Multivariate Curve Resolution in Analytical Chemistry

Multivariate curve resolution (MCR) encompasses a suite of chemometric methods designed to deconvolute overlapping analytical signals into pure component spectra and concentration profiles without prior separation. By exploiting the bilinear structure of spectroscopic, chromatographic or imaging data, MCR enables qualitative and quantitative analysis in complex mixtures. The alternating least squares (ALS) algorithm lies at the heart of most implementations, imposing constraints such as non-negativity, unimodality or closure to yield chemically meaningful results. MCR has found widespread application across environmental monitoring, pharmaceutical quality control, food safety and materials science, offering a pragmatic means to extract hidden information, enhance instrument performance and reduce reliance on physical separation steps.

Research from Nature Portfolio

Recent studies have demonstrated the power of combining algorithmic advances with conventional instrumentation to exceed classical limits. In one seminal work, super-resolution concepts were merged with an MCR-ALS framework in confocal Raman imaging, boosting spatial resolution by approximately 65% beyond the diffraction limit. This approach enabled characterisation of individual atmospheric aerosol particles at sub-micrometre scale, revealing heterogeneous chemical distributions and providing new insight into particle-level processes. The study illustrates how chemometric resolution can transform standard spectroscopic measurements into high-definition chemical maps without hardware modification.

Multivariate Curve Resolution in Analytical Chemistry publication trend

The graph below shows the total number of articles in multivariate curve resolution in analytical chemistry across all publications each year (not limited to Nature Index journals).

Technical terms

Multivariate curve resolution (MCR): Bilinear decomposition technique that extracts pure component spectral and concentration profiles from composite data arrays.

Alternating least squares (ALS): Iterative optimisation algorithm that alternately refines component concentration scores and spectral profiles under specified constraints.

Second‐order advantage: Capability of multi-way calibration methods to quantify analytes accurately despite the presence of uncalibrated interferents by exploiting three-way data structures.

Non-negativity constraint: Mathematical requirement ensuring that resolved component spectra and concentration values remain physically plausible by precluding negative amplitudes.

References

1. Modeling soil organic carbon content using mid-infrared absorbance spectra and a nonnegative MCR-ALS analysis. Soil & Environmental Health (2025).
2. Pushing back the limits of Raman imaging by coupling super-resolution and chemometrics for aerosols characterization. Scientific Reports (2015).
3. Chromatographic Applications in the Multi-Way Calibration Field. Molecules (2021).
4. Simultaneous Determination of Drugs Affecting Central Nervous System (CNS) in Bulk and Pharmaceutical Formulations Using Multivariate Curve Resolution‐Alternating Least Squares (MCR‐ALS). Journal of Analytical Methods in Chemistry (2020).