Genetic Networks 1: Clustering

An alternative to doing differential gene expression analysis for RNAseq data is to look for patterns in the data.

This can be particularly useful as the data sets get larger.

The 12 samples your worked with last week are part of a much larger data set. Today we will work with 48 samples from the same experiment.

1. Identify groups of samples with similar expression patterns (why?)
2. Identify groups of genes with similar expression patterns (why?)

We will explore three types of clustering:

1. Hierarchical Clustering (today)
2. K-means clustering (today)
3. Co-expression (Tuesday)

Basic idea:

1. Calculate distances between each pair of samples (or genes)
2. Pair the closest samples together
3. Recalculate distances
4. pair the closest samples
5. repeat 3 and 4

let's try it on some cities

Basic idea:

1. Define the number of clusters desired
2. Randomly assign each gene to a cluster
3. Calculate the mean position of each cluster (aka cluster centroid)
4. Assign each gene to the cluster whose centroid it is closest to
5. Repeat until stable.

library(animation) 

kmeans.ani(x = cbind(X1 = runif(50), X2 = runif(50)), centers = 3,
hints = c("Move centers!", "Find cluster?"), pch = 1:3, col = 1:3)

kmeans.ani(x = cbind(X1 = runif(50), X2 = runif(50)), centers = 10,
hints = c("Move centers!", "Find cluster?"), pch = 1:10, col = 1:10)

kmeans.ani(x = cbind(X1 = runif(50), X2 = runif(50)), centers = 5,
hints = c("Move centers!", "Find cluster?"), pch = 1:5, col = 1:5)

How many clusters are enough?

Cluster variance = average squared distance from cluster center to each member.

Calculate within-cluster variance for N random clusters = “Expected Random”

Calculate within-cluster variance for calculated K-means clusters = “Observed”

Choose the smallest number of clusters that maximizes the “gap” between observed and expected random within-cluster variance.