Partial Least Squares (PLS) is a powerful dimensionality reduction technique used to analyze relationships between two sets of variables, particularly in situations where the number of variables is greater than the number of observations and there is high collinearity between variables.

PLS has been widely applied in various fields, including genomics, proteomics, chemometrics, and computer vision. It has been extended and improved through several methods, such as penalized PLS, regularized PLS, and deep learning PLS. These advancements have addressed challenges like overfitting, nonlinearity, and scalability, making PLS more suitable for high-dimensional and large-scale datasets.

Recent research has focused on improving the efficiency and applicability of PLS. For instance, the Covariance-free Incremental Partial Least Squares (CIPLS) method enables PLS to be used on large datasets and streaming applications by processing one sample at a time. Another study introduced a unified parallel algorithm for regularized group PLS, making it scalable to big data sets.

Practical applications of PLS include image classification, face verification, and chemometrics. In image classification, CIPLS has outperformed other incremental dimensionality reduction techniques. In chemometrics, PLS has been used to model nonlinear regression problems and improve the accuracy of models for estimating elemental concentrations.

One company case study involves the use of PLS in predicting wine quality based on input characteristics. By incorporating deep learning within PLS, researchers were able to develop a nonlinear extension of PLS that provided better predictive performance and model diagnostics.

In conclusion, Partial Least Squares is a versatile and powerful technique for dimensionality reduction and data analysis. Its various extensions and improvements have made it more applicable to a wide range of problems and datasets, connecting it to broader theories in machine learning and data science.

# Partial Least Squares (PLS)

## Partial Least Squares (PLS) Further Reading

1.Penalized Partial Least Squares Based on B-Splines Transformations http://arxiv.org/abs/math/0608576v1 Nicole Kraemer, Anne-Laure Boulesteix, Gerhard Tutz2.Regularized Partial Least Squares with an Application to NMR Spectroscopy http://arxiv.org/abs/1204.3942v1 Genevera I. Allen, Christine Peterson, Marina Vannucci, Mirjana Maletic-Savatic3.Principal Model Analysis Based on Partial Least Squares http://arxiv.org/abs/1902.02422v1 Qiwei Xie, Liang Tang, Weifu Li, Vijay John, Yong Hu4.Classification of multivariate functional data on different domains with Partial Least Squares approaches http://arxiv.org/abs/2212.09145v2 Issam-Ali Moindjie, Sophie Dabo-Niang, Cristian Preda5.Deep Learning Partial Least Squares http://arxiv.org/abs/2106.14085v1 Nicholas Polson, Vadim Sokolov, Jianeng Xu6.Covariance-free Partial Least Squares: An Incremental Dimensionality Reduction Method http://arxiv.org/abs/1910.02319v2 Artur Jordao, Maiko Lie, Victor Hugo Cunha de Melo, William Robson Schwartz7.A Novel Multivariate Model Based on Dominant Factor for Laser-induced Breakdown Spectroscopy Measurements http://arxiv.org/abs/1012.2735v1 Zhe Wang, Jie Feng, Lizhi Li, Weidou Ni, Zheng Li8.A Unified Parallel Algorithm for Regularized Group PLS Scalable to Big Data http://arxiv.org/abs/1702.07066v1 Pierre Lafaye de Micheaux, Benoit Liquet, Matthew Sutton9.On some limitations of probabilistic models for dimension-reduction: Illustration in the case of probabilistic formulations of partial least squares http://arxiv.org/abs/2005.09498v2 Lola Etievant, Vivian Viallon10.Predictive Comparative QSAR analysis of Sulfathiazole Analogues as Mycobacterium Tuberculosis H37RV Inhabitors http://arxiv.org/abs/1402.5466v1 Doreswamy, Chanabasyya M. Vastrad## Partial Least Squares (PLS) Frequently Asked Questions

## What is PLS partial least squares?

Partial Least Squares (PLS) is a dimensionality reduction technique used to analyze relationships between two sets of variables, especially when the number of variables is greater than the number of observations and there is high collinearity between variables. It is widely applied in various fields, such as genomics, proteomics, chemometrics, and computer vision.

## What is partial least square PLS calibration?

Partial Least Squares (PLS) calibration is a process of building a PLS model using a set of known data points to predict the relationship between two sets of variables. This calibration process helps in understanding the underlying structure of the data and can be used for prediction, classification, or regression tasks.

## What is the difference between PCA and PLS?

Principal Component Analysis (PCA) and Partial Least Squares (PLS) are both dimensionality reduction techniques. The main difference between them is that PCA is an unsupervised method that focuses on reducing the dimensionality of a single dataset by finding the directions of maximum variance, while PLS is a supervised method that aims to find the relationship between two sets of variables by maximizing the covariance between them.

## What is partial least square PLS Python?

Partial Least Squares (PLS) in Python refers to the implementation of the PLS algorithm using Python programming language. There are several libraries available for implementing PLS in Python, such as scikit-learn and the PLS module in the Chemometrics toolbox.

## How does PLS handle multicollinearity?

PLS handles multicollinearity by finding latent variables that maximize the covariance between the two sets of variables. These latent variables are linear combinations of the original variables, which help in reducing the dimensionality and mitigating the effects of multicollinearity.

## What are some applications of PLS in machine learning?

Some practical applications of PLS in machine learning include image classification, face verification, chemometrics, and genomics. PLS has been used to model nonlinear regression problems, improve the accuracy of models for estimating elemental concentrations, and outperform other incremental dimensionality reduction techniques in image classification tasks.

## How can I implement PLS in Python?

To implement PLS in Python, you can use the scikit-learn library, which provides a PLSRegression class for PLS regression and a PLSCanonical class for PLS canonical analysis. You can install scikit-learn using pip and then import the required classes to build and train your PLS model.

## What are the limitations of PLS?

Some limitations of PLS include its sensitivity to noise, difficulty in handling nonlinearity, and potential overfitting when dealing with high-dimensional data. However, several extensions and improvements, such as penalized PLS, regularized PLS, and deep learning PLS, have been developed to address these challenges and make PLS more suitable for high-dimensional and large-scale datasets.

## How does PLS compare to other dimensionality reduction techniques?

PLS is a powerful and versatile technique for dimensionality reduction and data analysis. It is particularly useful when dealing with high-dimensional data and multicollinearity issues. Compared to other techniques like PCA, PLS is a supervised method that focuses on finding relationships between two sets of variables, making it more suitable for prediction, classification, and regression tasks. However, PLS may be more sensitive to noise and prone to overfitting than some other methods, depending on the specific problem and dataset.

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