Ordination

Wednesday, August 27, 2025

Ordination

  • Reduces high-dimensional data to a few informative axes
  • Projects samples into lower-dimensional space while preserving distances or variance
  • Helps identify patterns, clusters, and gradients across samples

Ordination methods

  • PCA, PCoA/MDS, RDA, …
  • Euclidean vs non-Euclidean
  • Unsupervised vs supervised

Principal component analysis (PCA)

  • Unsupervised ordination method
  • Euclidean distance
  • Aitchison distance: CLR + Euclidean distance

Principal coordinate analysis (PCoA)

  • Multidimensional scaling (MDS)
  • Unsupervised ordination method
  • Any dissimilarity metric (e.g., Bray-Curtis dissimilarity)

Redundancy analysis (RDA)

  • Supervised ordination method
  • Find variance explained by sample metadata

Matrix Decomposition

  • Conceptual basis of ordination: decompose sample × taxa matrix

\[ X = U \Sigma V^T \]

  • UΣ: sample coordinates in reduced space
  • Σ: importance of each axis
  • V: taxa contributions

Demonstration

library(mia)
library(scater)

# Apply transformation
tse <- transformAssay(tse, method = "rclr")

library(mia)
library(scater)

# Apply transformation
tse <- transformAssay(tse, method = "rclr")
# Apply PCA
tse <- runPCA(tse, assay.type = "clr")

library(mia)
library(scater)

# Apply transformation
tse <- transformAssay(tse, method = "rclr")
# Apply PCA
tse <- runPCA(tse, assay.type = "clr")
# Visualize
plotReducedDim(tse, "PCA", colour_by = "patient_status")

Exercises

From OMA online book, Chapter 15: Community similarity

  • Exercise 1
  • Exercise 2
  • Exercise 3

References

https://microbiome.github.io/