A Framework for Modelling Short, HighDimensional Multivariate Time Series: Preliminary Results in Vi

1
A Framework for Modelling Short, High-Dimensional
Multivariate Time Series Preliminary Results in
Virus Gene Expression Data Analysis

• Paul Kellam1, Xiaohui Liu2, Nigel Martin3,
  Christine Orengo4, Stephen Swift2, Allan Tucker2
• 1Dept of Immunology and Molecular Pathology, UCL,
  UK
• 2Dept of Information Systems and Computing,
  Brunel University, UK
• 3Dept of Computer Science, Birkbeck College,
  London, WC1E 7HX, UK
• 4Dept of Biochemistry and Molecular Biology, UCL,
  WC1E 6BT, UK

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Framework
Expression Data
Clustering Algorithms
ClusterFusion
Clusters
Model Building
RobustClusters
Forecasts
Explanations
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Clustering Algorithms

• Hierarchical
• The Grouping Genetic Algorithm
• K-Means
• The Self Organising Map

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Cluster Fusion (1)
Cluster Method 1
Cluster Method 2
Construct Agreement Matrix
. . .
Cluster Method N
Clusterfusion
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The Agreement Matrix
To Gene
F
From Gene
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Viral Gene Expression Data

• Kaposi's Sarcoma-Associated Human Herpesvirus 8
  (HHV8)
• 106 viral and human genes
• Induced with 12-O-TetradecoylPhorbol 13-Acetate
  (TPA)
• 13 Measurements over time
• Normalised expression levels

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Evaluation

• Compare cluster similarity using Weighted-Kappa
• Compare clusters against biologicaldomain
  knowledge
• Clusterfusion

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Weighted-Kappa Results
Hx Hierarchical Clustering with x ClustersKx
K-Means Clustering with x ClustersSx Self
Organising Map with x ClustersGx Grouping
Genetic Algorithm with x Clusters
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Domain Knowledge Results
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Clusterfusion Results

• 48 out of 106 genes unassigned
• Mostly pairs or triples
• Only 3 of feature 2 are present!
• Although there are some interesting results, e.g.
  unknown function genes placed with those of known
  function

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Modelling

• We have focussed on the Dynamic Bayesian Network
• Models a temporal domain probabilistically
• Consists of a graphical representation and
  conditional probability distributions
• Facilitates the combining of expert knowledge and
  data
• Models can be queried to investigate the
  relationships discovered from data
• Requires data discretisation

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Dynamic Bayesian Networks
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Modelling Results

• Example DBNs (compact representation
• without lags included)

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Forecast Results
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Explanation

• Apply inference given observations about certain
  nodes
• Insert observations into DBN
• Apply inference back in time
• Construct explanations using posterior
  probabilities

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Explanation - Results
P(C7 is 2) 1.000

• An example
• explanation
• using a
• discovered DBN

1
2
2
P(C7 is 1) 1.000
P(H8 is 2) 0.999
P(B12 is 2) 0.884
1
2
1
P(B6 is 2) 0.568
P(B12 is 1) 0.440
P(A7 is 1) 0.510
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Conclusions

• Modelling gene expression data is a challenging
  task
• Introduced a framework for modelling such data
• Encouraging preliminary results when applied to
  viral gene expression data
• More rigorous testing on different datasets

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Acknowledgements

• Biotechnology and Biological Sciences Research
  Council (BBSRC), UK
• The Engineering and Physical Sciences Research
  Council (EPSRC), UK