Post on 14-Dec-2015
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.
Similar genes.
Group genes that have similar expression profiles when observed over multiple samples.
Genes
Samples
Gene clustering
Similar samples.
Group samples that are similar when observed over multiple genes.
Genes
Samples
Sample clustering
Why cluster?
• Similar gene expression infers common biology.
Function of uncharacterized genes may be deduced from co-
expression with known genes.
• Associate expression patterns with:Response to environmental change.
Disease pathology/progression.
Clustering Mechanics
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Gene a
Gene e
Gene b
Gene c
Gene d
Gene f
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For gene clustering, we must measure similarity between genes.
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Distance (similarity) measure
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Euclidean distance
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(4.6, 0.5)
(1.0, 1.7)
22 7.15.00.16.4 bed
Distance Measure
Pearson Correlation
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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.
Complete linkage
The maximum distance between clusters.
Tends to form compact clusters.
Produces “chained” 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
EuclideanSingle Linkage
EuclideanComplete Linkage
Effect of distance measure
EuclideanUPGMA
EuclideanWard’s Method
Alternatives to hierarchical clustering
• Number of clusters specified by user.
• Good when prior knowledge available.
k-means
k-means clustering
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1. Number of clusters specified by user.
2. Genes randomly assigned to clusters.
3. Assess inter and intra-cluster similarity.
4. Move genes to alternative cluster if distance is reduced.
3. Assess inter and intra-cluster similarity.
4. Move genes to alternative cluster if distance is reduced.
Alternatives to hierarchical clustering
• Number of clusters specified by user.
• Good when prior knowledge available.
SOM Self-organizing maps
SOM
Gene a
Gene e
Gene b
Gene c
Gene d
Gene f
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cluster 1
cluster 2
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User specified number of clusters.
Each initially given a random expression representation.
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cluster 1
cluster 2
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For a gene, find the most similar cluster representation.
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cluster 1
cluster 2
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Increase the similarity by adjusting the cluster representation.
“Training”
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cluster 1
cluster 2
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Iteratively train the cluster representations.
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cluster 1
cluster 2
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After training, assign each gene to the most similar cluster.
Gene clustering
Eisen et al.,
Cluster analysis and display of genome-wide expression patterns.
PNAS v95,14863-14868, 1998
24 hour time course after re-introduction of
serum to serum-deprived human fibroblasts.
Pearson correlation, average linkage.
cholesterol biosynthesis
cell cycleimmediate-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
64 cancer cell lines clustered.
8,000 genes.
Clustering performed with 2 different subsets of genes. Similar results.
Pearson correlation, average linkage.
Note breast cancer cell lines, derived from the same patient.
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
Gene a
Gene e
Gene b
Gene c
Gene d
Gene f
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cluster 1
cluster 2
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After training, assign each gene to the most similar cluster.