/// <summary>
/// Creates a new linear regression from the regression coefficients.
/// </summary>
///
/// <param name="coefficients">The linear coefficients.</param>
/// <param name="intercept">The intercept (bias) values.</param>
///
/// <returns>A linear regression with the given coefficients.</returns>
///
public static MultivariateLinearRegression FromCoefficients(double[][] coefficients, double[] intercept)
{
var regression = new MultivariateLinearRegression(coefficients.Length, coefficients[0].Length);
regression.coefficients = coefficients.ToMatrix();
regression.intercepts = intercept;
return(regression);
}
/// <summary>
/// Creates a new linear regression directly from data points.
/// </summary>
///
/// <param name="x">The input vectors <c>x</c>.</param>
/// <param name="y">The output vectors <c>y</c>.</param>
///
/// <returns>A linear regression f(x) that most approximates y.</returns>
///
public static MultivariateLinearRegression FromData(double[][] x, double[][] y)
{
var regression = new MultivariateLinearRegression(x[0].Length, y[0].Length);
regression.Regress(x, y);
return(regression);
}
public void RegressTest()
{
double[][] X =
{
new double[] { 4.47 },
new double[] { 208.30 },
new double[] { 3400.00 },
};
double[][] Y =
{
new double[] { 0.51 },
new double[] { 105.66 },
new double[] { 1800.00 },
};
double eB = 0.5303528166;
double eA = -3.290915095;
var target = new MultivariateLinearRegression(1, 1, true);
target.Regress(X, Y);
Assert.AreEqual(target.Coefficients[0, 0], eB, 0.001);
Assert.AreEqual(target.Intercepts[0], eA, 0.001);
Assert.AreEqual(target.Inputs, 1);
Assert.AreEqual(target.Outputs, 1);
// Test manually including an constant term to generate an intercept
double[][] X1 =
{
new double[] { 4.47, 1 },
new double[] { 208.30, 1 },
new double[] { 3400.00, 1 },
};
var target2 = new MultivariateLinearRegression(2, 1, false);
target2.Regress(X1, Y);
Assert.AreEqual(target2.Coefficients[0, 0], eB, 0.001);
Assert.AreEqual(target2.Coefficients[1, 0], eA, 0.001);
Assert.AreEqual(target2.Inputs, 2);
Assert.AreEqual(target2.Outputs, 1);
}
public bool Learn()
{
try
{
this.Regression = this.ols.Learn(this.Inputs, this.Outputs);
this.IsTrained = true;
return(true);
}
catch (Exception e)
{
throw new Exception(
"Failed to learn using specified training data." + Environment.NewLine +
"Inner exception : " + e.Message
);
}
// return this as IAlgorithm;
}
public MultivariateLinearRegression()
{
this.Name = "Multivariate Linear Regression";
this.Type = AlgorithmType.Regression;
this.IsTrained = false;
this.PredictionType = typeof(double[][]);
this.ResultType = typeof(double[][]);
this.Inputs = null;
this.Outputs = null;
this.TestValue = null;
this.Result = null;
// initialise seed value for Accord framework
Generator.Seed = new Random().Next();
// set up linear regression using OrdinaryLeastSquares
this.Regression = new Accord.Statistics.Models.Regression.Linear.MultivariateLinearRegression();
this.ols = new OrdinaryLeastSquares();
}
public MultivariateLinearRegression GetPredictionModel(string userId)
{
var dataSet = this.trainings
.All()
.Where(x => x.UserId == userId)
.OrderByDescending(x => x.CreatedOn)
.Take(1000)
.ToArray();
var inputDataSet = new double[dataSet.Length][];
var outputDataSet = new double[dataSet.Length][];
int i = 0;
foreach (var dataSetTraining in dataSet)
{
var inputDataRow = new double[]
{
dataSetTraining.Track.Length,
dataSetTraining.Track.Ascent,
dataSetTraining.Track.AscentLength,
};
inputDataSet[i] = inputDataRow;
var duration = dataSetTraining.EndDate - dataSetTraining.StartDate;
var outputDataRow = new double[]
{
dataSetTraining.Calories,
dataSetTraining.Water,
duration.TotalHours
};
outputDataSet[i] = outputDataRow;
i++;
}
var regression = new MultivariateLinearRegression(3, 3);
double error = regression.Regress(inputDataSet, outputDataSet);
return regression;
}
/// <summary>
/// Construct a new Simple Linear Regression algorithm, using the specified training data.
/// </summary>
/// <param name="inputList">Use inputList as rows with equal numbers of featurs, which used for learning.</param>
/// <param name="outputList">Use outputList as the rows that define the result column for each</param>
public MultivariateLinearRegression(List <List <double> > inputList, List <List <double> > outputList)
{
Name = "Multivariate Linear Regression";
Type = AlgorithmType.Regression;
IsTrained = false;
PredictionType = typeof(double[][]);
ResultType = typeof(double[][]);
Inputs = null;
Outputs = null;
TestValue = null;
Result = null;
// initialise seed value for Accord framework
Generator.Seed = new Random().Next();
// Process training data
LoadTrainingData(inputList, outputList);
// set up linear regression using OrdinaryLeastSquares
regression = new Accord.Statistics.Models.Regression.Linear.MultivariateLinearRegression();
ols = new OrdinaryLeastSquares();
}
public List<Dish> CalculatePredictedRateForUnratedDishes(List<Rating> rates, List<Dish> unratedDishes)
{
List<Dish> recommendeDishes = new List<Dish>();
double[][] inputs = new double[rates.Count][];
double[][] outputs = new double[rates.Count][];
for (int i = 0; i < rates.Count; i++)
{
inputs[i] = rates[i].DishParameters;
outputs[i] = new double[] {rates[i].Rate};
}
MultivariateLinearRegression regression = new MultivariateLinearRegression(6, 1);
double errorRegression = regression.Regress(inputs, outputs);
foreach (var unratedDish in unratedDishes)
{
unratedDish.PredictedRate = regression.Compute(unratedDish.DishParameters)[0];
}
recommendeDishes.AddRange(unratedDishes.OrderByDescending(dish => dish.PredictedRate).ToList().Take(3));
return recommendeDishes;
}
public double[] CalculateParametersForUser(List<Rating> ratesAndParametersOfDishesRatedByUser)
{
double[][] inputs = new double[ratesAndParametersOfDishesRatedByUser.Count][];
double[][] outputs = new double[ratesAndParametersOfDishesRatedByUser.Count][];
for (int i = 0; i < ratesAndParametersOfDishesRatedByUser.Count; i++)
{
inputs[i] = ratesAndParametersOfDishesRatedByUser[i].DishParameters;
}
for (int i = 0; i < ratesAndParametersOfDishesRatedByUser.Count; i++)
{
outputs[i] = new double[] { ratesAndParametersOfDishesRatedByUser[i].Rate};
}
MultivariateLinearRegression regression = new MultivariateLinearRegression(6, 1);
double errorRegression = regression.Regress(inputs, outputs);
double[] coef = new double[6];
for (int k = 0; k < regression.Coefficients.Length; k++)
{
coef[k] = regression.Coefficients[k, 0];
}
return coef;
}
public void RegressTest2()
{
// The multivariate linear regression is a generalization of
// the multiple linear regression. In the multivariate linear
// regression, not only the input variables are multivariate,
// but also are the output dependent variables.
// In the following example, we will perform a regression of
// a 2-dimensional output variable over a 3-dimensional input
// variable.
double[][] inputs =
{
// variables: x1 x2 x3
new double[] { 1, 1, 1 }, // input sample 1
new double[] { 2, 1, 1 }, // input sample 2
new double[] { 3, 1, 1 }, // input sample 3
};
double[][] outputs =
{
// variables: y1 y2
new double[] { 2, 3 }, // corresponding output to sample 1
new double[] { 4, 6 }, // corresponding output to sample 2
new double[] { 6, 9 }, // corresponding output to sample 3
};
// With a quick eye inspection, it is possible to see that
// the first output variable y1 is always the double of the
// first input variable. The second output variable y2 is
// always the triple of the first input variable. The other
// input variables are unused. Nevertheless, we will fit a
// multivariate regression model and confirm the validity
// of our impressions:
// Create a new multivariate linear regression with 3 inputs and 2 outputs
var regression = new MultivariateLinearRegression(3, 2);
// Now, compute the multivariate linear regression:
double error = regression.Regress(inputs, outputs);
// At this point, the regression error will be 0 (the fit was
// perfect). The regression coefficients for the first input
// and first output variables will be 2. The coefficient for
// the first input and second output variables will be 3. All
// others will be 0.
//
// regression.Coefficients should be the matrix given by
//
// double[,] coefficients = {
// { 2, 3 },
// { 0, 0 },
// { 0, 0 },
// };
//
// The first input variable coefficients will be 2 and 3:
Assert.AreEqual(2, regression.Coefficients[0, 0], 1e-10);
Assert.AreEqual(3, regression.Coefficients[0, 1], 1e-10);
// And all other coefficients will be 0:
Assert.AreEqual(0, regression.Coefficients[1, 0], 1e-10);
Assert.AreEqual(0, regression.Coefficients[1, 1], 1e-10);
Assert.AreEqual(0, regression.Coefficients[2, 0], 1e-10);
Assert.AreEqual(0, regression.Coefficients[2, 1], 1e-10);
// We can also check the r-squared coefficients of determination:
double[] r2 = regression.CoefficientOfDetermination(inputs, outputs);
// Which should be one for both output variables:
Assert.AreEqual(1, r2[0]);
Assert.AreEqual(1, r2[1]);
foreach (var e in regression.Coefficients)
Assert.IsFalse(double.IsNaN(e));
Assert.AreEqual(0, error, 1e-10);
Assert.IsFalse(double.IsNaN(error));
}
/// <summary>
/// Creates a new linear regression directly from data points.
/// </summary>
///
/// <param name="x">The input vectors <c>x</c>.</param>
/// <param name="y">The output vectors <c>y</c>.</param>
///
/// <returns>A linear regression f(x) that most approximates y.</returns>
///
public static MultivariateLinearRegression FromData(double[][] x, double[][] y)
{
var regression = new MultivariateLinearRegression(x[0].Length, y[0].Length);
regression.Regress(x, y);
return regression;
}
private void btnRunAnalysis_Click(object sender, EventArgs e)
{
if (dgvAnalysisSource.DataSource == null)
{
MessageBox.Show("Please load some data first.");
return;
}
// Finishes and save any pending changes to the given data
dgvAnalysisSource.EndEdit();
DataTable table = dgvAnalysisSource.DataSource as DataTable;
// Creates a matrix from the source data table
double[,] sourceMatrix = table.ToMatrix(out inputColumnNames);
// Creates the Simple Descriptive Analysis of the given source
sda = new DescriptiveAnalysis(sourceMatrix, inputColumnNames);
sda.Compute();
// Populates statistics overview tab with analysis data
dgvDistributionMeasures.DataSource = sda.Measures;
// Extract variables
List<string> inputNames = new List<string>();
foreach (string name in clbInput.CheckedItems)
inputNames.Add(name);
this.inputColumnNames = inputNames.ToArray();
List<string> outputNames = new List<string>();
foreach (string name in clbOutput.CheckedItems)
outputNames.Add(name);
this.outputColumnNames = outputNames.ToArray();
DataTable inputTable = table.DefaultView.ToTable(false, inputColumnNames);
DataTable outputTable = table.DefaultView.ToTable(false, outputColumnNames);
double[,] inputs = inputTable.ToMatrix();
double[,] outputs = outputTable.ToMatrix();
// Creates the Partial Least Squares of the given source
pls = new PartialLeastSquaresAnalysis(inputs, outputs,
(AnalysisMethod)cbMethod.SelectedValue,
(PartialLeastSquaresAlgorithm)cbAlgorithm.SelectedValue);
// Computes the Partial Least Squares
pls.Compute();
// Populates components overview with analysis data
dgvWeightMatrix.DataSource = new ArrayDataView(pls.Weights);
dgvFactors.DataSource = pls.Factors;
dgvAnalysisLoadingsInput.DataSource = new ArrayDataView(pls.Predictors.FactorMatrix);
dgvAnalysisLoadingsOutput.DataSource = new ArrayDataView(pls.Dependents.FactorMatrix);
this.regression = pls.CreateRegression();
dgvRegressionCoefficients.DataSource = new ArrayDataView(regression.Coefficients, outputColumnNames);
dgvRegressionIntercept.DataSource = new ArrayDataView(regression.Intercepts, outputColumnNames);
dgvProjectionComponents.DataSource = pls.Factors;
numComponents.Maximum = pls.Factors.Count;
numComponents.Value = 1;
dgvRegressionComponents.DataSource = pls.Factors;
numComponentsRegression.Maximum = pls.Factors.Count;
numComponentsRegression.Value = 1;
CreateComponentCumulativeDistributionGraph(graphCurve);
CreateComponentDistributionGraph(graphShare);
dgvProjectionSourceX.DataSource = inputTable;
dgvProjectionSourceY.DataSource = outputTable;
dgvRegressionInput.DataSource = table.DefaultView.ToTable(false, inputColumnNames.Concatenate(outputColumnNames));
}
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);
}
