NIPALS PCA and PLS package

This package implements the nonlinear iterative partial least squares (NIPALS) algorithm for principal component analysis (PCA) and partial least squares (PLS) regression. The perspective is to publish this joint package open source.

Nipals PCA

Implements the NIPALS algorithm for principal components analysis in python.

One of the most concise definitions can be found in this paper on page 7: Geladi, P.; Kowalski, B. R. Partial Least-Squares Regression: A Tutorial. Analytica Chimica Acta 1986, 185, 1–17. https://doi.org/10.1016/0003-2670(86)80028-9.

For the transformation part also see: Nelson, P. R. C.; Taylor, P. A.; MacGregor, J. F. Missing data methods in PCA and PLS: Score calculations with incomplete observations. Chemometrics and Intelligent Laboratory Systems 1996, 35(1), 45-65.

Nipals PLS

Implements the NIPALS algorithm for partial least squares regression in python.

Algorithm implemented from Chapter 6 of: Chiang, Leo H., Evan L. Russell, and Richard D. Braatz. Fault detection and diagnosis in industrial systems. Springer Science & Business Media, 2000.

Alternative algorithm derivation from: Geladi, P.; Kowalski, B. R. Partial Least-Squares Regression: A Tutorial. Analytica Chimica Acta 1986, 185, 1–17. https://doi.org/10.1016/0003-2670(86)80028-9.

For the transformation part also see: Nelson, P. R. C.; Taylor, P. A.; MacGregor, J. F. Missing data methods in PCA and PLS: Score calculations with incomplete observations. Chemometrics and Intelligent Laboratory Systems 1996, 35(1), 45-65.

Installation

1. Clone git repository
2. Open a command line
3. Navigate to git repository
4. Run pip install .

NOTE: if you plan on working on the package please see CONTRIBUTING.md for installation and environment setup instructions

Example usage

Preprocessing

Both the NipalsPCA and NipalsPLS classes expect a numpy array as an input with rows as samples and columns as features. Additionally, these array columns should have zero mean for best performance; typically this is done with a sklearn StandardScaler object.

Note: If the input data is a pandas dataframe, you can train an ArrangeData object which will ensure all future datasets come to the appropriate shape and column order.

from open_nipals.utils import ArrangeData
import pandas as pd
from sklearn.preprocessing import StandardScaler

# Load some arbitrary data
df = pd.read_csv('my_data.csv')

# Invoke preprocessing pipeline
arrdat = ArrangeData()
scaler = StandardScaler()

# Both scaler and arrdat should be saved for future use
data = scaler.fit_transform(arrdat.fit_transform(df))

# data is ready to model

Model fitting

The number of components can be specified as an argument to the constructor, with the default n_components=2. After fitting, components can be added by the set_components() method without having to fit the entire model again from scratch.

PCA

from open_nipals.nipalsPCA import NipalsPCA

# data is the numpy data matrix generated in the preprocessing
model = NipalsPCA()
transformed_data = model.fit_transform(X=data)

PLS

from open_nipals.nipalsPLS import NipalsPLS

# note the X/Y data blocks would need to have
# separate arrangeData and StandardScaler objects
model = NipalsPLS()
transformed_x_data, transformed_y_data = model.fit_transform(X=data_x, y=data_y)

Distances

In-model distances (IMD) and out-of-model distances (OOMD) can be calculated for both PCA and PLS models

# Must be scaled data
hotelling_t2 = model.calc_imd(input_array = data)

# also must be scaled, default metric is QResiduals or 'QRes'
dmodx = model.calc_oomd(input_array = data, metric = "DModX")

PLS prediction

One particular feature of PLS models is that they can predict dependent variables. To this end, run model.predict(), where either a matrix of X data input_x, or a matrix of X scores scores_x need to be given as arguments, e.g.

predicted_y_data = model.predict(X=data_x)