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Procrustes cross-validation for Python

Package prcv implements Procrustes cross-validation in Python language.

Last main version of the package was released in August, 2023 and contains small improvements, better test coverage, as well as a new experimental feature — CV scope. See details in the overall project description.

Getting started

You can install the package directly from PyPI by running pip install prcv. If you already have the package installed and want to upgrade it to the newest version use: pip install prcv --upgrade

There are three main functions in the package:

  • pcvpca() is implementation of PCV for PCA/SIMCA models.

  • pcvpcr() is implementation of PCV for PCR models.

  • pcvpls() is implementation of PCV for PLS models.

All three functions return PV-set generated with given parameters. The PV-set has the same size as the calibration set. In case of regression (PCR or PLS) PV-set is generated only for predictors (X), the response values for PV-set are the same as for the calibration set.

The last two functions return the PV-set and an additional outcome, D, which is a matrix (2D Numpy array) containing scaling factors ($c_k/c$), for each segment and each component. See all details in the paper.

Below are examples of the function syntax with main parameters:

from prcv.methods import pcvpca, pcvpcr, pcvpls

# set cross-validation settings — common for all methods above
cv = {'type': 'ven', 'nseg': 4}

# for PCA/SIMCA models
Xpv = pcvpca(X, ncomp = 20, center = True, scale = False, cv = cv)

# for PCR models
Xpv, D = pcvpcr(X, Y, ncomp = 20, center = True, scale = False, cv = cv)

# for PLS models
Xpv, D = pcvpls(X, Y, ncomp = 20, center = True, scale = False, cv = cv)

Here X is a matrix with predictors for your calibration set (2D Numpy array). In case of regression model you also need to provide an array with response values for the training set, Y. The method generates PV-set only for predictors, the response values for the calibration set and for the PV-set are the same.

Parameter ncomp is a number of principal components in case of PCA/PCR models or number of latent variables in case of PLS based method. Number of components must be large enough, larger than the expected optimal number. In case of PCA use components which explain at least 99% of the data.

Parameters center and scale define if columns of X and Y should be mean centered and/or standardized. By default center = True and scale = False. Regardless which settings you use, the resulted PV-set will be in original units (uncentered and unstandardized), so you can compare it directly with the calibration set.

Finally, parameter cv defines how to split the rows of the training set. The split is similar to cross-validation splits, as PCV is based on cross-validation resampling. This parameter can have the following values:

  • A dictionary with 2 field: 'type' and 'nseg'. In this case 'type' defines the way to make the splits. You can select one of the following: 'loo' for leave-one-out, 'rand' for random splits or 'ven' for Venetian blinds (systematic) splits. The second field, 'nseg', should be a number of segments for splitting the rows into. For example, cv = {'type': 'ven', 'nseg': 4}, shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.

  • A vector with integer numbers, e.g. cv = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3], dtype = 'int'). In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. For the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.

As it is written above there is also additional parameter, cvscope, which can have one of the two values, 'global' or 'local'. The default value is 'global', if you want to try the local scope, just add this parameter when you call one of the functions, like shown below (in this example some of the arguments are skipped for simplicity):

# PCV for PLS models with local CV scope
Xpv, D = pcvpls(X, Y, ncomp = 20,  cv = {'type': 'ven', 'nseg': 4}, cvscope = 'local')

Directory demo, which is available from GitHub repository, contains several files with dataset and demo code. Thus file corn.csv contains Corn dataset used in the paper in Coma Separated Values format. File demo.py contains script with demo code and file demo.ipynb contains the same code but made as a Jupyter notebook. File misc.py contains several helper functions for the demo code, which are used in both the script and the notebook.

Download all files and make sure all files are located in the same folder in order to run the code.

The package code will be improved and extended gradually. If you found a bug please report using issues or send an email.