Food Analysis Lab · W12

Principal Component Analysis PCA: Classifying Edible Oils

Principal Component Analysis — Classifying Edible Oils by Spectra

Food Analysis Lab · 4-hour session
Six edible oils × Raman 785 nm / each group's NIR · Orange PCA (Data→Scatter, Components→Spectra) · Colab / R

PCA scores/loadingsmean-centeringno autoscalingscree plotOrange PCA

Before we start, watch three factory videos

A mislabeled “olive oil”:
can you tell from the spectrum?

Olive oil line (12:20–13:44, extra virgin grading, prone to adulteration) ↗ Canola oil line (12:02–13:31, deodorizing and refining / acid value / peroxide value) ↗ Soybean oil line (08:00–09:28, hexane extraction) ↗

A note from the videos: beyond sensory evaluation, grading extra virgin olive oil (EVOO) legally also requires indices such as K232/K270, and it is easily adulterated or mislabeled — which is exactly today's question.

Today's question: if a bottle of oil is mislabeled (say, labeled “extra virgin olive oil” but actually blended with refined olive oil or another oil), can spectra + PCA reveal it? (We'll come back to this at the score plot — but you'll also see that PCA can sometimes be fooled by a single outlier.)

W12 / PCA COURSE TOUR

Edible-oil PCA: from clusters to evidence

Full narration and captions; original simulated course spectra. Player and downloads · Interactive lab

W12 / PREDICT · OBSERVE · EXPLAIN

Six acts: projection, PCA, and outlier refitting

Open the full interactive lab

Today’s learning goals

After W12 you should be able to…

Know that spectral data is simply a table of numbers, samples × wavenumbers; PCA looks for the direction of greatest variance in the data, and PC1 ⟂ PC2
Know that a score is a weighted sum of the loadings — and tell apart what scores (where the samples sit) and loadings (which wavelengths drive it) each answer
Work through mean-centering and autoscaling by hand once, and explain why spectral data usually gets only the former

Understand how the eigenvalue and the explained variance are calculated, and say where the elbow of the scree plot is
In Orange, connect PCA's Data output (not Transformed Data) to Scatter Plot to color by class, and Components to Spectra to view the loadings
Read a score plot for replicate consistency and outlier samples, and know that a single outlier can hijack an entire PC — when you find one, go back to the spectrum, record the reason, and redo the PCA

Data table X

One row = one spectrum, one column = one wavenumber

Sample	900 cm⁻¹	915 cm⁻¹	931 cm⁻¹	946 cm⁻¹	961 cm⁻¹	…
EVOO_r1	0.005	0.013	-0.011	0.004	0.004	…
COC_r1	0.015	0.048	-0.002	-0.021	0.048	…
SOY_r1	-0.018	-0.041	-0.046	0.007	-0.016	…
PEA_r3	0.084	0.073	-0.026	0.077	0.095	…
…(18 spectra in total)	…(60 wavenumber columns in total)

Today's data: 18 spectra × 60 wavenumbers = 1080 numbers (6 oils × 3 replicates; 60 points taken from each spectrum between 900 and 1800 cm⁻¹)
Each spectrum = one row of the table; each wavenumber = one column; each sample is really a point in 60-dimensional space
Our eyes and screens can only handle 2–3 dimensions — what PCA does is project this 60-dimensional point cloud onto a few of the “most representative” directions

The table values come from the same CSV used in Colab NB10 (nb10_demo_spectra.csv), not made up separately.

Data · a small example

Look at two wavenumbers together: they vary together

Plot just 1655 cm⁻¹ against 1265 cm⁻¹ (both related to unsaturation): coconut oil is low on both, soybean oil is high on both
The 18 points line up almost on a diagonal: correlation coefficient r ≈ 0.99 (calculated as in W04 ↗, only here the two quantities are wavenumbers)
Because the two wavenumbers vary together (are correlated), PCA can describe both with a single direction — that direction is “degree of unsaturation”, i.e., PC1

Values are taken from column 50 (1647 cm⁻¹) and column 25 (1266 cm⁻¹) of the same spectral dataset, not invented.

Principle

What PCA looks for: the direction of greatest variance

PC1: the direction of greatest variance in the data; PC2: the direction perpendicular to PC1 with the next-greatest variance — the two are orthogonal to each other (⟂)
PCA is an unsupervised method — it has no idea which oil a sample is and separates samples using only the variance in the spectra
So if different oils really separate on the score plot, it means the input spectra differ; but whether the difference truly comes from chemical composition still has to be confirmed with the loadings, the raw spectra and the measurement conditions — and you'll shortly see that the difference can also be misled by a single outlier

Principle

Score = weighted sum of the loadings

t = p₁(x₁−x̄₁) + p₂(x₂−x̄₂) + p₃(x₃−x̄₃) + …

t = the sample's score on this PC; pⱼ = the loading (weight) of wavelength j; xⱼ−x̄ⱼ = the mean-centered value at that wavelength

p=[0.6, 0.6, 0.53], centered x=[0.5, 0.4, 0.3]
t = 0.6×0.5 + 0.6×0.4 + 0.53×0.3 = 0.30+0.24+0.159 ≈ 0.70

Loading: the “weight” of each wavelength on this PC — it determines “why” the samples separate
Score: multiply each wavelength's (mean-centered) signal by its weight and add them up — this is the sample's coordinate on the plot
The larger the loading (positive or negative), the more that wavelength influences this PC; a loading near 0 means that wavelength barely affects this PC

Mini-game ①Should this question look at scores or loadings?0 / 8

Sort the 8 questions below into “questions answered by scores” or “questions answered by loadings”.

Preprocessing · work one out

Work through mean-centering and autoscaling once

Wavelength	Raw value x	x − x̄ (mean-centered)	÷ SD (autoscaled)
Signal wavelength	0.8 / 1.0 / 1.2	−0.2 / 0 / 0.2	−1 / 0 / 1
Noise wavelength	1.001 / 0.999 / 1.000	0.001 / −0.001 / 0	1 / −1 / 0

Both rows use the sample standard deviation (SD) (calculated as in W01 ↗; signal row SD=0.2, noise row SD=0.001).

Mean-centering: subtract each row's own mean (1.0) from its three values — so PCA looks for variance “relative to the mean spectrum”; this preprocessing is almost always required
Autoscaling: divide by each row's own standard deviation after centering — the signal wavelength and the noise wavelength both end up on the same −1/0/1 scale
Here is the problem: the noise wavelength originally had a tiny signal (SD=0.001), yet after dividing it looks just as “prominent” as the signal wavelength — the noise has been amplified, which is why spectral data usually skips autoscaling

Preprocessing options

SNV / derivatives: whether to apply them before PCA

📐

SNV (standard normal variate)

Do an SNV first (see W11 ↗): it removes the intercept/slope differences caused by particle-size scattering, so the variance PCA finds is closer to real chemical differences

📉

First / second derivative

Do a derivative first (see W11 ↗): it removes baseline drift, but also amplifies high-frequency noise — think twice before using it

🧪

Today's demo: mean-centering only

Today's score plot and loadings come from PCA on the raw intensities with mean-centering only — no SNV or derivatives; we leave that comparison for the assignment

This demo uses mean-centering only, no autoscaling; in the Orange PCA widget, remember to uncheck “Normalize variables” (it is on by default).

Principle

Eigenvalue and explained variance

λₐ = variance of the scores on the a-th PC (eigenvalue)
Explained variance % = λₐ / Σλᵢ × 100%

The larger λₐ is, the more spread out the samples are along the a-th PC — and the more “important” that PC is.

Today's six-oil data: PC1 ≈ 46.3%, PC2 ≈ 28.3%, PC3 ≈ 23.0%, and everything from PC4 on adds up to only 0.53%
Scree plot: a bar chart of the explained variance of each PC, used to decide “how many PCs are enough to look at”
⚠️ Don’t confuse this λ with the λ (smoothness parameter) in W11 ↗ ALS baseline correction — they are two completely different things that just happen to share the Greek letter λ

Data · Scree

Scree plot: explained variance falls with each PC

Data come from the actual PCA of the same NB10 spectra. The first 3 PCs together explain 97.7%, PC4 only 0.53% (<1%): the elbow is clearly after PC3.

Score plot

PC1 vs PC2: score plot of six oils

PC1 (46.3%): driven mainly by 1655/1265 cm⁻¹ (unsaturation-related) — coconut oil (the most saturated) sits at the most negative end
PC2 (28.3%): it looks as if extra virgin olive oil separates, but a sum-of-squares check shows that 74% of the PC2 variance comes from one single point, peanut oil replicate 3; its loading peak near 1159 cm⁻¹ is an artifact left by a measurement anomaly, not a clean chemical signal
QC: the replicates of five oils cluster tightly; one peanut oil replicate sits far at the top — suspect the measurement first (air bubble? alignment?), and don't rush to say “peanut oil forms its own group”
Back to the opening question: whether PCA can catch a mislabeled oil depends first on making sure the PC you are looking at is not hijacked by a single outlier — on the next page we remove this point and redo the analysis

The data come from the same simulated Raman spectra used in Colab NB10 (nb10_demo_spectra.csv); the PCA was computed live when this page was built, so the numbers are guaranteed to match NB10. Point color = oil; three points of the same color = three replicates.

Hands-on: redo it

Redo the PCA after removing PEA-3

With peanut oil replicate 3 removed: PC1 = 63.5%, PC2 = 33.2% (higher than the 28.3% before removal — an increase, not a decrease), PC3 is down to just 0.74% — the 74% of PC2 sum of squares that PEA-3 alone had propped up is gone, and the remaining variance re-concentrates into one clean direction
Now the highest PC2 loading is near 1525 cm⁻¹ = the carotenoid band: extra virgin olive oil (EVOO) has a mean PC2 score of 0.99, while all the other oils lie between −0.39 and 0.03 — this is the “clean” carotenoid separation
Lesson: a single outlier can hijack an entire PC. When you find an outlier sample, first go back to the raw spectrum and record the reason (see W08 ↗), then redo the PCA to check whether the story changes
NB10 preview: this point’s Hotelling T² = 12.7, above the 95% limit of 7.7 — the formal definitions of T² / Q residual (SPE) are left for W14 ↗

Same data, with that one spectrum removed and PCA rerun live (Colab NB10 sections 3 and 7 have the full version).

Data · Loadings

PC1 loading: which wavenumbers drive this principal component

The PC1 loading has positive peaks near 1655 cm⁻¹ (C=C stretching) and near 1265 cm⁻¹ (=C–H bending) — both are Raman bands related to unsaturation, which also explains why coconut oil (highly saturated) is farthest away on PC1. Treat band assignments as approximate; real samples still need to be confirmed against standards or literature spectra.

What the signs mean: for a band with a positive loading, samples with higher intensity there also have higher scores on this PC; for a negative loading, a stronger signal gives a lower score. What if two groups overlap: look at PC3, or try a different preprocessing (such as the second derivative).

Orange OR12 step by step

How to click from spectra to score plot and loadings

File: set oil as the target; set sample_id / group / instrument / rep / oil_zh as meta — leave the numeric wavenumber columns as they are, as features
PCA: uncheck “Normalize variables” (spectra get mean-centering only); the default of 2 components gives PC1+PC2 — to see more (e.g., PC3), increase the “Components” number
Connect PCA's Data output (not Transformed Data) to Scatter Plot: x=PC1, y=PC2, Color=oil
Connect PCA's Components output to Spectra: plot loading vs wavenumber (wavelength)
In Scatter Plot, select the odd-looking points → check the raw values in Data Table (this is how PEA-3 was caught)

See also tools.html: Orange workflow OR12 ↗

Orange workflow

From spectra to score plot and loadings

The Colab / R code below is an advanced option — you can finish today's analysis with the Orange steps on the previous page, no coding needed.

Advanced: Colab (scikit-learn, 5 lines):

from sklearn.decomposition import PCA
import numpy as np
X = np.loadtxt("oils_X.csv", delimiter=",")     # one spectrum (one sample) per row
pca = PCA(n_components=5).fit(X - X.mean(axis=0))
scores = pca.transform(X - X.mean(axis=0))      # scores[:, :2] -> score plot

Advanced: R (prcomp):

X <- as.matrix(read.csv("oils_X.csv", header=FALSE))
pca <- prcomp(X, center=TRUE, scale.=FALSE)
scores <- pca$x[, 1:2]
loadings <- pca$rotation[, 1]
summary(pca)$importance[2, ]     # proportion of variance explained by each PC

Colab NB10: Open NB10 in Colab ↗. Backup dataset: Five-sugar NIR backup dataset (chemometrics-teaching) →

Samples, instruments and safety

Six edible oils × Raman 785 + each group's NIR

Six oils: extra virgin olive oil, refined olive oil, soybean oil, canola oil, coconut oil, peanut oil — every group measures all of them, each with 3 replicates (re-loaded / re-sampled)
Raman 785 nm (rotating station): extra virgin olive oil gives strong fluorescence interference at 532 nm — remember the lesson from W10; today we use 785 nm throughout
Each group's NIR: depending on your group, use one of Avantes (300–1100 / 900–1650 nm; 600–1100 nm awaiting delivery), InnoSpectra NIR-S-G1 / T1 / T11 / R14, NeoSpectra Scanner / Micro Dev Kit / fiber-optic module, or Spectral Engines NIRONE S2.0 / S2.2 / S2.5
Coconut oil: it solidifies at room temperature (below about 24°C), so warm it gently until melted into a liquid before measuring

🔴

Raman laser (532/785 nm)

Never look directly at the light source or aim the beam at anyone's eyes; wear appropriate eye protection as instructed for the instrument

🔥🛢️

Hot oil and slippery floors

Warm coconut oil only gently, just until liquid — do not overheat; wipe up any oil spill right away to avoid slipping

4-hour lab schedule

Measure spectra → preprocessing → PCA → cross-instrument comparison

Time	Contents
0:00–0:45	Lecture: data table, scores/loadings, mean-centering / autoscaling, explained variance, how a single outlier hijacks a PC
0:45–2:05	Six oils × 3 replicates: Raman 785 rotating-station measurement + each group's NIR measurement (melt coconut oil first)
2:05–2:30	Preprocess in SpectraView (SNV / derivatives optional) and export an X matrix with one sample per row
2:30–3:30	Run PCA in Orange: score plot (colored by oil), loadings (vs wavenumber), explained variance; if you find an outlier, first check the raw spectrum and the measurement log, confirm the anomaly and record the reason, then remove or re-measure it and redo the PCA
3:30–4:00	Groups swap data and compare whether the score plots from different instruments (NIR) agree

Mini-game ②Order the PCA workflow— / 6

Use ▲▼ to put the 6 steps from spectra to PCA results in the correct order.

Mini-game ③PCA concepts: live quiz0 / 5

Mini-game ④Does this preprocessing decision affect the PCA result?0 / 6

Sort the 6 decisions into “affects the PCA result” or “does not affect the PCA result”.

Mini-game ⑤Decision challenge: reading the score plot0 / 5

Mini-game ⑥Calculation challenge: PC1+PC2 explained variance (%)Unanswered

The eigenvalues of 5 principal components are 8.2, 3.1, 0.9, 0.5, 0.3. What percentage of the total variance do PC1 and PC2 explain together? Formula: (λ₁+λ₂)/Σλᵢ×100%.

Homework

Colab NB10

📊

Score plot + interpretation

Attach your group's PC1 vs PC2 score plot; explain which oils separate, which overlap, and whether there are outliers

🧬

Loading plot + chemical assignment

Attach the loading plot, point out 1–2 bands and try to assign a functional group (remember to write “approximately”)

🚩

Outlier exercise

Following today's PEA-3: find one outlier sample (or deliberately flag one), remove it and redo the PCA, then compare how the explained variance and loadings change

📡

Cross-instrument comparison

Swap score plots with another group, compare whether results from different NIR instruments agree, and discuss possible reasons

Colab NB10: Open NB10 in Colab ↗ · Beginner (no coding): Orange workflow OR12 ↗. Backup dataset: Five-sugar NIR backup dataset (chemometrics-teaching) →

Self-check

By the end of today you should be able to…

✓Explain in one sentence what PCA looks for: the direction of greatest variance in the data, PC1 ⟂ PC2
✓State that a score is a weighted sum of the loadings, and tell apart what scores (sample positions) and loadings (which wavelengths drive it) each answer
✓Explain why spectral data always gets mean-centering but usually not autoscaling, and work through a small example by hand
✓State how explained variance is calculated (λₐ/Σλ) and see where the scree plot shows a clear elbow
✓In Orange, connect PCA's Data (not Transformed Data) to Scatter Plot to color by class, and Components to Spectra to view the loadings
✓Read a score plot to judge whether replicates cluster tightly and whether there are outlier samples, and know to go back and check the raw spectra
✓Say “a single outlier can hijack an entire PC”, and know to redo the PCA after removing an outlier to check whether the story changes
✓Explain that PCA is an unsupervised method and what that means for “the groups separate on the score plot”
✓Follow the safety rules for the Raman laser, hot oil and slippery floors

Tap to tick — make sure you really can do it.