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Principal component analysis and near infrared (NIR) spectroscopy

White paper from FOSS shows how PCA and NIR spectroscopic data make a perfect fit.

A driving force in the development of chemometrics since the 1970s, NIR spectroscopy (NIR) measures the overtones and combination tones of the fundamental molecular vibrations in the infrared range. It is especially useful for measuring asymmetric vibrations, which are intense in the near infrared range.

Ideal for analysing all sorts of biological systems, NIR spectroscopy measures virtually the entire near infrared region. This means it can show strongly overlapping, almost holographic, NIR spectra that are extremely difficult to interpret in a traditional analysis system.


NIR spectroscopic data are, in general, highly co-linear. For example, two adjacent wavelengths usually have high correlation coefficients. Principal Component Analysis (PCA) is a multivariate chemometric method that can handle co-linearity, so PCA and NIR spectroscopic data make a perfect fit.

PCA on NIR data

A PCA model can be described as Raw data = Mean Level + Model + Noise. Often, the first step in PCA modelling is to mean centre the spectroscopic data. This puts the focus on the variations between individual samples rather than the absolute signal level. Mean centring is simply a subtraction of the average reflectance at each wavelength, so that the reflectance at each wavelength adds up to zero across all samples.

In order to calculate a PCA model, different algorithmic approaches can be applied. Several of these are implemented in commercial software packages that enable the user to calculate and present results from a PCA model.

PCA and Lambert-Beer’s law

PCA can be thought of as a ‘reverse’ Lambert-Beer law. This law is based on linearity and additivity: from measurements on whole spectra that consist of many contributions from chemical components in the sample, the method estimates the latent spectra (loadings) and determines the corresponding concentrations in the samples (scores) from the measured spectra.

PCA is a superior method for handling the highly co-linear data often found in spectroscopy. An exceptional tool for exploratory data analysis – PCA makes an excellent addition to NIR analysis. It lets you investigate the behaviour and characteristics of individual samples, and study the wavelength regions that are important in determining the similarity/difference between samples.

For the full report, download the white paper.