VB PLS1 Scores And Loadings Example

Imports System

Imports CenterSpace.NMath.Core


Namespace CenterSpace.NMath.Examples.VisualBasic

  A .NET example in Visual Basic showing Partial Least Squares (PLS) with scores
  and loadings.

  In chemometrics one often wishes to know the chemical composition of a
  sample of, say, a gas or liquid. One common technique is to study the absorption
  spectrum of light passing through the sample. Partial Least Squares (PLS) 
  is often used to construct a predictive model in this situation. Suppose we 
  wish to measure the concentration of a constituent in the
  substance and that we look at n different absorption spectra (an absorption
  spectra measures the amount of light absorbed at each wavelength). Pick p
  different wavelengths in the absorption spectra and let A = {aij} be the 
  be the nxp matrix where aij is the absorption measurement at the jth 
  wavelength in the ith sample. And let C = {ci} be the m vector where
  ci is the concentration of the constituent in the ith sample.
  This example constructs a predictive model for C given A using PLS. In
  particular the scores and loadings for the response variable, C, and the
  predictor variable, A, are examined.

  Module PLS1ScoresAndLoadingsExample

    Sub Main()

      Dim Rng As New RandGenUniform(124)
      Rng.LowerBound = 0.1
      Rng.UpperBound = 1.1
      Dim N As Integer = 7 number of samples (spectra)
      Dim P As Integer = 10 number of data points (wavelength)
      Dim F As Integer = 4  number of PLS eigenvectors

      Dim A As New DoubleMatrix(N, P, Rng) spectral absorbances
      Dim C As New DoubleVector(N, Rng)    constituent concentrations
      Dim PLS As New PLS1()

      Console.WriteLine()
      Console.WriteLine("Performing calculation...")
      PLS.Calculate(A, C, F)

      Console.WriteLine()
      Console.WriteLine("Is it good? " & PLS.IsGood)
      Console.WriteLine()

      Dim ALG = DirectCast(PLS.Calculator, PLS1NipalsAlgorithm)

      Get the spectral scores
      Dim S As DoubleMatrix = ALG.Scores
      Console.WriteLine()
      Console.WriteLine("Spectral Scores ------------------------------")
      Console.WriteLine()

      For I As Integer = 0 To (F - 1)
        Console.Write("spectral score ")
        Console.WriteLine(I)
        Console.WriteLine(S.Col(I).ToString("G5"))
        Console.WriteLine()
      Next
      Console.WriteLine()

      Get spectral loadings
      Dim Bx As DoubleMatrix = ALG.Loadings
      Console.WriteLine("Spectral Loadings ------------------------------")
      Console.WriteLine()

      For I As Integer = 0 To (F - 1)
        Console.Write("spectral loading ")
        Console.WriteLine(I)
        Console.WriteLine(Bx.Col(I).ToString("G5"))
        Console.WriteLine()
      Next
      Console.WriteLine()

      Predict the constituent concentrations from a vector of spectral responses.
      The regression vector, r, can be used for prediction as follows:
      Let Cu be the predicted concentration for the spectral response
      vector Au, let Abar the mean of the spectral data and Cbar be the mean
      of the concentrations data used to create the model. Then
      / Cu = Cbar + (Au - Abar)r.
      Dim Au As New DoubleVector(P, Rng) spectral responses
      Dim CBar As Double = ALG.ResponseMean
      Dim Abar As DoubleVector = ALG.PredictorMean
      Dim R As DoubleVector = ALG.RegressionVector

      Dim CU As Double = CBar + NMathFunctions.Dot((Au - Abar), R)
      Console.WriteLine()
      Console.WriteLine("Prediction Using Regression Vector ------------------")
      Console.WriteLine()
      Console.WriteLine("Predicted concentrations for spectral response ")
      Console.WriteLine()
      Console.WriteLine(Au.ToString("G5"))
      Console.WriteLine()
      Console.WriteLine("is")
      Console.WriteLine()
      Console.WriteLine(CU)

      Console.WriteLine()
      Console.WriteLine("Press Enter Key")
      Console.Read()

    End Sub
  End Module
End Namespace