Beta diversity

Similarity between samples
Dissimilarity/distance between samples, clustering, ordination…
Identify patterns of community variation across conditions or treatments

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

From many dimensions to a few

Keeping the essential shape

Hand shadow illustrating projection from 3D to 2D

Ordination methods

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

Different techniques depending on goal. PCA is the most basic one and commonly used. However, microbiome data has unique nature that must be taken into account when applying.

Transformation lecture…

There are different ways to calculate distance or dissimilarity between samples. We can use different measurements. Euclidean is the simplest (elementary school distance, real distance). But there are also other methods.

In ML, unsupervised means that the method does not take into account sample information (it odes it blindfoldedly). After applying the method, we can check if the results associates with some metadata, for instance, diagnosis. If it does, it is very robust indication of association.

In supervised ML, we specifically say to model to take the diagnosis information into account.

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)

Different methods, different views

PCoA with Bray-Curtis versus PCA with Aitchison distance on gut microbiota data

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 = "rclr")

library(mia)
library(scater)

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

Exercises

OMA online book, Chapter 15: Community similarity

microbiome.github.io/OMA › Community similarity

Exercises 1, 2, 3