Partial Least Squares Regression (PLS)
Also known as: PLS regression, projection to latent structures, PLSR, kısmi en küçük kareler
Partial least squares regression predicts a response from many, often highly collinear predictors by projecting them onto a small set of latent components — but, unlike principal components regression, it chooses those components to maximize their covariance with the response, not just the variance of the predictors. This supervised dimension reduction makes PLS a workhorse in chemometrics, spectroscopy, and other wide-data settings where predictors vastly outnumber observations.
Key highlights
- Handles many, highly collinear predictors and the p ≫ n regime gracefully.
- Supervised components capture predictive signal in fewer dimensions than PCR.
- Provides interpretable latent components, scores, and loadings.
- Extends naturally to multiple response variables (PLS2).
Intuition
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How it works
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When to use it
Use PLS regression when you have many predictors that are strongly correlated or even more numerous than your observations (p ≫ n) — the classic situation in spectroscopy, chemometrics, genomics, and sensor data — and you want a stable predictive model from a few interpretable components. It typically needs fewer components than PCR because its directions are tuned to the response, and it handles multivariate responses naturally (PLS2). It assumes a roughly linear relationship and, being covariance-driven, is sensitive to predictor scaling, so standardization is standard practice. When predictors are few and well-conditioned, ordinary or penalized regression (ridge/lasso) is simpler and often preferable; PLS shines specifically in the wide, collinear regime.
Strengths & limitations
- Handles many, highly collinear predictors and the p ≫ n regime gracefully.
- Supervised components capture predictive signal in fewer dimensions than PCR.
- Provides interpretable latent components, scores, and loadings.
- Extends naturally to multiple response variables (PLS2).
- Assumes an approximately linear predictor-response relationship.
- Sensitive to scaling, so predictors must usually be standardized.
- The number of components must be tuned, typically by cross-validation.
- Latent components can be harder to interpret than original variables, and inference is less standard.
Common pitfalls
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Applications
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Frequently asked
How is PLS different from principal components regression?
Both reduce many predictors to a few components before regressing, but PCR chooses components by predictor variance alone (unsupervised), whereas PLS chooses them to maximize covariance with the response (supervised). Because PLS uses the target when forming components, it often needs fewer of them to reach the same predictive accuracy.
How many components should I keep?
The number of latent components is chosen by cross-validation — typically by selecting the number that minimizes cross-validated prediction error (often with a one-standard-error rule for parsimony). Too few components underfit; too many start to fit noise.
Why must I standardize the predictors?
PLS components maximize covariance, which depends on the scale of the predictors. Without standardization, variables measured on large scales dominate the components regardless of their relevance. Centring and scaling the predictors (and often the response) puts them on equal footing.
Sources
- 1.Wold, S., Sjöström, M., & Eriksson, L. (2001). PLS-regression: a basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58(2), 109–130.
- 2.Geladi, P., & Kowalski, B. R. (1986). Partial least-squares regression: a tutorial. Analytica Chimica Acta, 185, 1–17.
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ScholarGate. (2026, June 2). Partial Least Squares. ScholarGate. https://scholargate.app/machine-learning/partial-least-squares