PartialLeastSquares 1.0.1

Version 1.0.1 includes a couple of CSV data files in the Examples directory that were inadvertently left out of Version 1.0 packaging of the module.

You may need this module if (1) you are trying to make multidimensional predictions from multidimensional observations; (2) the dimensionality of the observation space is large; and (3) the data you have available for constructing a prediction model is rather limited. The more traditional multiple linear regression (MLR) algorithms are likely to become numerically unstable under these conditions.

In addition to presenting the main Partial Least Squares (PLS) algorithm that can be used to make a multidimensional prediction from multidimensional data, this module also includes what is known as the PLS1 algorithm for the case when the predicted entity is just one-dimensional (as in, say, face recognition in computer vision).

Typical usage syntax:

In the notation that is typically used for describing PLS,
X denotes the matrix formed by multidimensional observations,
with each row of X standing for the values taken by all
the predictor variables.  And Y denotes the matrix
formed by the values for the predicted variables. Each
row of Y corresponds to the prediction that can be made on
the basis of the corresponding row of X.  Let's say that
you have some previously collected data for the X and Y
matrices in the form of CSV records in disk files. Given
these X and Y, you would want to calculate the matrix B of
regression coefficients with this module.  Toward that end,
you can make the following calls in your script:

    import PartialLeastSquares as PLS

    XMatrix_file = "X_data.csv"
    YMatrix_file = "Y_data.csv"

    pls = PLS.PartialLeastSquares(
            XMatrix_file =  XMatrix_file,
            YMatrix_file =  YMatrix_file,
            epsilon      = 0.0001,
          )
   pls.get_XMatrix_from_csv()
   pls.get_YMatrix_from_csv()
   B = pls.PLS()

The object B returned by the last call will be a numpy matrix
consisting of the calculated regression coefficients.  Let's say
that you now have a matrix Xtest of new data for the predictor
variables.  All you have to do to calculate the values for the
predicted variables is

   Ytest =  Xtest * B