PCA Analysis Script – README

📌 Overview

This repository contains an R script (pca.r) that performs Principal Component Analysis (PCA) on datasets with:

• Reference samples (ref) → used as a baseline group
• Unknown samples (unknown) → compared against the baseline

The script:

• Dynamically detects numeric analyte columns (names can change between runs)
• Handles missing values in reference samples by imputing the mean of the reference group for that analyte
• Optionally handles missing values in unknown samples
• Computes PCA scores and loadings
• Ranks reference samples by distance to each unknown in PCA space

Outputs:

• pca_plots.pdf – multi‑page PDF:
  1. PCA score plot (refs = grey points, unknowns = red points with labels)
  2. Scree plot (variance explained per PC, in numeric PC order)
  3. PCA loadings plot (PC1 vs PC2)
• unknown_<SampleID>.csv – per‑unknown CSV containing:
  • The unknown sample’s analyte values
  • The N closest reference samples (20 by default)
  • Sorted ascending by Euclidean distance in PCA space

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📊 Statistical Background

1. Principal Component Analysis (PCA)

PCA transforms the original set of correlated variables (analytes) into a set of uncorrelated variables called principal components (PCs):

• PC1 explains the largest variance in the dataset
• PC2 explains the next largest variance, and so on
• Data is centered and scaled before PCA

Mathematically:

Z = (X − X̄) / σ

PCA: Z · W = T

Where:

• X = original analyte data
• W = eigenvectors (loadings)
• T = scores (coordinates in PC space)

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2. Distance Metric

Distances are computed as Euclidean distance in PCA score space:

d(a, b) = √[ Σᵢ₌₁ᵏ (PCᵢ,ₐ − PCᵢ,ᵦ)² ]

where k is the number of PCs considered (all by default).

For each unknown:

• Distances to all refs are calculated
• The closest refs are ranked and saved

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3. PCA Loadings

PCA loadings indicate how strongly each analyte influences a PC:

• Large magnitude = greater influence on that PC
• Sign indicates the direction of the relationship

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🖥 Code Workflow

1. Data Input

   • Reads pca_data.csv from the script’s folder
   • Converts headers to lowercase
   • Confirms sample and type columns exist

2. Pre‑processing

   • Detects analyte columns automatically
   • Imputes missing reference analyte values with reference means
     (optional: also imputes unknown values if enabled in the script)

3. PCA Calculation

   • Uses prcomp() with scaling and centering
   • Extracts scores and loadings

4. Output Generation

   • Per unknown: Saves unknown_<SampleID>.csv with that unknown + N closest refs (default 20)
   • Generates PDF with:
     1. Score plot (refs = grey points, unknowns = red points with labels)
     2. Scree plot (% variance explained)
     3. Loadings plot (PC1 vs PC2)

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⚙️ Usage Instructions

1. Prepare your data

Save your dataset as pca_data.csv in the same directory as pca.r.

Required columns:

• Sample → unique sample ID
• Type → "ref" or "unknown"
• One or more numeric analyte columns

Example:

Sample,Type,As,Ba,Cd,Co,Cr
REF001,ref,1.2,0.5,0.3,0.6,0.8
REF002,ref,1.3,0.4,0.4,0.5,0.7
UNK001,unknown,0.9,0.6,0.5,0.7,0.9

2. Run the Script

• Rscript pca.r

3. Check the outputs

• pca_plots.pdf → open to see PCA score plot, scree plot, loadings plot

• unknown_.csv → inspect analyte values and ranked closest refs for each unknown