PartialLeastSquaresAnalysis Class

[SerializableAttribute]
public class PartialLeastSquaresAnalysis : MultipleTransformBase<double[], double>, 
	IMultivariateRegressionAnalysis, IMultivariateAnalysis, IAnalysis, IProjectionAnalysis, ISupervisedLearning<MultivariateLinearRegression, double[], double[]>

<SerializableAttribute>
Public Class PartialLeastSquaresAnalysis
	Inherits MultipleTransformBase(Of Double(), Double)
	Implements IMultivariateRegressionAnalysis, IMultivariateAnalysis, IAnalysis, IProjectionAnalysis, 
	ISupervisedLearning(Of MultivariateLinearRegression, Double(), Double())

// 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
    new double[] {   7,     7,      13,        7 },
    new double[] {   4,     3,      14,        7 },
    new double[] {  10,     5,      12,        5 },
    new double[] {  16,     7,      11,        3 },
    new double[] {  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
    new double[] {           14,          7,                 8 },
    new double[] {           10,          7,                 6 },
    new double[] {            8,          5,                 5 },
    new double[] {            2,          4,                 7 },
    new double[] {            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. 
var pls = new PartialLeastSquaresAnalysis()
{
    Method = AnalysisMethod.Center,
    Algorithm = PartialLeastSquaresAlgorithm.SIMPLS
};

// Compute the analysis with all factors. The number of factors
// could also have been specified in a overload of this method.

var regression = pls.Learn(inputs, outputs);

// 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.Transform(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 }.