// 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.

    double[,] inputs =
    {
    // 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.

    double[,] outputs =
    {
        // 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.NIPALS);

    // 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 { 13.98, 7.00, 7.75 }.