public void GammaSigmaTest()
{
var dtw = new DynamicTimeWarping(1);
var gaussian = new Gaussian<DynamicTimeWarping>(dtw, 1);
double expected, actual, gamma, sigma;
expected = 0.01;
gaussian.Sigma = expected;
gamma = gaussian.Gamma;
gaussian.Gamma = gamma;
actual = gaussian.Sigma;
Assert.AreEqual(expected, actual);
expected = 0.01;
gaussian.Gamma = expected;
sigma = gaussian.Sigma;
gaussian.Sigma = sigma;
actual = gaussian.Gamma;
Assert.AreEqual(expected, actual, 1e-12);
}
public void GaussianFunctionTest()
{
var x = new double[] { 0, 4, 2, 1 };
var y = new double[] { 3, 2, };
var dtw = new DynamicTimeWarping(1);
IKernel gaussian = new Gaussian<DynamicTimeWarping>(dtw, 1);
double actual = gaussian.Function(x, y);
Assert.AreEqual(0.3407192298459587, actual);
gaussian = new Gaussian<DynamicTimeWarping>(dtw, 11.5);
x = new double[] { 0.2, 5 };
y = new double[] { 3, 0.7 };
actual = gaussian.Function(x, y);
Assert.AreEqual(0.99065918303292089, actual);
}
public void GaussianEstimateTest()
{
// Suppose we have the following data
//
double[][] data =
{
new double[] { 5.1, 3.5, 1.4, 0.2 },
new double[] { 5.0, 3.6, 1.4, 0.2 },
new double[] { 4.9, 3.0, 1.4, 0.2 },
new double[] { 5.8, 4.0, 1.2, 0.2 },
new double[] { 4.7, 3.2, 1.3, 0.2 },
};
// Estimate an appropriate sigma from data
var dtw = new DynamicTimeWarping(1);
var kernel = Gaussian.Estimate(dtw, data);
double sigma = kernel.Sigma;
double sigma2 = kernel.SigmaSquared;
Assert.AreEqual(0.044282096049367413, sigma);
Assert.AreEqual(sigma * sigma, sigma2);
}
public void DynamicalTimeWarpingConstructorTest()
{
double[][] sequences =
{
new double[] // -1
{
0, 0, 0,
1, 1, 1,
2, 2, 2,
},
new double[] // -1
{
0, 1, 0,
0, 2, 0,
0, 3, 0
},
new double[] // +1
{
1, 1, 0,
1, 2, 0,
2, 1, 0,
},
new double[] // +1
{
0, 0, 1,
0, 0, 2,
0, 1, 3,
},
};
int[] outputs = { -1, -1, +1, +1 };
// Set the parameters of the kernel
double alpha = 0.85;
int innerVectorLength = 3;
// Create the kernel. Note that the input vector will be given out automatically
DynamicTimeWarping target = new DynamicTimeWarping(innerVectorLength, alpha);
// When using variable-length kernels, specify 0 as the input length.
KernelSupportVectorMachine svm = new KernelSupportVectorMachine(target, 0);
// Create the Sequential Minimal Optimization as usual
SequentialMinimalOptimization smo = new SequentialMinimalOptimization(svm, sequences, outputs);
smo.Complexity = 1.5;
double error = smo.Run();
// Computing the training values
var a0 = svm.Compute(sequences[0]);
var a1 = svm.Compute(sequences[1]);
var a2 = svm.Compute(sequences[2]);
var a3 = svm.Compute(sequences[3]);
Assert.AreEqual(-1, System.Math.Sign(a0));
Assert.AreEqual(-1, System.Math.Sign(a1));
Assert.AreEqual(+1, System.Math.Sign(a2));
Assert.AreEqual(+1, System.Math.Sign(a3));
// Computing a new testing value
double[] test =
{
1, 0, 1,
0, 0, 2,
0, 1, 3,
};
var a4 = svm.Compute(test);
}
public void GammaSigmaSquaredTest()
{
var dtw = new DynamicTimeWarping(1);
var gaussian = new Gaussian<DynamicTimeWarping>(dtw, 3.6);
Assert.AreEqual(3.6 * 3.6, gaussian.SigmaSquared);
Assert.AreEqual(3.6, gaussian.Sigma);
Assert.AreEqual(1.0 / (2 * 3.6 * 3.6), gaussian.Gamma);
gaussian.SigmaSquared = 81;
Assert.AreEqual(81, gaussian.SigmaSquared);
Assert.AreEqual(9, gaussian.Sigma);
Assert.AreEqual(1.0 / (2 * 81), gaussian.Gamma);
gaussian.Sigma = 6;
Assert.AreEqual(36, gaussian.SigmaSquared);
Assert.AreEqual(6, gaussian.Sigma);
Assert.AreEqual(1.0 / (2 * 36), gaussian.Gamma);
gaussian.Gamma = 1.0 / (2 * 49);
Assert.AreEqual(49, gaussian.SigmaSquared, 1e-10);
Assert.AreEqual(7, gaussian.Sigma, 1e-10);
Assert.AreEqual(1.0 / (2 * 49), gaussian.Gamma);
}
public void DynamicalTimeWarpingConstructorTest2()
{
// Declare some testing data
double[][] inputs =
{
// Class -1
new double[] { 0,1,1,0 },
new double[] { 0,0,1,0 },
new double[] { 0,1,1,1,0 },
new double[] { 0,1,0 },
// Class +1
new double[] { 1,0,0,1 },
new double[] { 1,1,0,1 },
new double[] { 1,0,0,0,1 },
new double[] { 1,0,1 },
new double[] { 1,0,0,0,1,1 }
};
int[] outputs =
{
-1,-1,-1,-1, // First four sequences are of class -1
1, 1, 1, 1, 1 // Last five sequences are of class +1
};
// Set the parameters of the kernel
double alpha = 1.0;
int degree = 1;
int innerVectorLength = 1;
// Create the kernel. Note that the input vector will be given out automatically
DynamicTimeWarping target = new DynamicTimeWarping(innerVectorLength, alpha, degree);
// When using variable-length kernels, specify 0 as the input length.
KernelSupportVectorMachine svm = new KernelSupportVectorMachine(target, 0);
// Create the Sequential Minimal Optimization as usual
SequentialMinimalOptimization smo = new SequentialMinimalOptimization(svm, inputs, outputs);
smo.Complexity = 1.5;
double error = smo.Run();
// Check if the model has learnt the sequences correctly.
for (int i = 0; i < inputs.Length; i++)
{
int expected = outputs[i];
int actual = System.Math.Sign(svm.Compute(inputs[i]));
Assert.AreEqual(expected, actual);
}
// Testing new sequences
Assert.AreEqual(-1,System.Math.Sign(svm.Compute(new double[] { 0, 1, 1, 0, 0 })));
Assert.AreEqual(+1,System.Math.Sign(svm.Compute(new double[] { 1, 1, 0, 0, 1, 1 })));
}
public void FunctionTest()
{
var x = new double[] { 0, 4, 2, 1 };
var y = new double[] { 3, 2, };
DynamicTimeWarping target;
double expected, actual;
target = new DynamicTimeWarping(1);
expected = 1;
actual = target.Function(x, x);
Assert.AreEqual(expected, actual, 0.000001);
expected = 1;
actual = target.Function(y, y);
Assert.AreEqual(expected, actual, 0.000001);
expected = -0.076696513742007991;
actual = target.Function(x, y);
Assert.AreEqual(expected, actual, 0.000001);
actual = target.Function(y, x);
Assert.AreEqual(expected, actual, 0.000001);
target = new DynamicTimeWarping(2, 1.42);
var z = new double[] { 3, 2, 1, 5, 7, 8 };
expected = 1;
actual = target.Function(x, x);
Assert.AreEqual(expected, actual, 0.000001);
expected = 1;
actual = target.Function(y, y);
Assert.AreEqual(expected, actual, 0.000001);
expected = 1;
actual = target.Function(z, z);
Assert.AreEqual(expected, actual, 0.000001);
expected = -0.10903562560104614;
actual = target.Function(x, z);
Assert.AreEqual(expected, actual, 0.000001);
actual = target.Function(z, x);
Assert.AreEqual(expected, actual, 0.000001);
expected = 0.4208878392918925;
actual = target.Function(x, y);
Assert.AreEqual(expected, actual, 0.000001);
actual = target.Function(y, x);
Assert.AreEqual(expected, actual, 0.000001);
target = new DynamicTimeWarping(1, 0.0000000001);
expected = 1;
actual = target.Function(x, x);
Assert.AreEqual(expected, actual);
expected = 1;
actual = target.Function(y, y);
Assert.AreEqual(expected, actual);
expected = 0.000000000033333397321663391;
actual = target.Function(x, y);
Assert.AreEqual(expected, actual);
actual = target.Function(y, x);
Assert.AreEqual(expected, actual);
target = new DynamicTimeWarping(1, 292.12);
expected = 1;
actual = target.Function(x, x);
Assert.AreEqual(expected, actual, 0.000001);
actual = target.Function(y, y);
Assert.AreEqual(expected, actual, 0.000001);
expected = 0.99985353675500488;
actual = target.Function(x, y);
Assert.AreEqual(expected, actual);
actual = target.Function(y, x);
Assert.AreEqual(expected, actual);
}
public void FunctionTest_EqualInputs()
{
var x = new double[] { 1, 2, 5, 1 };
var y = new double[] { 1, 2, 5, 1 };
var target = new DynamicTimeWarping(1, 4.2);
double expected = target.Function(x, y);
double actual = target.Function(x, x);
Assert.AreEqual(expected, actual);
}
public void DistanceTest()
{
var x = new double[] { 0, 4, 2, 1 };
var y = new double[] { 3, 2, };
DynamicTimeWarping target;
double expected, actual;
target = new DynamicTimeWarping(1);
expected = 0;
actual = target.Distance(x, x);
Assert.AreEqual(expected, actual, 0);
expected = 0;
actual = target.Distance(y, y);
Assert.AreEqual(expected, actual, 0);
expected = 2.1533930274840158;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
actual = target.Distance(y, x);
Assert.AreEqual(expected, actual);
target = new DynamicTimeWarping(2, 1.42);
var z = new double[] { 3, 2, 1, 5, 7, 8 };
expected = 0;
actual = target.Distance(x, x);
Assert.AreEqual(expected, actual);
expected = 0;
actual = target.Distance(y, y);
Assert.AreEqual(expected, actual);
expected = 0;
actual = target.Distance(z, z);
Assert.AreEqual(expected, actual);
expected = 2.2180712512020921;
actual = target.Distance(x, z);
Assert.AreEqual(expected, actual);
actual = target.Distance(z, x);
Assert.AreEqual(expected, actual);
expected = 1.1582243214162151;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
actual = target.Distance(y, x);
Assert.AreEqual(expected, actual);
target = new DynamicTimeWarping(1, 0.0000000001);
expected = 0;
actual = target.Distance(x, x);
Assert.AreEqual(expected, actual);
expected = 0;
actual = target.Distance(y, y);
Assert.AreEqual(expected, actual);
expected = 1.9999999999333331;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
actual = target.Distance(y, x);
Assert.AreEqual(expected, actual);
target = new DynamicTimeWarping(1, 292.12);
expected = 0;
actual = target.Distance(x, x);
Assert.AreEqual(expected, actual);
actual = target.Distance(y, y);
Assert.AreEqual(expected, actual);
expected = 0.00029292648999024173;
actual = target.Distance(x, y);
Assert.AreEqual(expected, actual);
actual = target.Distance(y, x);
Assert.AreEqual(expected, actual);
}
public void DynamicalTimeWarpingConstructorTest3()
{
// Suppose you have sequences of multivariate observations, and that
// those sequences could be of arbitrary length. On the other hand,
// each observation have a fixed, delimited number of dimensions.
// In this example, we have sequences of 3-dimensional observations.
// Each sequence can have an arbitrary length, but each observation
// will always have length 3:
double[][][] sequences =
{
new double[][] // first sequence
{
new double[] { 1, 1, 1 }, // first observation of the first sequence
new double[] { 1, 2, 1 }, // second observation of the first sequence
new double[] { 1, 4, 2 }, // third observation of the first sequence
new double[] { 2, 2, 2 }, // fourth observation of the first sequence
},
new double[][] // second sequence (note that this sequence has a different length)
{
new double[] { 1, 1, 1 }, // first observation of the second sequence
new double[] { 1, 5, 6 }, // second observation of the second sequence
new double[] { 2, 7, 1 }, // third observation of the second sequence
},
new double[][] // third sequence
{
new double[] { 8, 2, 1 }, // first observation of the third sequence
},
new double[][] // fourth sequence
{
new double[] { 8, 2, 5 }, // first observation of the fourth sequence
new double[] { 1, 5, 4 }, // second observation of the fourth sequence
}
};
// Now, we will also have different class labels associated which each
// sequence. We will assign -1 to sequences whose observations start
// with { 1, 1, 1 } and +1 to those that do not:
int[] outputs =
{
-1,-1, // First two sequences are of class -1 (those start with {1,1,1})
1, 1, // Last two sequences are of class +1 (don't start with {1,1,1})
};
// At this point, we will have to "flat" out the input sequences from double[][][]
// to a double[][] so they can be properly understood by the SVMs. The problem is
// that, normally, SVMs usually expect the data to be comprised of fixed-length
// input vectors and associated class labels. But in this case, we will be feeding
// them arbitrary-length sequences of input vectors and class labels associated with
// each sequence, instead of each vector.
double[][] inputs = new double[sequences.Length][];
for (int i = 0; i < sequences.Length; i++)
inputs[i] = Matrix.Concatenate(sequences[i]);
// Now we have to setup the Dynamic Time Warping kernel. We will have to
// inform the length of the fixed-length observations contained in each
// arbitrary-length sequence:
//
DynamicTimeWarping kernel = new DynamicTimeWarping(length: 3);
// Now we can create the machine. When using variable-length
// kernels, we will need to pass zero as the input length:
var svm = new KernelSupportVectorMachine(kernel, inputs: 0);
// Create the Sequential Minimal Optimization learning algorithm
var smo = new SequentialMinimalOptimization(svm, inputs, outputs)
{
Complexity = 1.5
};
// And start learning it!
double error = smo.Run(); // error will be 0.0
// At this point, we should have obtained an useful machine. Let's
// see if it can understand a few examples it hasn't seem before:
double[][] a =
{
new double[] { 1, 1, 1 },
new double[] { 7, 2, 5 },
new double[] { 2, 5, 1 },
};
double[][] b =
{
new double[] { 7, 5, 2 },
new double[] { 4, 2, 5 },
new double[] { 1, 1, 1 },
};
// Following the aforementioned logic, sequence (a) should be
// classified as -1, and sequence (b) should be classified as +1.
int resultA = System.Math.Sign(svm.Compute(Matrix.Concatenate(a))); // -1
int resultB = System.Math.Sign(svm.Compute(Matrix.Concatenate(b))); // +1
Assert.AreEqual(0, error);
Assert.AreEqual(-1, resultA);
Assert.AreEqual(+1, resultB);
}