CZ5225: Modeling and Simulation in CZ5225: Modeling and Simulation in Biology Biology Lecture 3: Clustering Analysis for Lecture 3: Clustering Analysis for Microarray Data I Microarray Data I Prof. Chen Yu Zong Prof. Chen Yu Zong Tel: 6874-6877 Tel: 6874-6877 Email: Email: [email protected][email protected]http://xin.cz3.nus.edu.sg http://xin.cz3.nus.edu.sg Room 07-24, level 7, SOC1, NUS Room 07-24, level 7, SOC1, NUS
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CZ5225: Modeling and Simulation in Biology Lecture 3: Clustering Analysis for Microarray Data I Prof. Chen Yu Zong Tel: 6874-6877 Email: [email protected].
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CZ5225: Modeling and Simulation in BiologyCZ5225: Modeling and Simulation in Biology
Lecture 3: Clustering Analysis for Microarray Data ILecture 3: Clustering Analysis for Microarray Data I
• Be weary - confounding computational artifacts are associated with all clustering algorithms. -You should always understand the basic concepts behind an algorithm before using it.
• Anything will cluster! Garbage In means Garbage Out.
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Supervised vs. Unsupervised LearningSupervised vs. Unsupervised Learning
• Supervised: there is a teacher, class labels are known
• Support vector machines• Backpropagation neural networks
• Unsupervised: No teacher, class labels are unknown
Expression VectorsExpression VectorsGene Expression Vectors encapsulate the
expression of a gene over a set of experimental conditions or sample types.
-0.8 0.8 1.5 1.8 0.5 -1.3 -0.4 1.5
-2
0
2
1 2 3 4 5 6 7 8Line Graph
-2 2
Numeric Vector
Heatmap
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Expression Vectors As Points in ‘Expression Space’Expression Vectors As Points in ‘Expression Space’
Experiment 1
Experiment 2
Experiment 3
Similar Expression
-0.8
-0.60.9 1.2
-0.3
1.3
-0.7t 1 t 2 t 3
G1
G2
G3
G4
G5
-0.4-0.4
-0.8-0.8
-0.7
1.3 0.9 -0.6
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Cluster AnalysisCluster Analysis
• Group a collection of objects into subsets or “clusters” such that objects within a cluster are closely related to one another than objects assigned to different clusters.
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How can we do this?How can we do this?
• What is closely related?• Distance or similarity metric• What is close?
• Clustering algorithm• How do we minimize distance between objects in a
group while maximizing distances between groups?
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Distance MetricsDistance Metrics
• Euclidean Distance measures average distance
• Manhattan (City Block) measures average in each dimension
• Correlation measures difference with respect to linear trends
Gene Expression 1
Gen
e E
xpre
ssio
n 2
(5.5,6)
(3.5,4)
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Clustering Gene Expression DataClustering Gene Expression Data
• Cluster across the rows, group genes together that behave similarly across different conditions.
• Cluster across the columns, group different conditions together that behave similarly across most genes.
Gen
es
Expression Measurements
i
j
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Clustering Time Series DataClustering Time Series Data
Data StandardizationData Standardization• Data points are normalized with respect to mean
and variance, “sphering” the data
• After sphering, Euclidean and correlation distance are equivalent
• Standardization makes sense if you are not interested in the size of the effects, but in the effect itself
• Results are misleading for noisy data
ˆ
ˆx
x
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Distance CommentsDistance Comments
• Every clustering method is based SOLELY on the measure of distance or similarity
• E.G. Correlation: measures linear association between two genes• What if data are not properly transformed?• What about outliers?• What about saturation effects?
• Even good data can be ruined with the wrong choice of distance metric
• Pros:– Commonly used algorithm– Simple and quick to calculate
• Cons:– Real genes probably do not have a
hierarchical organization
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Using Hierarchical ClusteringUsing Hierarchical Clustering
1. Choose what samples and genes to use in your analysis
2. Choose similarity/distance metric
3. Choose clustering direction
4. Choose linkage method
5. Calculate the dendrogram
6. Choose height/number of clusters for interpretation
7. Assess results
8. Interpret cluster structure
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Choose what samples/genes to includeChoose what samples/genes to include
• Very important step• Do you want to include housekeeping genes or genes
that didn’t change in your results?• How do you handle replicates from the same sample?• Noisy samples?• Dendrogram is a mess if everything is included in large
• Nearest Neighbor Algorithm is an agglomerative approach (bottom-up).
• Starts with n nodes (n is the size of our sample), merges the 2 most similar nodes at each step, and stops when the desired number of clusters is reached.
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Nearest Neighbor, Level 3, k = 6 clusters.
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Nearest Neighbor, Level 4, k = 5 clusters.
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Nearest Neighbor, Level 5, k = 4 clusters.
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Nearest Neighbor, Level 6, k = 3 clusters.
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Nearest Neighbor, Level 7, k = 2 clusters.
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Nearest Neighbor, Level 8, k = 1 cluster.
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Calculate the similarity between all possible
combinations of two profiles
Two most similar clusters are grouped together to form
a new cluster
Calculate the similarity between the new cluster and
all remaining clusters.
Hierarchical ClusteringHierarchical Clustering
Keys• Similarity• Clustering
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Hierarchical ClusteringHierarchical Clustering
C1
C2
C3
Merge which pair of clusters?
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+
+
Hierarchical ClusteringHierarchical Clustering
Single Linkage
C1
C2
Dissimilarity between two clusters = Minimum dissimilarity between the members of two clusters
Tend to generate “long chains”
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Hierarchical ClusteringHierarchical Clustering
Complete Linkage
C1
C2
Dissimilarity between two clusters = Maximum dissimilarity between the members of two clusters
Tend to generate “clumps”
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+
Hierarchical ClusteringHierarchical Clustering
Average Linkage
C1
C2
Dissimilarity between two clusters = Averaged distances of all pairs of objects (one from each cluster).
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+
+
Hierarchical ClusteringHierarchical Clustering
Average Group Linkage
C1
C2
Dissimilarity between two clusters = Distance between two cluster means.
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Which one?Which one?
• Both methods are “step-wise” optimal, at each step the optimal split or merge is performed
• Doesn’t mean that the final result is optimal• Merging:
• Computationally simple• Precise at bottom of tree• Good for many small clusters
• Divisive• More complex, but more precise at the top of the tree• Good for looking at large and/or few clusters
• For Gene expression applications, divisive makes more sense