Clustering of Leaflabelled Trees on Free Leafset

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Clustering of Leaf-labelled Trees on Free Leafset

• Jakub Koperwas
• Krzysztof Walczak
• Institute of Computer Science
• Warsaw University of Technology

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Agenda

• Background
• Introduction to phylogenetic trees
• Consensus and distance methods
• Clustering of leaf-labelled trees
• Clustering motivation
• Clustering Quality Measure
• Clustering Approaches
• Free leafset extension
• Experiments and results
• Future works

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Phylogenetic Tree
ancestor

cat
CACCTGT
dog
CAACTGT
mouse
CACCTAT
rat
CACTTGT
CACCTCT
horse
cow
CACCTCT
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Tree Representation
Splits
a
b
abcdef
bacdef
cabdef
dabcef
c
eabcdf
fabcde
abcdef
abcdef
abcdef
d
e
f
Clusters
abcde
ab
cde
cd
e
a
b
a
b
c
d
e
c
d
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Robinson Foulds Distance
Splits for tree T1 abcdef, bacdef, cabdef,
dabcef, eabcdf, fabcde, abcdef, abcdef,
abcdef
Splits for tree T2 abcdef, bacdef, cabdef,
dabcef, eabcdf, fabcde, abcdef, abcdef,
abcefd
Uncommon splits abcdef, abcefd
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Strict Consensus Tree
Splits for tree T1 abcdef, bacdef, cabdef,
dabcef, eabcdf, fabcde, abcdef,
abcdef, abcdef
Splits for tree T2 abcdef, bacdef, cabdef,
dabcef, eabcdf, fabcde, abcdef,
abcdef, abcefd
The common splits abcdef, bacdef, cabdef,
dabcef, eabcdf, fabcde, abcdef,
abcdef
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Clustering motivation

• Phylogenetic trees reconstruction methods may
  produce many candidate trees
• Hard to apply consensus methods to achieve one
  tree from profile of hundreds of trees
• Clustering helps to designate small number of
  candidate trees form a large number of trees

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Representative Tree

• Representative tree tree that shares common
  knowledge of all trees in cluster.
• Strict Consensus Tree
• Majoruty-rule Consensus Tree
• Other

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Information in Tree
a
a
b
c
a
b
b
e
e
c
e
d
d
d
c
a
a
a
b
b
b
e
e
e
c
c
c
d
d
d
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Information Loss

• Cluster Information Loss the amount of
  information that will be lost while replacing the
  cluster of trees with one representative tree

• Clustering Information Loss the amount of
  information that will be lost while replacing the
  input profile of trees with k representative
  trees

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Information Loss - Example
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K-best problem

• K-best problem is the problem of finding
  partition of dataset on k clusters (where k is an
  given value), in such way that this partition
  maximizes Information Gain towards given type of
  representative tree.
• Proposition
• K-mean algorithm for majority-rule consensus tree
  as representative tree
• Agg-inf algorithm for strict consensus tree as
  representative tree

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K-mean Approach(Majority-rule CT)

• Majority-rule consensus tree is a center tree,
  therefore can be used as centroid
• The objective of k-mean for trees is identical
  with the k-best objective if the majority-rule
  consensus tree is chosen as representative tree
• Conclusion K-mean is a good candidate when a
  majority-rule consensus tree is used as
  representative tree

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Agglomerative approach (Strict CT)

• Typical Merging Strategies
• Single linkage
• Complete linkage
• Average Linkage
• Our Merging Strategy minimize information loss
  after merging
• For Strict Consensus Tree as Representative Tree

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Free leafset extension
a
a
c
c
b
b
f
d
e
d
T2 abcdf, bacdf, cabdf, dabcf acbdf, abcdf
T1 abcde, bacde, cabde, dabce acbde, abcde
No two splits can ever be equal Consensus
methods always empty set Distance always sum
of splits in all trees
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Z-restriction

abcdefgy
abcdefgx
abcdefg
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Z-restricted consensus tree
Zabcd
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Z-restricted distance
dRF(T1,T2)15
dRFabcde2
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Z-restriction in Clustering

• 1. Z-Restricted Majority rule consensus tree is a
  middle tree
• K-mean can be used

2.

• Agg-inf improvement can be used

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Pros and cons of z-restriction

• Pros
• Simple and efficient
• Nice Mathematical Features
• Cons
• Arbitrary Information discarding
• Hard to choose the z parameter

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Results Strict consensus (same leafset)
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Results (free leafset)
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Future Work

• Extension of presented methods with frequent
  subsplits approach
• Developing an algorithm for general
  representative tree
• Incorporate more biologically-significant
  features into clustering objective function
• Experiments on datasets from other disciplines
  like linguistics

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Thank You