] { 0, 0 }), // the XOR function takes two booleans
Sparse.FromDense(new double[] { 0, 1 }), // and computes their exclusive or: the
Sparse.FromDense(new double[] { 1, 0 }), // output is true only if the two booleans
Sparse.FromDense(new double[] { 1, 1 }) // are different
};
int[] xor = // this is the output of the xor function
{
0, // 0 xor 0 = 0 (inputs are equal)
1, // 0 xor 1 = 1 (inputs are different)
1, // 1 xor 0 = 1 (inputs are different)
0, // 1 xor 1 = 0 (inputs are equal)
};
// Now, we can create the sequential minimal optimization teacher
var learn = new LinearNewtonMethod <Linear, Sparse <double> >()
{
UseComplexityHeuristic = true,
UseKernelEstimation = false
};
// And then we can obtain a trained SVM by calling its Learn method
var svm = learn.Learn(inputs, xor);
// Finally, we can obtain the decisions predicted by the machine:
bool[] prediction = svm.Decide(inputs);
#endregion
Assert.AreEqual(prediction[0], false);
Assert.AreEqual(prediction[1], false);
Assert.AreEqual(prediction[2], false);
Assert.AreEqual(prediction[3], false);
int[] or = // this is the output of the xor function
{
0, // 0 or 0 = 0 (inputs are equal)
1, // 0 or 1 = 1 (inputs are different)
1, // 1 or 0 = 1 (inputs are different)
1, // 1 or 1 = 1 (inputs are equal)
};
learn = new LinearNewtonMethod <Linear, Sparse <double> >()
{
Complexity = 1e+8,
UseKernelEstimation = false
};
svm = learn.Learn(inputs, or);
prediction = svm.Decide(inputs);
Assert.AreEqual(0, inputs[0].Indices.Length);
Assert.AreEqual(1, inputs[1].Indices.Length);
Assert.AreEqual(1, inputs[2].Indices.Length);
Assert.AreEqual(2, inputs[3].Indices.Length);
Assert.AreEqual(prediction[0], false);
Assert.AreEqual(prediction[1], true);
Assert.AreEqual(prediction[2], true);
Assert.AreEqual(prediction[3], true);
}
public static void train_one(Problem prob, Parameters param, out double[] w, double Cp, double Cn)
{
double[][] inputs = prob.Inputs;
int[] labels = prob.Outputs.Apply(x => x >= 0 ? 1 : -1);
double eps = param.Tolerance;
int pos = 0;
for (int i = 0; i < labels.Length; i++)
{
if (labels[i] >= 0)
{
pos++;
}
}
int neg = prob.Outputs.Length - pos;
double primal_solver_tol = eps * Math.Max(Math.Min(pos, neg), 1.0) / prob.Inputs.Length;
SupportVectorMachine svm = new SupportVectorMachine(prob.Dimensions);
ISupportVectorMachineLearning teacher = null;
switch (param.Solver)
{
case LibSvmSolverType.L2RegularizedLogisticRegression:
// l2r_lr_fun
teacher = new ProbabilisticNewtonMethod(svm, inputs, labels)
{
PositiveWeight = Cp,
NegativeWeight = Cn,
Tolerance = primal_solver_tol
}; break;
case LibSvmSolverType.L2RegularizedL2LossSvc:
// fun_obj=new l2r_l2_svc_fun(prob, C);
teacher = new LinearNewtonMethod(svm, inputs, labels)
{
PositiveWeight = Cp,
NegativeWeight = Cn,
Tolerance = primal_solver_tol
}; break;
case LibSvmSolverType.L2RegularizedL2LossSvcDual:
// solve_l2r_l1l2_svc(prob, w, eps, Cp, Cn, L2R_L2LOSS_SVC_DUAL);
teacher = new LinearDualCoordinateDescent(svm, inputs, labels)
{
Loss = Loss.L2,
PositiveWeight = Cp,
NegativeWeight = Cn,
}; break;
case LibSvmSolverType.L2RegularizedL1LossSvcDual:
// solve_l2r_l1l2_svc(prob, w, eps, Cp, Cn, L2R_L1LOSS_SVC_DUAL);
teacher = new LinearDualCoordinateDescent(svm, inputs, labels)
{
Loss = Loss.L1,
PositiveWeight = Cp,
NegativeWeight = Cn,
}; break;
case LibSvmSolverType.L1RegularizedLogisticRegression:
// solve_l1r_lr(&prob_col, w, primal_solver_tol, Cp, Cn);
teacher = new ProbabilisticCoordinateDescent(svm, inputs, labels)
{
PositiveWeight = Cp,
NegativeWeight = Cn,
Tolerance = primal_solver_tol
}; break;
case LibSvmSolverType.L2RegularizedLogisticRegressionDual:
// solve_l2r_lr_dual(prob, w, eps, Cp, Cn);
teacher = new ProbabilisticDualCoordinateDescent(svm, inputs, labels)
{
PositiveWeight = Cp,
NegativeWeight = Cn,
Tolerance = primal_solver_tol,
}; break;
}
Trace.WriteLine("Training " + param.Solver);
// run the learning algorithm
var sw = Stopwatch.StartNew();
double error = teacher.Run();
sw.Stop();
// save the solution
w = svm.ToWeights();
Trace.WriteLine(String.Format("Finished {0}: {1} in {2}",
param.Solver, error, sw.Elapsed));
}
