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PartialLeastSquares 1.0

A Python module for regression and classification with the Partial Least Squares algorithm

Latest Version: 1.0.3

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 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 typical PLS notation, X denotes the matrix formed by
multidimensional observation vectors, with each row of X standing
for the values taken by all the predictor variables.  And Y denotes
the matrix formed by the multidimensional prediction vectors. 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 the
observed data for the X and the Y matrices in the form of CSV
records in disk files. Your goal is to calculate the matrix B of
regression coefficients with this module.  All you have to do is
make the following calls:

    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,
   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 data for the predictor
variables.  All you have to do to calculate the values for the
predicted variables is

   Ytest =  Xtest * B
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