CLUSTER ANALYSIS

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CLUSTER ANALYSIS
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Clustering - Goal

• Partition of the genes in the dataset into
  distinct sets (clusters), according to similarity
  in their expression profiles across the probed
  conditions

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Clustering yeast cell cycle dataset
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Clustering why?

• Reduce the dimensionality of the problem
  identify the major patterns in the dataset
• Co-expression ? Co-function
• Functional annotation of ESTs
• Links among pathways
• Co-expression ? Co-regulation
• Dissection of regulatory networks

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Similarity measures

• Clustering identifies group of genes with
  similar expression profiles
• How similarity/distance between genes expression
  profiles is measured?
• Euclidian distance
• Correlation coefficient
• Others

M conditions X (x1, x2, x3, , xm) Y (y1,
y2, y3, , ym)
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Similarity measure - Euclidian distance
In general m experiments X (x1, x2, x3, ,
xm) Y (y1, y2, y3, , ym)
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Similarity measure Correlation Coefficient

• X (x1, x2, x3, , xm)
• Y (y1, y2, y3, , ym)

-1 S(X,Y) 1
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Euclidian vs Correlation

• Euclidian distance takes into account the
  magnitude of the expression
• Correlation coef - insensitive to the amplitude
  of expression, takes into account the trends of
  the change.
• Common trends are considered very biologically
  relevant, the magnitude is considered less
  important ? correlation

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Standardization of expression levels
X (x1, x2, x3, , xm) Xj ? Xj
mean(X)/std(X), (doesnt change corr(X,Y))
Before standardization
After standardization
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Clustering Algorithms

• Kmeans
• SOMs
• CLICK
• Hierarchical clustering

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K-MEANS

• The user sets the number of clusters- k
• Initialization each gene is randomly assigned to
  one of the k clusters
• Average expression vector is calculated for each
  cluster (clusters profile)
• Iterate over the genes
• For each gene- compute its similarity to the
  cluster profiles.
• Move the gene to the cluster it is most similar
  to.
• Recalculated cluster profiles.
• Score current partition sum of distances between
  genes and the profile of the cluster they are
  assigned to (homogeneity of the solution).
• Stop criteria further shuffling of genes results
  in minor improvement in the clustering score

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How Many Clusters?

• Try several parameters and compare the clustering
  solutions
• Criteria for comparison later in the
  presentation
• PCA (Principle Component Analysis)
• A technique for projecting the gene expression
  data set onto a reduced (2 or 3 dimensional)
  easily visualized space

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PCA - Example

• Dataset Thousands of genes probed in 5
  conditions (time points relative to treatment)
• The expression profile of each gene is presented
  by the vector of its expression levels X (X1,
  X2, X3, X4, X5)
• Imagine each gene X as a point in a 5-dimentional
  space.
• Each direction/axis corresponds to a specific
  condition
• Genes with similar profiles are close to each
  other in this space
• PCA- Project this dataset to 2 dimensions,
  preserving as much information as possible

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PCA Example
Visual estimation of the number of clusters in
the data
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K-MEANS example 4 clusters
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Cluster 1
Cluster 3
Mis-classified
Cluster 4
Cluster 2
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K-means example 3 clusters
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Too few clusters K2
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SOMs (Self-Organizing Maps)

• User sets the number of clusters in a form of a
  rectangular grid (e.g., 3x2) map nodes
• Imagine genes as points in (M-dimensional) space
• Initialization map nodes are randomly placed in
  the data space

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Genes data points
Clusters map nodes
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SOM - Scheme

• Randomly choose a data point (gene).
• Find its closest map node
• Move this map node towards the data point
• Move the neighbor map nodes towards this point,
  but to lesser extent
• Iterate over data points

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• The extent of node displacements is relaxed with
  the iteration number
• After thousands of iterations
• Assign each gene to the map node (cluster) it is
  most similar to

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CLICK (CLuster Identification via Connectivity
Kernels)

• Compute similarity between all pairs of genes
• Construct weighted similarity graph
• Genes represented by nodes
• The weight of an edge connecting 2 genes reflects
  their expression similarity
• Find minimum weight cut that separates the
  graph into 2 un-connected sub-graphs
• Iterate on cutting subgraphs
• Stop criteria for cutting

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CLICK

• Estimates the optimal number of clusters in the
  dataset
• Identify outlier genes and leave them
  un-clustered (singletons)

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Hierarchical Clustering

• Organize the genes in a structure of a
  hierarchical tree
• Initial step each gene is regarded as a cluster
  with one item
• Find the 2 most similar clusters and merge them
  into a common node
• The length of the branch is proportional to the
  distance
• Iterate on merging nodes until all genes are
  contained in one cluster- the root of the tree.

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Hierarchical Clustering distance between
clusters
Single-linkage
Average-linkage
Complete-linkage
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Mathematical evaluation of clustering solution

• Merits of a good clustering solution
• Homogeneity
• Genes inside a cluster are highly similar to each
  other.
• Average similarity between a gene and the center
  (average profile) of its cluster.
• Separation
• Genes from different clusters have low similarity
  to each other.
• Weighted average similarity between centers of
  clusters.
• These are conflicting features increasing the
  number of clusters tends to improve with-in
  cluster Homogeneity on the expense of
  between-cluster Separation

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Performance on Yeast Cell Cycle Data
698 genes, 72 conditions (Spellman et al. 1998).
Each algorithm was run by its authors in a
blind test.
Ben-Dor, Shamir, Yakhini 1999
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Which genes to cluster?

• Apply filtering prior to clustering focus the
  analysis on the responding genes
• Applying controlled statistical tests to identify
  responding genes usually ends up with too few
  genes that doesnt allow global characterization
  of the response
• Fold change choose genes that changed by at
  least M-folds in at least L conditions
• Variance choose top P genes with the highest
  variance over the dataset
• Try various filtering scheme to find the setting
  that gives the best results (biologically)

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Clustering Tools

• Cluster (Eisen) hierarchical
• GeneCluster (Tamayo) SOM
• TIGR MeV K-Means, SOM, hierarchical, QTC, CAST
• Expander CLICK, SOM, K-means, hierarchical
• Many others

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Ascribe Biological Meaning to Clusters

• Identify over-represented functional categories
  in the clusters (i.e., cluster contains much more
  genes of specific biological process than
  expected by chance)
• Requirements for systematic analysis
• Controlled vocabulary for describing biological
  processes (protein biosynthesis\translation,
  apoptosis\programmed cell death)
• Standard assignment of genes into functional
  categories

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Gene Ontology (GO) project

• Defined controlled terms (ontologies) for
  description of gene products from 3 aspects
• Biological process (DNA repair, mitosis)
• Molecular function (protein serine/threonine
  kinase activity, transcription factor activity)
• Cellular component (nucleus, ribosome)
• Unified framework for genes annotation
  species-independent vocabularies
• A gene can have multiple associations in each
  ontology
• GO terms are organized in hierarchical structures
  called directed acyclic graphs (DAGs)
• Very general terms at top levels of the graph
• Terms get more specialized at lower levels

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Genes annotations using GO

• Human LocusLink (NCBI) GOA (EBI) 15K genes
  with biological process annotation
• Mouse MGI GOA 10K annotated genes
• Rat RGD 2.5k annotated genes
• Fly FlyBase 4.5k annotated genes
• Arabidopsis TAIR 12k annotated genes
• Yeast SGD
• Affymetrix chips Netaffx

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Ascribe Biological Meaning to Clusters

• This analysis is NOT INFORMATIVE!
• Some of the abundances can be explained just by
  chance
• Statistical tests are essential to detect
  significant phenomena

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Identifying enriched GO categories in clusters

• In the previous example
• Total number of chips genes with annotation
  5000
• Total number of chips genes associated with
  metabolism GO category 3,600
• Number of annotated genes in cluster 3 73
• Number of metabolic genes in cluster 3 50
• Is it statistically significant phenomena?
• Hyper-Geometric probability score

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Functional GO enrichment - Tools

• FatiGO
• GoMiner
• Expander
• DAVID
• EPGO (EBI)

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Acknowledgements

• SOM Figures in this presentations were taken from
  presentation of Benedikt Brors