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Building a
clustering tree
Luke Zappia
@_lazappi_
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My data
OpenStax College, CC BY 3.0 via Wikimedia Commons
Single-cell RNA-sequencing
Gene activity in thousands of cells
~20000 rows x ~7000 columns
Look for different cell types
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How many
clusters?
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Can we build a tree of
clusters?
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Nodes
Resolution (k)
Cluster
Size
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Edges
Cluster from
(lower resolution)
Cluster to
(higher resolution)
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Edges
Cluster from
(lower resolution)
Cluster to
(higher resolution)
Number
Proportion
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Proportions
size = 100
60
40
k = 1 k = 2
n = 60
n = 40
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Proportions
100
60
40
k = 1 k = 2
p
from
= n / size
low
n = 60
n = 40
p
to
= n / size
high
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Proportions
100
60
40
k = 1 k = 2
p
from
= 0.6
n = 60
n = 40
p
to
= 1.0
p
from
= 0.4
p
to
= 1.0
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Proportions
100
60
40
k = 1 k = 2 p
from
= 0.67
60
40
p
to
= 1.0
40
30
40
20
30
10
30
k = 3
p
from
= 0.33
p
to
= 0.67
p
from
= 0.25
p
to
= 0.33
p
from
= 0.75
p
to
= 1.0
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Algorithm
For each resolution r = 1, ..., R - 1
For each unique cluster C
low
in r
For each unique cluster C
high
in r + 1
Count C
low
, C
high
pairs
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
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Algorithm
For each resolution r = 1, ..., R - 1
Res1, Res2
For each unique cluster C
low
in r
For each unique cluster C
high
in r + 1
Count C
low
, C
high
pairs
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
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Algorithm
For each resolution r = 1, ..., R - 1
For each unique cluster C
low
in r
1, 2
For each unique cluster C
high
in r + 1
Count C
low
, C
high
pairs
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
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Algorithm
For each resolution r = 1, ..., R - 1
For each unique cluster C
low
in r
For each unique cluster C
high
in r + 1
1, 2, 3
Count C
low
, C
high
pairs
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
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Algorithm
For each resolution r = 1, ..., R - 1
For each unique cluster C
low
in r
For each unique cluster C
high
in r + 1
Count C
low
, C
high
pairs
1
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
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Edge table
Res1 Res2 Res3
S1 1 1 1
S2 2 1 2
S3 1 2 2
S4 1 3 3
S5 2 1 4
ResFrom ClusterFrom ResTo ClusterTo Number
Res1 1 Res2 1 1
Res1 1 Res2 2 1
Res1 1 Res2 3 1
Res1 2 Res2 1 2
Res1 2 Res2 2 0
Res1 2 Res2 3 0
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Tree
Resolution
0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
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Resolution
0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
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Resolution
0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
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Summary
Choosing the number of clusters is hard but important
A clustering tree can help by showing:
- Relationships between clusters
- Which clusters are distinct
- Where samples are changing
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Acknowledgements
Everyone that makes tools and data available
Supervisors
Alicia Oshlack
Melissa Little
MCRI Bioinformatics
Belinda Phipson
MCRI KDDR
Alex Combes
@_lazappi_
oshlacklab.com
R Tutorial
lazappi.id.au/building-a-clustering-tree/
Slides
speakerdeck.com/lazappi/building-a-clustering-tree