PartialLeastSquares 1.0.4

Consult the module API page at

https://engineering.purdue.edu/kak/distPLS/PartialLeastSquares-1.0.4.html

for all information related to this module, including that related to the latest changes to the code. The page at the URL shown above lists all of the module functionality you can invoke in your own code.

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 an implementation of the main Partial Least Squares (PLS) algorithm that can be used to make a multidimensional prediction from a multidimensional observation, 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 - pls.mean0X) * B  +  pls.mean0Y

where pls.mean0X is the column-wise mean of the X matrix and
pls.mean0Y the same for the Y matrix.