//Protected methods (called by the public methods in parent class)
protected override void DoTrain(System.Drawing.Bitmap[] charImgs)
{
double[][] input = charImgs.Select(img => Converters.ThresholdedBitmapToDoubleArray(img)).ToArray();
kpca = new KernelPrincipalComponentAnalysis(input, kernel, AnalysisMethod.Center);
kpca.Compute();
}
public void TransformTest()
{
// Using a linear kernel should be equivalent to standard PCA
IKernel kernel = new Linear();
// Create analysis
var target = new KernelPrincipalComponentAnalysis(data, kernel, AnalysisMethod.Center);
// Compute
target.Compute();
double[,] actual = target.Transform(data, 2);
// first inversed.. ?
double[,] expected = new double[,]
{
{ -0.827970186, 0.175115307 },
{ 1.77758033, -0.142857227 },
{ -0.992197494, -0.384374989 },
{ -0.274210416, -0.130417207 },
{ -1.67580142, 0.209498461 },
{ -0.912949103, -0.175282444 },
{ 0.099109437, 0.349824698 },
{ 1.14457216, -0.046417258 },
{ 0.438046137, -0.017764629 },
{ 1.22382056, 0.162675287 },
};
// Verify both are equal with 0.001 tolerance value
Assert.IsTrue(Matrix.IsEqual(actual, expected, 0.0001));
// Assert the result equals the transformation of the input
double[,] result = target.Result;
double[,] projection = target.Transform(data);
Assert.IsTrue(Matrix.IsEqual(result, projection, 0.000001));
Assert.AreEqual(2, target.Eigenvalues.Length);
Assert.AreEqual(10, target.ComponentMatrix.GetLength(0));
Assert.AreEqual(2, target.ComponentMatrix.GetLength(1));
}
public void TransformTest2()
{
// Using a linear kernel should be equivalent to standard PCA
IKernel kernel = new Linear();
// Create analysis
KernelPrincipalComponentAnalysis target =
new KernelPrincipalComponentAnalysis(data, kernel, AnalysisMethod.Center);
// Set the minimum variance threshold to 0.001
target.Threshold = 0.001;
// Compute
target.Compute();
var r = target.Result;
double[,] actual = target.Transform(data, 1);
// first inversed.. ?
double[,] expected = new double[,]
{
{ -0.827970186 },
{ 1.77758033 },
{ -0.992197494 },
{ -0.274210416 },
{ -1.67580142 },
{ -0.912949103 },
{ 0.099109437 },
{ 1.14457216 },
{ 0.438046137 },
{ 1.22382056 },
};
// Verify both are equal with 0.001 tolerance value
Assert.IsTrue(Matrix.IsEqual(actual, expected, 0.0001));
// Assert the result equals the transformation of the input
double[,] result = target.Result;
double[,] projection = target.Transform(data);
Assert.IsTrue(Matrix.IsEqual(result, projection, 0.000001));
}
public void RevertTest3()
{
string path = @"..\..\..\..\Unit Tests\Accord.Tests.Statistics\Resources\examples.xls";
// Create a new reader, opening a given path
ExcelReader reader = new ExcelReader(path);
// Afterwards, we can query the file for all
// worksheets within the specified workbook:
string[] sheets = reader.GetWorksheetList();
// Finally, we can request an specific sheet:
DataTable table = reader.GetWorksheet("Wikipedia");
// Now, we have loaded the Excel file into a DataTable. We
// can go further and transform it into a matrix to start
// running other algorithms on it:
double[,] matrix = table.ToMatrix();
IKernel kernel = new Polynomial(2);
// Create analysis
KernelPrincipalComponentAnalysis target = new KernelPrincipalComponentAnalysis(matrix,
kernel, AnalysisMethod.Center, centerInFeatureSpace: true);
target.Compute();
double[,] forward = target.Result;
double[,] reversion = target.Revert(forward);
Assert.IsTrue(!reversion.HasNaN());
}
public void RevertTest()
{
// Using a linear kernel should be equivalent to standard PCA
IKernel kernel = new Linear();
// Create analysis
KernelPrincipalComponentAnalysis target = new KernelPrincipalComponentAnalysis(data, kernel, AnalysisMethod.Center);
// Compute
target.Compute();
// Compute image
double[,] image = target.Transform(data, 2);
// Compute pre-image
double[,] preimage = target.Revert(image);
// Check if pre-image equals the original data
Assert.IsTrue(Matrix.IsEqual(data, preimage, 0.0001));
}
public void TransformTest_Jagged()
{
double[][] sourceMatrix = new double[][]
{
new double[] { 2.5, 2.4 },
new double[] { 0.5, 0.7 },
new double[] { 2.2, 2.9 },
new double[] { 1.9, 2.2 },
new double[] { 3.1, 3.0 },
new double[] { 2.3, 2.7 },
new double[] { 2.0, 1.6 },
new double[] { 1.0, 1.1 },
new double[] { 1.5, 1.6 },
new double[] { 1.1, 0.9 }
};
// Create a new linear kernel
IKernel kernel = new Linear();
// Creates the Kernel Principal Component Analysis of the given data
var kpca = new KernelPrincipalComponentAnalysis(sourceMatrix, kernel);
// Compute the Kernel Principal Component Analysis
kpca.Compute();
// The following statement throws an exception:
// An unhandled exception of type 'System.IndexOutOfRangeException' occurred in Accord.Math.dll
double[] actual1 = kpca.Transform(sourceMatrix[0]);
double[][] actual = kpca.Transform(sourceMatrix);
double[][] expected =
{
new double[] { -0.827970186, 0.175115307 },
new double[] { 1.77758033, -0.142857227 },
new double[] { -0.992197494, -0.384374989 },
new double[] { -0.274210416, -0.130417207 },
new double[] { -1.67580142, 0.209498461 },
new double[] { -0.912949103, -0.175282444 },
new double[] { 0.099109437, 0.349824698 },
new double[] { 1.14457216, -0.046417258 },
new double[] { 0.438046137, -0.017764629 },
new double[] { 1.22382056, 0.162675287 },
};
Assert.IsTrue(Matrix.IsEqual(expected[0], expected[0]));
// Verify both are equal with 0.001 tolerance value
Assert.IsTrue(Matrix.IsEqual(actual, expected, 0.0001));
// Assert the result equals the transformation of the input
double[,] result = kpca.Result;
double[,] projection = kpca.Transform(data);
Assert.IsTrue(Matrix.IsEqual(result, projection, 0.000001));
}
public void TransformTest5()
{
int element = 10;
int dimension = 20;
double[,] data = new double[element, dimension];
int x = 0;
for (int i = 0; i < element; i++)
{
for (int j = 0; j < dimension; j++)
data[i, j] = x;
x += 10;
}
IKernel kernel = new Gaussian(10.0);
var kpca = new KernelPrincipalComponentAnalysis(data, kernel, AnalysisMethod.Center);
kpca.Compute();
double[,] result = kpca.Transform(data, 2);
double[,] expected = new double[,]
{
{ -0.23053882357602, -0.284413654763538 },
{ -0.387883199575312, -0.331485820285834 },
{ -0.422077400361521, -0.11134948984113 },
{ -0.322265008788599, 0.23632015508648 },
{ -0.12013575394419, 0.490928809797139 },
{ 0.120135753938394, 0.490928809796094 },
{ 0.322265008787236, 0.236320155085067 },
{ 0.422077400363969, -0.111349489837512 },
{ 0.38788319957867, -0.331485820278937 },
{ 0.230538823577373, -0.28441365475783 }
};
Assert.IsTrue(result.IsEqual(expected, 1e-10));
}
public void learn_whiten_success()
{
double[,] data =
{
{ 2.5, 2.4 },
{ 0.5, 0.7 },
{ 2.2, 2.9 },
{ 1.9, 2.2 },
{ 3.1, 3.0 },
{ 2.3, 2.7 },
{ 2.0, 1.6 },
{ 1.0, 1.1 },
{ 1.5, 1.6 },
{ 1.1, 0.9 }
};
var method = PrincipalComponentMethod.Center; // PrincipalComponentMethod.Standardize
var pca = new KernelPrincipalComponentAnalysis(new Linear(), method, whiten: true);
pca.Learn(data);
double[] eigenvalues = { 1.28402771, 0.0490833989 };
double[] proportion = eigenvalues.Divide(eigenvalues.Sum());
double[,] eigenvectors =
{
{ 0.19940687993951403, -1.1061252858739095 },
{ 0.21626410214440508, 1.0199057073792104 }
};
// Everything is alright (up to the 9 decimal places shown in the tutorial)
// Assert.IsTrue(eigenvectors.IsEqual(pca.ComponentMatrix, rtol: 1e-9));
Assert.IsTrue(proportion.IsEqual(pca.ComponentProportions, rtol: 1e-9));
Assert.IsTrue(eigenvalues.IsEqual(pca.Eigenvalues.Divide(data.GetLength(0) - 1), rtol: 1e-5));
double[,] actual = pca.Transform(data);
double[][] expected = new double[][]
{
new double[] { 0.243560157209023, -0.263472650637184 },
new double[] { -0.522902576315494, 0.214938218565977 },
new double[] { 0.291870144299372, 0.578317788814594 },
new double[] { 0.0806632088164338, 0.19622137941132 },
new double[] { 0.492962746459375, -0.315204397734004 },
new double[] { 0.268558011864442, 0.263724118751361 },
new double[] { -0.0291545644762578, -0.526334573603598 },
new double[] { -0.336693495487974, 0.0698378585807067 },
new double[] { -0.128858004446015, 0.0267280693333571 },
new double[] { -0.360005627922904, -0.244755811482527 }
}.Multiply(-1);
// Everything is correct (up to 8 decimal places)
Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));
}
public void TransformTest3()
{
// Using a linear kernel should be equivalent to standard PCA
IKernel kernel = new Linear();
// Create analysis
KernelPrincipalComponentAnalysis target = new KernelPrincipalComponentAnalysis(data, kernel);
// Compute
target.Compute();
bool thrown = false;
try
{
double[,] actual = target.Transform(data, 11);
}
catch
{
thrown = true;
}
Assert.IsTrue(thrown);
}
public void learn_success()
{
#region doc_learn_1
// Reproducing Lindsay Smith's "Tutorial on Principal Component Analysis"
// using the framework's default method. The tutorial can be found online
// at http://www.sccg.sk/~haladova/principal_components.pdf
// Step 1. Get some data
// ---------------------
double[][] data =
{
new double[] { 2.5, 2.4 },
new double[] { 0.5, 0.7 },
new double[] { 2.2, 2.9 },
new double[] { 1.9, 2.2 },
new double[] { 3.1, 3.0 },
new double[] { 2.3, 2.7 },
new double[] { 2.0, 1.6 },
new double[] { 1.0, 1.1 },
new double[] { 1.5, 1.6 },
new double[] { 1.1, 0.9 }
};
// Step 2. Subtract the mean
// -------------------------
// Note: The framework does this automatically. By default, the framework
// uses the "Center" method, which only subtracts the mean. However, it is
// also possible to remove the mean *and* divide by the standard deviation
// (thus performing the correlation method) by specifying "Standardize"
// instead of "Center" as the AnalysisMethod.
var method = PrincipalComponentMethod.Center; // PrincipalComponentMethod.Standardize
// Step 3. Compute the covariance matrix
// -------------------------------------
// Note: Accord.NET does not need to compute the covariance
// matrix in order to compute PCA. The framework uses the SVD
// method which is more numerically stable, but may require
// more processing or memory. In order to replicate the tutorial
// using covariance matrices, please see the next unit test.
// Create the analysis using the selected method
var pca = new KernelPrincipalComponentAnalysis(new Linear(), method);
// Compute it
pca.Learn(data);
// Step 4. Compute the eigenvectors and eigenvalues of the covariance matrix
// -------------------------------------------------------------------------
// Note: Since Accord.NET uses the SVD method rather than the Eigendecomposition
// method, the Eigenvalues are computed from the singular values. However, it is
// not the Eigenvalues themselves which are important, but rather their proportion:
// Those are the expected eigenvalues, in descending order:
double[] eigenvalues = { 1.28402771, 0.0490833989 };
// And this will be their proportion:
double[] proportion = eigenvalues.Divide(eigenvalues.Sum());
Assert.IsTrue(proportion.IsEqual(pca.ComponentProportions, rtol: 1e-9));
Assert.IsTrue(eigenvalues.IsEqual(pca.Eigenvalues.Divide(data.GetLength(0) - 1), rtol: 1e-5));
// Step 5. Deriving the new data set
// ---------------------------------
double[][] actual = pca.Transform(data);
// transformedData shown in pg. 18
double[,] expected = new double[,]
{
{ 0.827970186, -0.175115307 },
{ -1.77758033, 0.142857227 },
{ 0.992197494, 0.384374989 },
{ 0.274210416, 0.130417207 },
{ 1.67580142, -0.209498461 },
{ 0.912949103, 0.175282444 },
{ -0.099109437, -0.349824698 },
{ -1.14457216, 0.046417258 },
{ -0.438046137, 0.017764629 },
{ -1.22382056, -0.162675287 },
}.Multiply(-1);
// Everything is correct (up to 8 decimal places)
Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));
// Finally, we can project all the data
double[][] output1 = pca.Transform(data);
// Or just its first components by setting
// NumberOfOutputs to the desired components:
pca.NumberOfOutputs = 1;
// And then calling transform again:
double[][] output2 = pca.Transform(data);
// We can also limit to 80% of explained variance:
pca.ExplainedVariance = 0.8;
// And then call transform again:
double[][] output3 = pca.Transform(data);
#endregion
actual = pca.Transform(data);
// transformedData shown in pg. 18
expected = new double[,]
{
{ 0.827970186 },
{ -1.77758033, },
{ 0.992197494 },
{ 0.274210416 },
{ 1.67580142, },
{ 0.912949103 },
{ -0.099109437 },
{ -1.14457216, },
{ -0.438046137 },
{ -1.22382056, },
}.Multiply(-1);
// Everything is correct (up to 8 decimal places)
Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));
// Create the analysis using the selected method
pca = new KernelPrincipalComponentAnalysis()
{
Kernel = new Linear(),
Method = method,
NumberOfOutputs = 1
};
// Compute it
pca.Learn(data);
actual = pca.Transform(data);
// transformedData shown in pg. 18
expected = new double[,]
{
{ 0.827970186 },
{ -1.77758033, },
{ 0.992197494 },
{ 0.274210416 },
{ 1.67580142, },
{ 0.912949103 },
{ -0.099109437 },
{ -1.14457216, },
{ -0.438046137 },
{ -1.22382056, },
}.Multiply(-1);
// Everything is correct (up to 8 decimal places)
Assert.IsTrue(expected.IsEqual(actual, atol: 1e-8));
}
public void kernel_matrix_success()
{
var actual = new KernelPrincipalComponentAnalysis(new Linear(), PrincipalComponentMethod.KernelMatrix);
var expected = new KernelPrincipalComponentAnalysis(data, new Linear(), AnalysisMethod.Standardize);
Linear kernel = new Linear();
double[][] K = kernel.ToJagged(data.ZScores().ToJagged());
// Compute
actual.Learn(K);
expected.Compute();
// Transform
double[][] actualTransform = actual.Transform(K);
double[][] expectedTransform1 = expected.Transform(data).ToJagged();
double[][] expectedTransform2 = expected.Transform(data.ToJagged());
// Verify both are equal with 0.01 tolerance value
Assert.IsTrue(Matrix.IsEqual(actualTransform, expectedTransform1, 0.01));
Assert.IsTrue(Matrix.IsEqual(actualTransform, expectedTransform2, 0.01));
}
public void transform_more_columns_than_samples_new_interface()
{
// Lindsay's tutorial data
double[,] datat = data.Transpose();
var target = new KernelPrincipalComponentAnalysis(new Linear());
// Compute
target.Learn(datat);
// Transform
double[,] actual = target.Transform(datat);
// Assert the scores equals the transformation of the input
double[,] result = target.Result;
double[,] expected = new double[,]
{
{ 0.50497524691810358 },
{ -0.504975246918104 }
}.Multiply(-1);
Assert.IsTrue(Matrix.IsEqual(expected, actual, 0.01));
Assert.IsTrue(Matrix.IsEqual(result, actual, 0.01));
}
public void RevertTest2_new_method()
{
string path = @"Resources\examples.xls";
// Create a new reader, opening a given path
ExcelReader reader = new ExcelReader(path);
// Afterwards, we can query the file for all
// worksheets within the specified workbook:
string[] sheets = reader.GetWorksheetList();
// Finally, we can request an specific sheet:
DataTable table = reader.GetWorksheet("Wikipedia");
// Now, we have loaded the Excel file into a DataTable. We
// can go further and transform it into a matrix to start
// running other algorithms on it:
double[][] matrix = table.ToArray();
IKernel kernel = new Gaussian(5);
// Create analysis
var target = new KernelPrincipalComponentAnalysis(kernel)
{
Method = PrincipalComponentMethod.Center,
Center = true // Center in feature space
};
var regression = target.Learn(matrix);
double[][] forward = regression.Transform(matrix);
double[][] reversion = target.Revert(forward);
Assert.IsTrue(!reversion.HasNaN());
}
public void test_kernlab_new_method()
{
// Tested against R's kernlab
// test <- c(16, 117, 94, 132, 13, 73, 68, 129, 91, 50, 56, 12, 145, 105, 35, 53, 38, 51, 85, 116)
int[] test = { 15, 116, 93, 131, 12, 72, 67, 128, 90, 49, 55, 11, 144, 104, 34, 52, 37, 50, 84, 115 };
// data(iris)
double[,] iris = create_iris();
// kpc <- kpca(~.,data=iris[-test,-5],kernel="rbfdot",kpar=list(sigma=0.2),features=2)
var data = iris.Remove(test, new[] { 4 });
var kernel = new Gaussian() { Gamma = 1 };
var kpc = new KernelPrincipalComponentAnalysis(kernel);
kpc.NumberOfOutputs = 2;
var transform = kpc.Learn(data);
var rotated = kpc.Result;
var pcv = kpc.ComponentMatrix;
var eig = kpc.Eigenvalues;
double[] expected_eig = { 28.542404060412132, 15.235596653653861 };
double[,] expected_pcv = expected_r();
Assert.IsTrue(Matrix.IsEqual(expected_eig, eig, 1e-10));
Assert.IsTrue(Matrix.IsEqual(expected_pcv, pcv, 1e-10));
double[,] irisSubset = iris_sub();
var testing = iris.Submatrix(test, new[] { 0, 1, 2, 3 });
Assert.IsTrue(Matrix.IsEqual(irisSubset, testing));
double[,] expectedProjection = expected_p();
double[,] proj = kpc.Transform(testing);
Assert.IsTrue(expectedProjection.IsEqual(proj, 1e-6));
double[][] proj2 = kpc.Transform(testing.ToJagged());
Assert.IsTrue(expectedProjection.IsEqual(proj, 1e-6));
double[][] proj3 = transform.Transform(testing.ToJagged());
Assert.IsTrue(expectedProjection.IsEqual(proj, 1e-6));
}
/// <summary>
/// Launched when the user clicks the "Run analysis" button.
/// </summary>
///
private void btnCompute_Click(object sender, EventArgs e)
{
// Save any pending changes
dgvAnalysisSource.EndEdit();
if (dgvAnalysisSource.DataSource == null)
{
MessageBox.Show("Please load some data using File > Open!");
return;
}
// Create a matrix from the source data table
double[,] sourceMatrix = (dgvAnalysisSource.DataSource as DataTable).ToMatrix(out columnNames);
int rows = sourceMatrix.GetLength(0);
int cols = sourceMatrix.GetLength(1);
// Create and compute a new Simple Descriptive Analysis
sda = new DescriptiveAnalysis(sourceMatrix, columnNames);
sda.Compute();
// Show the descriptive analysis on the screen
dgvDistributionMeasures.DataSource = sda.Measures;
// Create the kernel function
IKernel kernel = createKernel();
// Get the input values (the two first columns)
double[,] inputs = sourceMatrix.GetColumns(0, 1);
// Get only the associated labels (last column)
int[] outputs = sourceMatrix.GetColumn(2).ToInt32();
AnalysisMethod method = (AnalysisMethod)cbMethod.SelectedValue;
// Creates the Kernel Principal Component Analysis of the given source
kpca = new KernelPrincipalComponentAnalysis(inputs, kernel, method);
// Whether to center in space
kpca.Center = cbCenter.Checked;
kpca.Compute(); // Finally, compute the analysis!
double[,] result;
if (kpca.Components.Count >= 2)
{
// Perform the transformation of the data using two components
result = kpca.Transform(inputs, 2);
}
else
{
result = kpca.Transform(inputs, 1);
result = result.InsertColumn(Matrix.Vector(result.GetLength(0), 0.0));
}
// Create a new plot with the original Z column
double[,] points = result.InsertColumn(sourceMatrix.GetColumn(2));
// Create output scatter plot
outputScatterplot.DataSource = points;
CreateScatterplot(graphMapFeature, points);
// Create output table
dgvProjectionResult.DataSource = new ArrayDataView(points, columnNames);
dgvReversionSource.DataSource = new ArrayDataView(kpca.Result);
// Populates components overview with analysis data
dgvFeatureVectors.DataSource = new ArrayDataView(kpca.ComponentMatrix);
dgvPrincipalComponents.DataSource = kpca.Components;
dgvProjectionComponents.DataSource = kpca.Components;
dgvReversionComponents.DataSource = kpca.Components;
cumulativeView.DataSource = kpca.Components;
distributionView.DataSource = kpca.Components;
numComponents.Maximum = kpca.Components.Count;
numNeighbor.Maximum = kpca.Result.GetLength(0);
numNeighbor.Value = System.Math.Min(10, numNeighbor.Maximum);
lbStatus.Text = "Good! Feel free to browse the other tabs to see what has been found.";
}
public void TransformTest4()
{
// Tested against R's kernlab
// test <- c(16, 117, 94, 132, 13, 73, 68, 129, 91, 50, 56, 12, 145, 105, 35, 53, 38, 51, 85, 116)
int[] test = { 15, 116, 93, 131, 12, 72, 67, 128, 90, 49, 55, 11, 144, 104, 34, 52, 37, 50, 84, 115 };
// data(iris)
double[,] iris =
{
#region Fisher's iris dataset
{ 5.1, 3.5, 1.4, 0.2, 0 },
{ 4.9, 3.0, 1.4, 0.2, 0 },
{ 4.7, 3.2, 1.3, 0.2, 0 },
{ 4.6, 3.1, 1.5, 0.2, 0 },
{ 5.0, 3.6, 1.4, 0.2, 0 },
{ 5.4, 3.9, 1.7, 0.4, 0 },
{ 4.6, 3.4, 1.4, 0.3, 0 },
{ 5.0, 3.4, 1.5, 0.2, 0 },
{ 4.4, 2.9, 1.4, 0.2, 0 },
{ 4.9, 3.1, 1.5, 0.1, 0 },
{ 5.4, 3.7, 1.5, 0.2, 0 },
{ 4.8, 3.4, 1.6, 0.2, 0 },
{ 4.8, 3.0, 1.4, 0.1, 0 },
{ 4.3, 3.0, 1.1, 0.1, 0 },
{ 5.8, 4.0, 1.2, 0.2, 0 },
{ 5.7, 4.4, 1.5, 0.4, 0 },
{ 5.4, 3.9, 1.3, 0.4, 0 },
{ 5.1, 3.5, 1.4, 0.3, 0 },
{ 5.7, 3.8, 1.7, 0.3, 0 },
{ 5.1, 3.8, 1.5, 0.3, 0 },
{ 5.4, 3.4, 1.7, 0.2, 0 },
{ 5.1, 3.7, 1.5, 0.4, 0 },
{ 4.6, 3.6, 1.0, 0.2, 0 },
{ 5.1, 3.3, 1.7, 0.5, 0 },
{ 4.8, 3.4, 1.9, 0.2, 0 },
{ 5.0, 3.0, 1.6, 0.2, 0 },
{ 5.0, 3.4, 1.6, 0.4, 0 },
{ 5.2, 3.5, 1.5, 0.2, 0 },
{ 5.2, 3.4, 1.4, 0.2, 0 },
{ 4.7, 3.2, 1.6, 0.2, 0 },
{ 4.8, 3.1, 1.6, 0.2, 0 },
{ 5.4, 3.4, 1.5, 0.4, 0 },
{ 5.2, 4.1, 1.5, 0.1, 0 },
{ 5.5, 4.2, 1.4, 0.2, 0 },
{ 4.9, 3.1, 1.5, 0.2, 0 },
{ 5.0, 3.2, 1.2, 0.2, 0 },
{ 5.5, 3.5, 1.3, 0.2, 0 },
{ 4.9, 3.6, 1.4, 0.1, 0 },
{ 4.4, 3.0, 1.3, 0.2, 0 },
{ 5.1, 3.4, 1.5, 0.2, 0 },
{ 5.0, 3.5, 1.3, 0.3, 0 },
{ 4.5, 2.3, 1.3, 0.3, 0 },
{ 4.4, 3.2, 1.3, 0.2, 0 },
{ 5.0, 3.5, 1.6, 0.6, 0 },
{ 5.1, 3.8, 1.9, 0.4, 0 },
{ 4.8, 3.0, 1.4, 0.3, 0 },
{ 5.1, 3.8, 1.6, 0.2, 0 },
{ 4.6, 3.2, 1.4, 0.2, 0 },
{ 5.3, 3.7, 1.5, 0.2, 0 },
{ 5.0, 3.3, 1.4, 0.2, 0 },
{ 7.0, 3.2, 4.7, 1.4, 1 },
{ 6.4, 3.2, 4.5, 1.5, 1 },
{ 6.9, 3.1, 4.9, 1.5, 1 },
{ 5.5, 2.3, 4.0, 1.3, 1 },
{ 6.5, 2.8, 4.6, 1.5, 1 },
{ 5.7, 2.8, 4.5, 1.3, 1 },
{ 6.3, 3.3, 4.7, 1.6, 1 },
{ 4.9, 2.4, 3.3, 1.0, 1 },
{ 6.6, 2.9, 4.6, 1.3, 1 },
{ 5.2, 2.7, 3.9, 1.4, 1 },
{ 5.0, 2.0, 3.5, 1.0, 1 },
{ 5.9, 3.0, 4.2, 1.5, 1 },
{ 6.0, 2.2, 4.0, 1.0, 1 },
{ 6.1, 2.9, 4.7, 1.4, 1 },
{ 5.6, 2.9, 3.6, 1.3, 1 },
{ 6.7, 3.1, 4.4, 1.4, 1 },
{ 5.6, 3.0, 4.5, 1.5, 1 },
{ 5.8, 2.7, 4.1, 1.0, 1 },
{ 6.2, 2.2, 4.5, 1.5, 1 },
{ 5.6, 2.5, 3.9, 1.1, 1 },
{ 5.9, 3.2, 4.8, 1.8, 1 },
{ 6.1, 2.8, 4.0, 1.3, 1 },
{ 6.3, 2.5, 4.9, 1.5, 1 },
{ 6.1, 2.8, 4.7, 1.2, 1 },
{ 6.4, 2.9, 4.3, 1.3, 1 },
{ 6.6, 3.0, 4.4, 1.4, 1 },
{ 6.8, 2.8, 4.8, 1.4, 1 },
{ 6.7, 3.0, 5.0, 1.7, 1 },
{ 6.0, 2.9, 4.5, 1.5, 1 },
{ 5.7, 2.6, 3.5, 1.0, 1 },
{ 5.5, 2.4, 3.8, 1.1, 1 },
{ 5.5, 2.4, 3.7, 1.0, 1 },
{ 5.8, 2.7, 3.9, 1.2, 1 },
{ 6.0, 2.7, 5.1, 1.6, 1 },
{ 5.4, 3.0, 4.5, 1.5, 1 },
{ 6.0, 3.4, 4.5, 1.6, 1 },
{ 6.7, 3.1, 4.7, 1.5, 1 },
{ 6.3, 2.3, 4.4, 1.3, 1 },
{ 5.6, 3.0, 4.1, 1.3, 1 },
{ 5.5, 2.5, 4.0, 1.3, 1 },
{ 5.5, 2.6, 4.4, 1.2, 1 },
{ 6.1, 3.0, 4.6, 1.4, 1 },
{ 5.8, 2.6, 4.0, 1.2, 1 },
{ 5.0, 2.3, 3.3, 1.0, 1 },
{ 5.6, 2.7, 4.2, 1.3, 1 },
{ 5.7, 3.0, 4.2, 1.2, 1 },
{ 5.7, 2.9, 4.2, 1.3, 1 },
{ 6.2, 2.9, 4.3, 1.3, 1 },
{ 5.1, 2.5, 3.0, 1.1, 1 },
{ 5.7, 2.8, 4.1, 1.3, 1 },
{ 6.3, 3.3, 6.0, 2.5, 2 },
{ 5.8, 2.7, 5.1, 1.9, 2 },
{ 7.1, 3.0, 5.9, 2.1, 2 },
{ 6.3, 2.9, 5.6, 1.8, 2 },
{ 6.5, 3.0, 5.8, 2.2, 2 },
{ 7.6, 3.0, 6.6, 2.1, 2 },
{ 4.9, 2.5, 4.5, 1.7, 2 },
{ 7.3, 2.9, 6.3, 1.8, 2 },
{ 6.7, 2.5, 5.8, 1.8, 2 },
{ 7.2, 3.6, 6.1, 2.5, 2 },
{ 6.5, 3.2, 5.1, 2.0, 2 },
{ 6.4, 2.7, 5.3, 1.9, 2 },
{ 6.8, 3.0, 5.5, 2.1, 2 },
{ 5.7, 2.5, 5.0, 2.0, 2 },
{ 5.8, 2.8, 5.1, 2.4, 2 },
{ 6.4, 3.2, 5.3, 2.3, 2 },
{ 6.5, 3.0, 5.5, 1.8, 2 },
{ 7.7, 3.8, 6.7, 2.2, 2 },
{ 7.7, 2.6, 6.9, 2.3, 2 },
{ 6.0, 2.2, 5.0, 1.5, 2 },
{ 6.9, 3.2, 5.7, 2.3, 2 },
{ 5.6, 2.8, 4.9, 2.0, 2 },
{ 7.7, 2.8, 6.7, 2.0, 2 },
{ 6.3, 2.7, 4.9, 1.8, 2 },
{ 6.7, 3.3, 5.7, 2.1, 2 },
{ 7.2, 3.2, 6.0, 1.8, 2 },
{ 6.2, 2.8, 4.8, 1.8, 2 },
{ 6.1, 3.0, 4.9, 1.8, 2 },
{ 6.4, 2.8, 5.6, 2.1, 2 },
{ 7.2, 3.0, 5.8, 1.6, 2 },
{ 7.4, 2.8, 6.1, 1.9, 2 },
{ 7.9, 3.8, 6.4, 2.0, 2 },
{ 6.4, 2.8, 5.6, 2.2, 2 },
{ 6.3, 2.8, 5.1, 1.5, 2 },
{ 6.1, 2.6, 5.6, 1.4, 2 },
{ 7.7, 3.0, 6.1, 2.3, 2 },
{ 6.3, 3.4, 5.6, 2.4, 2 },
{ 6.4, 3.1, 5.5, 1.8, 2 },
{ 6.0, 3.0, 4.8, 1.8, 2 },
{ 6.9, 3.1, 5.4, 2.1, 2 },
{ 6.7, 3.1, 5.6, 2.4, 2 },
{ 6.9, 3.1, 5.1, 2.3, 2 },
{ 5.8, 2.7, 5.1, 1.9, 2 },
{ 6.8, 3.2, 5.9, 2.3, 2 },
{ 6.7, 3.3, 5.7, 2.5, 2 },
{ 6.7, 3.0, 5.2, 2.3, 2 },
{ 6.3, 2.5, 5.0, 1.9, 2 },
{ 6.5, 3.0, 5.2, 2.0, 2 },
{ 6.2, 3.4, 5.4, 2.3, 2 },
{ 5.9, 3.0, 5.1, 1.8, 2 },
#endregion
};
// kpc <- kpca(~.,data=iris[-test,-5],kernel="rbfdot",kpar=list(sigma=0.2),features=2)
var data = iris.Remove(test, new[] { 4 });
var kernel = new Gaussian() { Gamma = 1 };
var kpc = new KernelPrincipalComponentAnalysis(data, kernel);
kpc.Compute(2);
var rotated = kpc.Result;
var pcv = kpc.ComponentMatrix;
var eig = kpc.Eigenvalues;
double[] expected_eig = { 28.542404060412132, 15.235596653653861 };
double[,] expected_pcv =
{
#region expected PCV without R's / m normalization
{ -0.0266876243479222, -0.00236424647855596 },
{ -0.0230827502249994, -0.00182207284533632 },
{ -0.0235846044938792, -0.00184417084258023 },
{ -0.0219741114149703, -0.00162806197434679 },
{ -0.0262369254935451, -0.00228351232176506 },
{ -0.0194129527129315, -0.00128157547584046 },
{ -0.0233710173690426, -0.00183018780267092 },
{ -0.0270621345426091, -0.00244551460941156 },
{ -0.01660360115437, -0.000759995006404066 },
{ -0.0241543595644871, -0.00200028851593623 },
{ -0.0229396684027426, -0.00178791975184668 },
{ -0.0141003945759371, -0.000349601250510858 },
{ -0.0122801944616023, -0.00011745003303124 },
{ -0.0195599909514198, -0.00123924882430174 },
{ -0.0267285199984888, -0.00237835151986576 },
{ -0.0164051441608544, -0.000826433392421186 },
{ -0.0241385103747907, -0.00196921837902471 },
{ -0.0228276819006861, -0.00190280719845395 },
{ -0.0250090125071634, -0.00212322482498387 },
{ -0.018268574949505, -0.00103729989327242 },
{ -0.0239555047501124, -0.00216590896337712 },
{ -0.0218837974825259, -0.00180921340210779 },
{ -0.0228699114274226, -0.00189079843025579 },
{ -0.0262414571955617, -0.00238666692022459 },
{ -0.02628286882499, -0.00232756740052467 },
{ -0.0261369413490628, -0.00229661111040973 },
{ -0.0237893959503383, -0.00195315162891338 },
{ -0.0237354902927562, -0.00197089686864334 },
{ -0.0234996712936547, -0.0019545398678434 },
{ -0.0179796342021205, -0.00100004281923827 },
{ -0.0143171193045046, -0.000421228427584423 },
{ -0.0241702773143143, -0.00196078350204665 },
{ -0.0215781675204649, -0.00158425565875557 },
{ -0.0174405137049866, -0.000872162100068597 },
{ -0.0268982927662575, -0.00242925852652081 },
{ -0.0261930727206913, -0.00227548913089953 },
{ -0.00807266421494459, 0.000505384268295841 },
{ -0.0189832707329651, -0.00111618515851182 },
{ -0.023789443724428, -0.00203239968623136 },
{ -0.0201457716377357, -0.00150731437393246 },
{ -0.0226387870826046, -0.00174799717649726 },
{ -0.0237772220904885, -0.00192536309172948 },
{ -0.0227864577886965, -0.00172757669197999 },
{ -0.0241368046325238, -0.00197147776349598 },
{ 0.0162307596401467, -0.00932217153629181 },
{ 0.00924104683890504, -0.0371256298132236 },
{ 0.0172460604733757, -0.00601678602419225 },
{ 0.0164784470762724, -0.00012129053123478 },
{ 0.00225808467595593, -0.0155701555363185 },
{ 0.0152659569368524, -0.00695503994803249 },
{ 0.00795619200816849, -0.034188555904496 },
{ 0.00255986394744671, -0.0156335839305463 },
{ 0.0157735235376026, -0.0339711483141172 },
{ 0.00860192955815661, -0.0310332456913026 },
{ 0.0188286198627367, -0.0143146603067418 },
{ 0.0081385823965042, -0.0358483794263587 },
{ 0.0131727085950618, -0.00748671161967017 },
{ 0.0150373592446138, -0.0269773780381651 },
{ 0.0126779242124717, -0.0162727482334416 },
{ 0.00983265072294127, -0.0416039968698012 },
{ 0.0162669562079483, -0.000151449934923387 },
{ 0.0137854766363786, -0.0375070307423622 },
{ 0.0170058660389757, -0.0184237621007135 },
{ 0.0154946725649067, -0.0227889410670457 },
{ 0.014708096275464, -0.011169199019916 },
{ 0.0135541309647514, 0.00627293040317239 },
{ 0.0153982178833786, 0.0228745884070871 },
{ 0.0186116855914761, -0.0238281923214434 },
{ 0.00661605660296714, -0.0332168101819555 },
{ 0.00812230548276198, -0.0380947707628449 },
{ 0.00704157480127114, -0.0353293378234606 },
{ 0.0118813500247593, -0.0433955442329169 },
{ 0.0168403649935284, 0.00717417511929008 },
{ 0.0144885311444922, -0.0128879186387195 },
{ 0.0148385454088314, 0.00481616750741218 },
{ 0.0127847825706042, -0.0211295878510692 },
{ 0.0126141523297424, -0.0394948238730571 },
{ 0.0105804278587419, -0.0411832808826231 },
{ 0.0185081272399827, -0.0181339486962481 },
{ 0.0124993892884636, -0.0434407731971394 },
{ 0.0135227934497893, -0.0415894662412569 },
{ 0.0136028421755366, -0.0388446289823116 },
{ 0.0144604273990706, -0.0404041262573942 },
{ 0.0165646866155949, -0.0294021220435322 },
{ 0.00146858312783178, -0.0134333124454357 },
{ 0.0137785343752508, -0.0429733697468562 },
{ 0.00510997410924024, 0.0292833047881736 },
{ 0.014720812085274, 0.00944264118212137 },
{ 0.00598583015620509, 0.038742545754176 },
{ 0.0125544895333347, 0.0349170237345097 },
{ 0.00140911493699792, 0.0164126558963803 },
{ 0.00546764790022381, -0.0140904440836446 },
{ 0.0029496609416271, 0.0249945804373137 },
{ 0.00769932014045035, 0.0313261912102264 },
{ 0.00266139821119332, 0.0231665860038695 },
{ 0.0147368620502789, 0.0315131740192214 },
{ 0.0149582869669828, 0.0314622232024109 },
{ 0.0106818628524054, 0.0443273862959601 },
{ 0.0123400540017047, 0.00422397833506881 },
{ 0.0101542521522688, 0.0157643916651046 },
{ 0.000660568495239385, 0.0087957765410289 },
{ 0.000634971613911479, 0.00896839373841372 },
{ 0.0119909422310846, -0.0019235494568038 },
{ 0.00742254354227651, 0.0421145349479265 },
{ 0.0130658707704511, 0.000658712215109605 },
{ 0.00103199141821948, 0.0130131637684367 },
{ 0.0180388007633923, 0.0112135357385706 },
{ 0.00879897568153878, 0.0428371609763469 },
{ 0.00466754803065601, 0.0321456973019424 },
{ 0.0188135431637204, 0.00458127473828957 },
{ 0.0184728744733845, 0.00843677964296344 },
{ 0.0055676853191067, 0.0305087649038716 },
{ 0.0033635667326866, 0.026834775073324 },
{ 0.0108405706484462, 0.0394739066547236 },
{ 0.0172770225385115, 0.0124967454210229 },
{ 0.0100507351970463, 0.0166565450918105 },
{ 0.00209404741665691, 0.0205532162586405 },
{ 0.0078782378323636, 0.0341148825697675 },
{ 0.0132731813046484, 0.0368540207320806 },
{ 0.0182550250587539, 0.000797957664175355 },
{ 0.0102561686092287, 0.0420705939254378 },
{ 0.00857331992305152, 0.0423810139397453 },
{ 0.00964648674506066, 0.0337591223497657 },
{ 0.014720812085274, 0.00944264118212137 },
{ 0.00659947194015947, 0.0404655648392282 },
{ 0.011337029514041, 0.0378339231578959 },
{ 0.0154602034267052, 0.0153085911335171 },
{ 0.0152371977428677, 0.0355309408870963 },
{ 0.0096520854263212, 0.0316677099444034 },
{ 0.016280981143395, 0.011860068380509 }
#endregion
};
Assert.IsTrue(Matrix.IsEqual(expected_eig, eig, 1e-10));
Assert.IsTrue(Matrix.IsEqual(expected_pcv, pcv, 1e-10));
double[,] irisSubset =
{
#region Iris subset for testing
{ 5.7, 4.4, 1.5, 0.4 },
{ 6.5, 3.0, 5.5, 1.8 },
{ 5.0, 2.3, 3.3, 1.0 },
{ 7.9, 3.8, 6.4, 2.0 },
{ 4.8, 3.0, 1.4, 0.1 },
{ 6.3, 2.5, 4.9, 1.5 },
{ 5.8, 2.7, 4.1, 1.0 },
{ 6.4, 2.8, 5.6, 2.1 },
{ 5.5, 2.6, 4.4, 1.2 },
{ 5.0, 3.3, 1.4, 0.2 },
{ 5.7, 2.8, 4.5, 1.3 },
{ 4.8, 3.4, 1.6, 0.2 },
{ 6.7, 3.3, 5.7, 2.5 },
{ 6.5, 3.0, 5.8, 2.2 },
{ 4.9, 3.1, 1.5, 0.2 },
{ 6.9, 3.1, 4.9, 1.5 },
{ 4.9, 3.6, 1.4, 0.1 },
{ 7.0, 3.2, 4.7, 1.4 },
{ 5.4, 3.0, 4.5, 1.5 },
{ 6.4, 3.2, 5.3, 2.3 },
#endregion
};
var testing = iris.Submatrix(test, new[] { 0, 1, 2, 3 });
Assert.IsTrue(Matrix.IsEqual(irisSubset, testing));
double[,] proj = kpc.Transform(testing);
double[,] expectedProjection =
{
#region expected projection without R's /m normalization
{ -0.262045246354652, 0.00522592803297944 },
{ 0.379100878015288, 0.588655883281293 },
{ 0.071459976634984, -0.256289120689712 },
{ 0.0208479105625222, 0.139976227370984 },
{ -0.634360697174036, -0.0253624940325211 },
{ 0.467841054198416, 0.0142078237631541 },
{ 0.3464723948387, -0.62695357333265 },
{ 0.327328144102457, 0.603762286061834 },
{ 0.351964514241981, -0.539035845068089 },
{ -0.759054821003877, -0.035920361137046 },
{ 0.449638018323254, -0.492049890038061 },
{ -0.732335083049923, -0.0341252836840602 },
{ 0.192183096200302, 0.580343336854431 },
{ 0.256170478557119, 0.639157216957949 },
{ -0.703212303846621, -0.0317868463626801 },
{ 0.3515430820112, 0.224868844202495 },
{ -0.722813976459246, -0.0325608519534802 },
{ 0.286990265042346, 0.102161459040097 },
{ 0.354904620698745, -0.390810675482863 },
{ 0.332125880099634, 0.566660263312128 }
#endregion
};
Assert.IsTrue(expectedProjection.IsEqual(proj, 1e-6));
}
private void button1_Click(object sender, EventArgs e)
{
// Finishes and save any pending changes to the given data
dgvAnalysisSource.EndEdit();
if (dgvAnalysisSource.DataSource == null) return;
// Creates a matrix from the source data table
double[,] sourceMatrix = (dgvAnalysisSource.DataSource as DataTable).ToMatrix(out sourceColumns);
int rows = sourceMatrix.GetLength(0);
int cols = sourceMatrix.GetLength(1);
// Creates a new Simple Descriptive Analysis
sda = new DescriptiveAnalysis(sourceMatrix, sourceColumns);
sda.Compute();
// Populates statistics overview tab with analysis data
dgvDistributionMeasures.DataSource = sda.Measures;
IKernel kernel;
if (rbGaussian.Checked)
{
kernel = new Gaussian((double)numSigma.Value);
}
else
{
kernel = new Polynomial((int)numDegree.Value, (double)numConstant.Value);
}
// Get only the input values (exclude the class label indicator column)
double[,] data = sourceMatrix.Submatrix(null, startColumn: 0, endColumn: 1);
// Get only the associated labels
int[] labels = sourceMatrix.GetColumn(2).ToInt32();
// Creates the Kernel Principal Component Analysis of the given source
kpca = new KernelPrincipalComponentAnalysis(data, kernel,
(AnalysisMethod)cbMethod.SelectedValue);
kpca.Center = cbCenter.Checked;
// Compute the analysis
kpca.Compute();
double[,] result;
if (kpca.Components.Count >= 2)
{
// Perform the transformation of the data using two components
result = kpca.Transform(data, 2);
}
else
{
result = kpca.Transform(data, 1);
result = result.InsertColumn(Matrix.Vector(result.GetLength(0), 0.0));
}
// Create a new plot with the original Z column
double[,] points = result.InsertColumn(sourceMatrix.GetColumn(2));
// Create output scatter plot
outputScatterplot.DataSource = points;
CreateScatterplot(graphMapFeature, points);
// Create output table
dgvProjectionResult.DataSource = new ArrayDataView(points, sourceColumns);
dgvReversionSource.DataSource = new ArrayDataView(kpca.Result);
// Populates components overview with analysis data
dgvFeatureVectors.DataSource = new ArrayDataView(kpca.ComponentMatrix);
dgvPrincipalComponents.DataSource = kpca.Components;
dgvProjectionComponents.DataSource = kpca.Components;
dgvReversionComponents.DataSource = kpca.Components;
numComponents.Maximum = kpca.Components.Count;
numNeighbor.Maximum = kpca.Result.GetLength(0);
numNeighbor.Value = System.Math.Min(10, numNeighbor.Maximum);
CreateComponentCumulativeDistributionGraph(graphCurve);
CreateComponentDistributionGraph(graphShare);
}
