The PLS regression (Partial Least Squares): The pillar of chemometrics. Behind this somewhat formal formula, there is a tool that has already saved me entire analytical campaigns. From my first calibrations in spectroscopy to the models deployed in the factory, I always return to this approach. It knows how to extract the essential when signals overlap, when variables are numerous, and when one expects a reliable and interpretable result. In this guide, I show you how I use PLS on a daily basis, where it shines, and how to avoid the most common traps, without unnecessary jargon but with concrete examples. Yes, PLS is the pillar, and it deserves a central place in your projects.
The PLS regression (Partial Least Squares): the pillar of chemometrics in everyday practice
When I teach PLS, I start with a simple gesture: projecting X and y into a common factor space. We talk about partial least squares. The algorithm builds components that summarize X while maximizing the covariance with the response. It is not an “blind” dimensionality reduction; it is a prediction-oriented reduction. We obtain latent variables that carry directly the information useful to estimate properties (humidity, content of active ingredient, sensory quality…). This logic fits perfectly with modern, dense, and correlated analytical data, notably coming from NIR spectroscopy.
What PLS regression solves in the laboratory
In spectral matrices, everything gets mixed. Bands overlap, baselines drift, and one ends up with thousands of descriptors for a few dozen samples. PLS holds up against multicollinearity by condensing the useful information into a few factors. It also handles several responses simultaneously if needed, for example moisture and lipid content measured at once, via PLS1 (one response) or PLS2 (multiple responses). This flexibility allows us to move quickly while remaining faithful to the physico-chemical reality of the samples.
A field memory
On a granulation line, our laboratory measurements arrived with a 24-hour delay. A PLS trained on a historical batch enabled monitoring the active ingredient content in near real time. The model wasn’t perfect, but it reduced the variability by 30% in the first week. This transition gave the team confidence, and allowed us to calmly investigate the remaining deviations.
Choosing the number of components in PLS regression without getting it wrong
The classic dilemma: too few factors, underfit; too many factors, you mold the noise. I always proceed with rigorous cross-validation, by blocks when samples are time-correlated. I watch the error curve and its stable minimum, often combining two indicators like the RMSEP and the R². When both converge, the decision becomes obvious. If the difference between two factor values is marginal, I favor the simpler model.
Keep a cool head
Explosive calibration performances can hide overfitting. I recommend keeping an external test set aside from the very start. PLS is robust, but it does not escape selection bias. When stability is critical, periodic re-estimation with a sliding window avoids drift while capitalizing on new samples.
Preprocessings and variables: PLS gains with clean data
Before modeling, I tackle artifacts. A good spectral preprocessing often makes the difference between a fragile model and an industrial tool. Depending on the context, I combine normalization, baseline correction, derivatives, or smoothing. For heterogeneous matrices, SNV eliminates the diffusion effect; for extracting fine bands, the derivative of Savitzky–Golay reveals structures otherwise invisible. These steps are tested methodically, not by instinct, and always with a validation protocol coherent with the final use.
Need a structured refresher on these upstream steps? A clear synthesis is available here: Spectral data preprocessing, crucial step. And to place latent components in the landscape of methods, this PCA guide will help you link the dots: Understanding PCA in chemometrics.
Practitioner tip
- Avoid stacking too many transformations. Two or three well-chosen operations are worth more than an opaque stack.
- Validate preprocessing by batch; a decision made on three representative samples will pay off in the next series.
- Document every step to make models auditable and transferable.
Interpreting a PLS regression: beyond prediction
PLS is not a black box. The weights, loadings and contributions tell a story. The variables that “pull” the prediction are identified via the VIP and the coefficients. I like to cross-check this information with chemistry: a band near a known vibration that rises across all concentrated samples, that’s a credible signal; a variable isolated at the edge of the spectrum that explains a lot on its own, caution. The aim is not to recreate a spectroscopy course, but to verify that the model breathes the physics of the samples.
Map the domain of application
The PLS scores help visualize where your samples lie relative to the training space. A low density in a region informs about a lack of representativity. Statistical checks on the distance in the latent space secure routine use. This mapping also facilitates discussions with production or quality control.
PLS vs alternatives: PCR, ridge regression and networks
I often use this table when choosing a method. It does not replace empirical tests, but it provides a simple framework to decide quickly.
| Method | Key idea | Typical usage | Strengths | Limitations |
|---|---|---|---|---|
| PLS | Factors oriented toward y | Spectra, processes, multi-response | Strong with correlated variables, interpretable | Requires a choice of factors and solid validation |
| PCR | PCA followed by regression | Exploration, robust baseline | Simple, clear separation between X and the model | Factors not optimized for y, sometimes less accurate |
| Ridge/Lasso | Coefficient penalization | Tabular data, moderate noise | Control of overfitting, selection (Lasso) | Less natural for continuous spectra |
A word on networks
Deep models can shine on large volumes and with stable sensors. For our limited series, with aging instruments and changing lots, PLS often preserves the advantage of the precision/interpretablity/cost ratio. Nothing prevents hybridization: careful preprocessing, basic PLS, then a local nonlinear model for edge cases. The essential thing remains traceability.
Best practices for deploying PLS in production
Moving from the lab to the plant is a different sport. You gain in responsiveness and volume, but you lose a bit of control. Here is the protocol I apply to turn a proof of concept into a robust tool.
Design
- Define early the domain of application (raw materials, temperature ranges, operators, maintenance).
- Plan recalibration samples: seasonality, secondary suppliers, formulation changes.
- Decide acceptance metrics at startup and in routine, with pragmatic limits.
Implementation
- Lock the preprocessing chain on the instrument side and on the software side to avoid divergences.
- Install integrity controls (metadata, versions, sensors) and drift alarms.
- Train the teams; no need for a full course, but a clear understanding of the levers and limits.
Model lifecycle
- Monitor error on a control chart; trigger a re-estimation when a threshold is sustainably breached.
- Archive out-of-domain samples to feed the next version.
- Test backward compatibility before any update and document the production deployment.
« The best PLS models are often modest on paper and heroic in the field. » I say this after having seen record calibrations collapse at the first change in ambient humidity.
The PLS regression (Partial Least Squares): a roadmap to go further
If you’re just starting, begin with a clear setup, a simple property, parsimonious preprocessing, then a selection of factors by cross-validation. Add a properly conducted external test apart. Explore the curves of RMSEP, the coefficients, and check the stability regions of the R². Avoid the temptation to “gain” 0.01 in error at the expense of unnecessary complexity. Once the foundation is solid, introduce targeted refinements.
Paths for deeper exploration that are worth the effort
- Advanced interpretation via VIP and variable selection to reduce unnecessary variance.
- Controlled experiments on SNV and derivative of Savitzky–Golay to boost signal separability.
- Multi-response models with PLS2 when chemical coherence between properties yields a gain.
In my courses, I always take a detour through PCA so that the notion of factors is intuitive. If it’s not yet clear, take a look at this concise reminder: PCA, its scores and its loadings. Then return to PLS with a fresh, prediction-oriented view.
Quick checklist before publishing a model
- External test set locked, representative of the usage domain.
- Documented preprocessing, batch-tested and verified under real conditions.
- Number of factors chosen by stable criteria, not opportunism.
- Traceability of versions, instrument metrology aligned with the maintenance schedule.
- Routine monitoring plan, shared thresholds and decision rules.
Final professorial remark, drawn from long evenings with capricious spectra: PLS rewards discreet rigor. A clear calibration protocol, data cleaned with tact, transparent decisions, and you have a model that accompanies the workshop without making noise. It is this type of tool that truly changes the lives of teams. Your turn, and if needed, return to the fundamentals of preprocessing to further consolidate the base.