A Primer on Block Clustering with Probabilistic Distances

An accessible overview of block (co-)clustering — simultaneously grouping rows and columns of a data matrix using probabilistic distance methods.

What Is Block Clustering?

Unlike traditional clustering that groups only rows (observations), block clustering (also called co-clustering or biclustering) simultaneously groups both rows and columns of a data matrix. This reveals hidden block structures in the data.

Why Block Clustering?

Consider a gene expression dataset: you want to find groups of genes (rows) that behave similarly across groups of experimental conditions (columns). Block clustering finds these meaningful row–column combinations automatically.

The Probabilistic Distance Approach

Our framework combines:

1. Probabilistic distances — measuring how “far” each observation is from each cluster center in probability space
2. Block structure — jointly partitioning rows and columns
3. Flexible distributions — supporting Gaussian, \(t\)-distributions, and non-parametric distances

\[d_{PD}(x_i, \mu_k) = -2 \log f(x_i \mid \theta_k)\]

Evaluating Block Clustering

We modified the Extended Silhouette Index to assess block clustering quality alongside the Co-clustering Adjusted Rand Index.

# Coming soon: blockclusterPDQ example
library(blockclusterPDQ)

# Fit block clustering model
# Evaluate using Extended Silhouette
# Visualize co-cluster structure

Coming Soon

Detailed tutorials with code examples and real-data applications will be published here. Watch this space!

References

• Bhat, S. K. & Kiruthika, C. (2025). Block Probabilistic Distance Clustering: A Unified Framework and Evaluation.