public SupportVectorMachine<Polynomial> v3_1_0()
{
ksvm = new SupportVectorMachine<Polynomial>(inputs: 2, kernel: new Polynomial(2));
smo = new SequentialMinimalOptimization<Polynomial>()
{
Model = ksvm
};
smo.Learn(inputs, outputs);
return ksvm;
}
/// <summary>
/// Creates a Support Vector Machine and teaches it to recognize
/// the previously loaded dataset using the current UI settings.
/// </summary>
///
private void btnCreate_Click(object sender, EventArgs e)
{
if (dgvLearningSource.DataSource == null)
{
MessageBox.Show("Please load some data first.");
return;
}
// Finishes and save any pending changes to the given data
dgvLearningSource.EndEdit();
// Creates a matrix from the entire source data table
double[,] table = (dgvLearningSource.DataSource as DataTable).ToMatrix(out columnNames);
// Get only the input vector values (first two columns)
double[][] inputs = table.GetColumns(0, 1).ToJagged();
// Get only the output labels (last column)
int[] outputs = table.GetColumn(2).ToInt32();
// Creates a new instance of the SMO learning algorithm
var smo = new SequentialMinimalOptimization<IKernel>()
{
// Set learning parameters
Complexity = (double)numC.Value,
Tolerance = (double)numT.Value,
PositiveWeight = (double)numPositiveWeight.Value,
NegativeWeight = (double)numNegativeWeight.Value,
Kernel = createKernel()
};
try
{
// Run
svm = smo.Learn(inputs, outputs);
lbStatus.Text = "Training complete!";
}
catch (ConvergenceException)
{
lbStatus.Text = "Convergence could not be attained. "+
"The learned machine might still be usable.";
}
createSurface(table);
// Check if we got support vectors
if (svm.SupportVectors == null || svm.SupportVectors.Length == 0)
{
dgvSupportVectors.DataSource = null;
graphSupportVectors.GraphPane.CurveList.Clear();
return;
}
// Show support vectors on the Support Vectors tab page
double[][] supportVectorsWeights = svm.SupportVectors.InsertColumn(svm.Weights);
string[] supportVectorNames = columnNames.RemoveAt(columnNames.Length - 1).Concatenate("Weight");
dgvSupportVectors.DataSource = new ArrayDataView(supportVectorsWeights, supportVectorNames);
// Show the support vector labels on the scatter plot
double[] supportVectorLabels = new double[svm.SupportVectors.Length];
for (int i = 0; i < supportVectorLabels.Length; i++)
{
int j = inputs.Find(sv => sv == svm.SupportVectors[i])[0];
supportVectorLabels[i] = outputs[j];
}
double[][] graph = svm.SupportVectors.InsertColumn(supportVectorLabels);
CreateScatterplot(graphSupportVectors, graph.ToMatrix());
}
public void learn_linear()
{
#region doc_xor_linear
// 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:
double[][] inputs =
{
new double[] { 0, 0 }, // the XOR function takes two booleans
new double[] { 0, 1 }, // and computes their exclusive or: the
new double[] { 1, 0 }, // output is true only if the two booleans
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 SequentialMinimalOptimization()
{
UseComplexityHeuristic = true,
UseKernelEstimation = false
};
// And then we can obtain a trained SVM by calling its Learn method
SupportVectorMachine 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 SequentialMinimalOptimization()
{
Complexity = 1e+8,
UseKernelEstimation = false
};
svm = learn.Learn(inputs, or);
prediction = svm.Decide(inputs);
Assert.AreEqual(prediction[0], false);
Assert.AreEqual(prediction[1], true);
Assert.AreEqual(prediction[2], true);
Assert.AreEqual(prediction[3], true);
}
public void linear_without_threshold_doesnt_solve_xor()
{
double[][] inputs =
{
new double[] { -1, -1 },
new double[] { -1, 1 },
new double[] { 1, -1 },
new double[] { 1, 1 }
};
int[] xor =
{
-1,
1,
1,
-1
};
// Create the sequential minimal optimization teacher
var learn = new SequentialMinimalOptimization()
{
Complexity = 1e-5
};
// Run the learning algorithm
SupportVectorMachine machine = learn.Learn(inputs, xor);
bool[] output = machine.Decide(inputs);
for (int i = 0; i < output.Length; i++)
Assert.AreEqual(false, output[i]);
}
public void learn_sparse_kernel()
{
#region doc_xor_sparse
// As an example, we will try to learn a decision machine
// that can replicate the "exclusive-or" logical function:
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 SequentialMinimalOptimization<Gaussian, Sparse<double>>()
{
UseComplexityHeuristic = true,
UseKernelEstimation = true
};
// 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, Classes.Decide(xor));
}
public void learn_precomputed()
{
#region doc_precomputed
// As an example, we will try to learn a decision machine
// that can replicate the "exclusive-or" logical function:
double[][] inputs =
{
new double[] { 0, 0 }, // the XOR function takes two booleans
new double[] { 0, 1 }, // and computes their exclusive or: the
new double[] { 1, 0 }, // output is true only if the two booleans
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)
};
// Let's use a Gaussian kernel
var kernel = new Gaussian(0.1);
// Create a pre-computed Gaussian kernel matrix
var precomputed = new Precomputed(kernel.ToJagged(inputs));
// Now, we can create the sequential minimal optimization teacher
var learn = new SequentialMinimalOptimization<Precomputed, int>()
{
Kernel = precomputed // set the precomputed kernel we created
};
// And then we can obtain the SVM by using Learn
var svm = learn.Learn(precomputed.Indices, xor);
// Finally, we can obtain the decisions predicted by the machine:
bool[] prediction = svm.Decide(precomputed.Indices);
// We can also compute the machine prediction to new samples
double[][] sample =
{
new double[] { 0, 1 }
};
// Update the precomputed kernel with the new samples
precomputed = new Precomputed(kernel.ToJagged2(inputs, sample));
// Update the SVM kernel
svm.Kernel = precomputed;
// Compute the predictions to the new samples
bool[] newPrediction = svm.Decide(precomputed.Indices);
#endregion
Assert.AreEqual(prediction, Classes.Decide(xor));
Assert.AreEqual(newPrediction.Length, 1);
Assert.AreEqual(newPrediction[0], true);
}
public void learn_test()
{
#region doc_learn
double[][] inputs = // Example XOR problem
{
new double[] { 0, 0 }, // 0 xor 0: 1 (label +1)
new double[] { 0, 1 }, // 0 xor 1: 0 (label -1)
new double[] { 1, 0 }, // 1 xor 0: 0 (label -1)
new double[] { 1, 1 } // 1 xor 1: 1 (label +1)
};
int[] outputs = // XOR outputs
{
1, 0, 0, 1
};
// Instantiate a new SMO learning algorithm for SVMs
var smo = new SequentialMinimalOptimization<Gaussian>()
{
Kernel = new Gaussian(0.1),
Complexity = 1.0
};
// Learn a SVM using the algorithm
var svm = smo.Learn(inputs, outputs);
// Predict labels for each input sample
bool[] predicted = svm.Decide(inputs);
// Compute classification error
double error = new ZeroOneLoss(outputs).Loss(predicted);
// Instantiate the probabilistic calibration (using Platt's scaling)
var calibration = new ProbabilisticOutputCalibration<Gaussian>(svm);
// Run the calibration algorithm
calibration.Learn(inputs, outputs); // returns the same machine
// Predict probabilities of each input sample
double[] probabilities = svm.Probability(inputs);
// Compute the error based on a hard decision
double loss = new BinaryCrossEntropyLoss(outputs).Loss(probabilities);
// Compute the decision output for one of the input vectors,
// while also retrieving the probability of the answer
bool decision;
double probability = svm.Probability(inputs[0], out decision);
#endregion
// At this point, decision is +1 with a probability of 75%
Assert.AreEqual(true, decision);
Assert.AreEqual(0, error);
Assert.AreEqual(5.5451735748925355, loss);
Assert.AreEqual(0.74999975815069375, probability, 1e-10);
Assert.IsTrue(svm.IsProbabilistic);
Assert.AreEqual(-1.0986109988055595, svm.Weights[0]);
Assert.AreEqual(1.0986109988055595, svm.Weights[1]);
Assert.AreEqual(-1.0986109988055595, svm.Weights[2]);
Assert.AreEqual(1.0986109988055595, svm.Weights[3]);
}