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An Overview of Clustering Methods
Michael D. Kane, Ph.D.
Topics
• What is clustering?
• Clustering mechanics (how the computer does it).
• Parameter choices and their effect.
• Examples.
What is clustering?
Grouping by similarity.
Samples
Gene clustering
Similar genes.
Group genes that have
similar expression
profiles when
observed over
multiple samples.
Genes
Samples
Sample clustering
Similar samples.
Genes
Group samples that
are similar when
observed over
multiple genes.
Why cluster?
• Similar gene expression infers common biology.
Function of uncharacterized genes may be deduced from coexpression with known genes.
• Associate expression patterns with:
Response to environmental change.
Disease pathology/progression.
Clustering Mechanics
For gene clustering, we must
measure similarity between genes.
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Gene a
Gene b
Gene c
Gene d
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Gene e
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Gene f
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Distance (similarity) measure
Euclidean distance
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(1.0, 1.7)
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dbe 
 4.6 1.0  0.5 1.7
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(4.6, 0.5)
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Distance Measure
Pearson Correlation
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S a, b  
N
N

i 1
 ai  a  bi  b 



    
 a  b 
S=(-1 . . . +1)
Used in “Eisen” clustering
Hierarchical Clustering
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Measuring distance between clusters
Single linkage
The minimum distance between clusters.
May form loose clusters.
Produces “chained” clusters.
Complete linkage
The maximum distance between clusters.
Tends to form compact clusters.
Methods for joining clusters
UPGMA unweighted pair group method (Average linkage)
The average distance between clusters.
Weighted pair group method
Same as UPGMA but the distance is weighted by cluster size.
Use when clusters are expected to be significantly uneven in size!
Effect of distance measure
Euclidean
Single Linkage
Euclidean
Complete Linkage
Effect of distance measure
Euclidean
UPGMA
Euclidean
Ward’s Method
Alternatives to hierarchical clustering
k-means
• Number of clusters specified by user.
• Good when prior knowledge available.
k-means clustering
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1. Number of clusters specified by user.
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2. Genes randomly assigned to clusters.
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3. Assess inter and intra-cluster similarity.
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4. Move genes to alternative cluster if distance is reduced.
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Alternatives to hierarchical clustering
SOM
Self-organizing maps
• Number of clusters specified by user.
• Good when prior knowledge available.
SOM
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Gene a
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Gene b
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Gene c
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Gene d
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Gene e
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Gene f
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cluster 1
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cluster 2
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cluster 3
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Usera specified
For
Increase
Iteratively
After
gene,
training,
thetrain
find
similarity
assign
number
the
the cluster
most
each
by
of similar
adjusting
clusters.
gene
representations.
tocluster
the
themost
cluster
representation.
similar
representation.
cluster.
Each initially given a random expression representation.
“Training”
Gene clustering
Eisen et al.,
Cluster analysis and display of genome-wide
expression patterns.
PNAS v95,14863-14868, 1998
cholesterol biosynthesis
24 hour time course after re-introduction of
serum to serum-deprived human
fibroblasts.
Pearson correlation, average linkage.
cell cycle
immediate-early response
signaling
wound healing
Sample
clustering
Ross et al.,
Systematic variation in gene expression patterns in
human cancer cell lines.
Nature Genetics v24, 227-235, 2000
Note breast cancer cell
lines, derived from the
same patient.
64 cancer cell lines clustered.
8,000 genes.
Clustering performed with 2 different
subsets of genes. Similar results.
Pearson correlation, average linkage.
Summary
• Different methods often provide different clusters.
• No overall “best” clustering method.
• Clustering applied to unrelated data will still provide clusters.
• Use biological insight in method selection and interpretation.
Clustering
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SOM
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Gene a
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Gene b
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Gene c
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Gene d
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Gene e
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Gene f
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cluster 1
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cluster 2
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cluster 3
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After training, assign each gene to the most similar cluster.