private void btnRegress_Click(object sender, EventArgs e)
{
if (pls == null || dgvRegressionInput.DataSource == null)
{
MessageBox.Show("Please compute the analysis first.");
return;
}
int components = (int)numComponentsRegression.Value;
regression = pls.CreateRegression(components);
DataTable table = dgvRegressionInput.DataSource as DataTable;
DataTable inputTable = table.DefaultView.ToTable(false, inputColumnNames);
DataTable outputTable = table.DefaultView.ToTable(false, outputColumnNames);
double[][] sourceInput = Matrix.ToArray(inputTable as DataTable);
double[][] sourceOutput = Matrix.ToArray(outputTable as DataTable);
double[,] result = Matrix.ToMatrix(regression.Compute(sourceInput));
double[] rSquared = regression.CoefficientOfDetermination(sourceInput, sourceOutput, cbAdjusted.Checked);
dgvRegressionOutput.DataSource = new ArrayDataView(result, outputColumnNames);
dgvRSquared.DataSource = new ArrayDataView(rSquared, outputColumnNames);
}
public void SimplsRegressionTest()
{
double[,] inputs;
double[,] outputs;
var pls = CreateWineExample(out inputs, out outputs);
MultivariateLinearRegression regression = pls.CreateRegression();
// test regression intercepts
double[] intercepts = regression.Intercepts;
double[] expectedI = { 60.717, -8.509, -4.362 };
Assert.IsTrue(intercepts.IsEqual(expectedI, 0.01));
// test regression coefficients
double[,] coefficients = regression.Coefficients;
double[,] expectedC =
{
{ -1.6981, -0.0566, 0.07075 },
{ 1.2735, 0.2924, 0.57193 },
{ -4.0000, 1.0000, 0.50000 },
{ 1.1792, 0.1226, 0.15919 }
};
Assert.IsTrue(coefficients.IsEqual(expectedC, 0.01));
// Test computation
double[][] aY = regression.Compute(inputs.ToArray());
for (int i = 0; i < outputs.GetLength(0); i++)
{
for (int j = 0; j < outputs.GetLength(1); j++)
{
double actualOutput = aY[i][j];
double expectedOutput = outputs[i, j];
double delta = System.Math.Abs(actualOutput - expectedOutput);
double tol = 0.21 * expectedOutput;
Assert.IsTrue(delta <= tol);
}
}
}
public override ConfusionMatrix Execute()
{
//The Least Squares algorithm
//It uses a PartialLeastSquaresAnalysis library object using a non-linear iterative partial least squares algorithm
//and runs on the mean-centered and standardized data
//Create an analysis
var pls = new PartialLeastSquaresAnalysis(trainingSet,
trainingOutput,
AnalysisMethod.Standardize,
PartialLeastSquaresAlgorithm.NIPALS);
pls.Compute();
//After computing the analysis
//create a linear model to predict new variables
MultivariateLinearRegression regression = pls.CreateRegression();
//This will hold the result of the classifications
var predictedLifted = new int[testSet.GetLength(0)][];
for (int i = 0; i < predictedLifted.Length; ++i)
{
predictedLifted[i] = regression
.Compute(testSet.GetRow(i)) //Retrieve the row vector of the test set
.Select(x => Convert.ToInt32(x)) // Convert the result to int
.ToArray();
}
//Unlift the prediction vector
var predicted = predictedLifted
.SelectMany(x => x)
.ToArray();
//Create a new confusion matrix with the calculated parameters
ConfusionMatrix cmatrix = new ConfusionMatrix(predicted, expected, POSITIVE, NEGATIVE);
return(cmatrix);
}
private static PartialLeastSquaresAnalysis CreateWineExample(out double[,] inputs, out double[,] outputs)
{
// References: http://www.utdallas.edu/~herve/Abdi-PLSR2007-pretty.pdf
// Following the small example by Hervé Abdi (Hervé Abdi, Partial Least Square Regression),
// we will create a simple example where the goal is to predict the subjective evaluation of
// a set of 5 wines. The dependent variables that we want to predict for each wine are its
// likeability, and how well it goes with meat, or dessert (as rated by a panel of experts).
// The predictors are the price, the sugar, alcohol, and acidity content of each wine.
// Here we will list the inputs, or characteristics we would like to use in order to infer
// information from our wines. Each row denotes a different wine and lists its corresponding
// observable characteristics. The inputs are usually denoted by X in the literature.
inputs = new double[, ]
{
// Wine | Price | Sugar | Alcohol | Acidity
{ 7, 7, 13, 7 },
{ 4, 3, 14, 7 },
{ 10, 5, 12, 5 },
{ 16, 7, 11, 3 },
{ 13, 3, 10, 3 },
};
// Here we will list our dependent variables. Dependent variables are the outputs, or what we
// would like to infer or predict from our available data, given a new observation. The outputs
// are usually denotes as Y in the literature.
outputs = new double[, ]
{
// Wine | Hedonic | Goes with meat | Goes with dessert
{ 14, 7, 8 },
{ 10, 7, 6 },
{ 8, 5, 5 },
{ 2, 4, 7 },
{ 6, 2, 4 },
};
// Next, we will create our Partial Least Squares Analysis passing the inputs (values for
// predictor variables) and the associated outputs (values for dependent variables).
// We will also be using the using the Covariance Matrix/Center method (data will only
// be mean centered but not normalized) and the NIPALS algorithm.
PartialLeastSquaresAnalysis pls = new PartialLeastSquaresAnalysis(inputs, outputs,
AnalysisMethod.Center, PartialLeastSquaresAlgorithm.SIMPLS);
// Compute the analysis with all factors. The number of factors
// could also have been specified in a overload of this method.
pls.Compute();
// After computing the analysis, we can create a linear regression model in order
// to predict new variables. To do that, we may call the CreateRegression() method.
MultivariateLinearRegression regression = pls.CreateRegression();
// After the regression has been created, we will be able to classify new instances.
// For example, we will compute the outputs for the first input sample:
double[] y = regression.Compute(new double[] { 7, 7, 13, 7 });
// The y output will be very close to the corresponding output used as reference.
// In this case, y is a vector of length 3 with values { 14.00, 7.00, 7.75 }.
Assert.AreEqual(14.00, y[0], 1e-2);
Assert.AreEqual(+7.00, y[1], 1e-2);
Assert.AreEqual(+7.75, y[2], 1e-2);
return(pls);
}
