Clustering of Gene Expression Time Series with Conditional Random Fields

1
Clustering of Gene Expression Time Series with
Conditional Random Fields

• Yinyin Yuan and Chang-Tsun Li
• Computer Science Department

2
Microarray and Gene Expression

• Microarray is a high throughput technique that
  can assay gene expression levels of a large
  number of genes in a tissue
• Gene expression level is the relative amounts of
  mRNA produced at specific time point and under
  certain experiment conditions.
• Thus microarray provides a mean to decipher the
  logic of gene regulation, by monitoring the gene
  expression of all genes in a tissue.

3
Gene Expression

• Gene expression data are obtained from
  microarrays and organized into gene expression
  matrix for analysis in various methodologies for
  medical and biological purposes.

4
Gene Series Time Series

• A sequence of gene expression measured at
  successive time points at either uniform or
  uneven time intervals.
• Reveal more information than static data as time
  series data have strong correlations between
  successive points.

Time Series Clustering

• Assumption co-expression indicates
  co-regulation, thus clustering identify genes
  that share similar functions.

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Probabilistic models

• A key challenge of gene expression time series
  research is the development of efficient and
  reliable probabilistic models
• Allow measurements of uncertainty
• Give analytical measurement of the confidence of
  the clustering result
• Indicate the significance of a data point
• Reflect temporal dependencies in the data points

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Goal

• Identify highly informative genes
• Cluster genes in the dataset
• GO (Gene Ontology) analysis of biological
  function for each cluster.

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HMMs and CRFs

• HMMs
  CRFs
• HMMs are trained to maximize the joint
  probability of a set of observed data and their
  corresponding labels.
• Independence assumptions are needed in order to
  be computationally tractable.
• Representing long-range dependencies between
  genes and gene interactions are computationally
  impossible.

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Conditional Random Fields

• CRFs are undirected graphical models that define
  a probability distribution over the label
  sequences, globally conditioned on a set of
  observed features.

• X x1, x2,, xn variable over the
  observations
• Y y1, y2,, yn variable over the
  corresponding labels.
• Observed data xj and class labels yj for all j
  in a voting pool Ni for sample xi

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CRFs Model

• The CRFs model can be formulated as follows

• The CRFs model can be expressed in a Gibbs form
  in terms of cost functions

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Cost function

• The conditional random field model can also be
  expressed in a Gibbs form in terms of cost
  functions

• Cost function

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Potential function

• Real-value potential functions are obtained and
  used to form the cost function

• D the estimated threshold dividing the set of
  Euclidean distances into intra- and inter-class
  distances

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Finding the optimal labels

• We adopt deterministic label selection, the
  optimal label is determined by

13
Pre-processing

• Linear Warping for data alignment
• t -time point data transformed into t-1feature
  space
• Differences between consecutive time points
  inversely proportional to time intervals are used
  as features as they can reflect the temporal
  structures in the time series.
• Voting pool keeps one most similar sample, one
  most-different sample and k-2 randomly selected
  samples.

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Process

• Initialization
• Each sample is assigned a random label
• Voting pools are formed randomly
• Samples interact with each other via its voting
  pool progressively
• Update labels
• Updata voting pool
• Until steady

15
Experimental Validation

• Both biological dataset and simulated dataset
• Adjusted Rand index Similarity measure of two
  partitions
• Yeast galactose dataset
• Gene expression measurements in galactose
  utilization in Saccharomyces cerevisiae
• Subset of meansurements of 205 genes whose
  expression patterns reflect four functional
  categories in the Gene Ontology (GO) listings
• 4 repeated measurements across 20 time points

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Results for Yeast galactose dataset

• The four functional categories of
• Yeast galactose dataset

Experimental results on Yeast galactose dataset
We obtained an average Rand index value of 0.943
in 10 experiments, greater than the result 0.7 in
Tjaden et al. 2006.
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Simulated Dataset

• Data are generated for 400 genes across 20 time
  points from six artificial patterns to model
  periodic, up-regulated and down regulated gene
  expression profiles.
• High Gaussian noise is added.
• Perfect partitions are obtained with 10 iterations

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Conclusions

• A novel unsupervised Conditional Random Fields
  model for efficient and accurate gene expression
  time series clustering
• All data points are randomly initialized
• The randomness of the voting pool facilitates
  global interactions

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Future work

• Various similarity measurement
• Advantage of information from repeated
  measurements
• Training and testing procedures