Modelbased clustering of gene expression data from microarray experiments

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Model-based clustering of gene expression data
from microarray experiments

• Debashis Ghosh, Arul M. Chinnaiyan
• Department of Biostatistics, University of
  Michigan
• Department of Pathology, University of Michigan
• yfhuang

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Outline

• Introduction
• Systems and Methods
• Algorithm
• Implementation
• Results
• Discussion

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Introduction

• Large collections of gene will be rapidly
  available for parallel genomic studies
• Currently two platforms to dominate the
  microarray field oligonucleotide arrays and
  spotted cDNA arrays

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Introduction (Cont)

• Clustering methods are useful when the goal is to
  discover grouping in the gene expression data,
  and no external information exists.
• An attractive feature of the model-based approach
  is that it provide a statistical criterion for
  accessing the number of true clusters in the
  dataset of interest.

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Systems and Methods

• Data Preprocessing
• Model Specification
• Density function
• Multivariate normal density

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Algorithm

• Two Steps in fitting model to the data
• Initialization by model-based hierarchical
  agglomerative clustering
• Maximum likelihood estimation using EM algorithm
• A criteria for determining the number of clusters
  in the data

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Hierarchical Agglomerative Clustering

• Classification log-likelihood
• To find the maximizer of classification
  log-likelihood
• Base on a combination of the dissimilarity matrix
  and a method of defining distance between clusters

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Expectation-Maximization Algorithm

• Complete-data likelihood
• Log-likelihood

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Expectation-Maximization Algorithm (Cont)

• Estimator

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Selecting the number of clusters

• Determining the number of clusters based on Bayes
  Factor
• Bayes Factor
• Bayesian Information Criterion (BIC)

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Implementation

• Model-based clustering in microarray studies
• Analysis of genes and ESTs (Expression Sequence
  Tag)
• Number of samples profiled (n) ltlt the number of
  genes on a microarray (p) ? impossible to fit the
  model to these data

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Implementation (Cont)

• Model-based clustering of genes
• Using k-means clustering for preprocessing step
• Model-based clustering of samples
• Using principal components analysis for dimension
  reduction
• Using Bayes factors to determine the number of
  clusters
• Software
• Using MCLUST

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Result

• Cutaneous melanoma data
• Data cDNA microarray experiments performed by
  Bittner et al.
• 31 melanoma samples
• Microarray contains 8150 human cDNA, of which
  6912 were sequence verified.

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Result (Cont)

• Prostate cancer data
• Data 3955 genes across the 26 samples
• Original data 9984 (5000 known gene from
  Research Genetics human cDNA clone set, 4400
  ESTs, 500 control elements)

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Cluster Dendrogram (Bittner)
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PCA of Melanoma Data
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PCA of Prostate Cancer Data
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Discussion

• A attractive feature of the model-based
  clustering methodology is that the strength of
  evidence measure for the number of true clusters
  in the data is computed
• Bayes factor for model specification

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Reference

• Principal Components Analysis(PCA)
• Bayes Factor