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Making Sense of Complicated Microarray Data Part II Gene Clustering and Data Analysis. Gabriel Eichler Boston University Some slides adapted from: MeV documentation slides. Why Cluster?. Clustering is a process by which you can explore your data in an efficient manner. - PowerPoint PPT Presentation
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Making Sense of Complicated Microarray Data
Part II Gene Clustering and Data AnalysisGabriel EichlerBoston UniversitySome slides adapted from: MeV documentation slides
Why Cluster?
Clustering is a process by which you can explore your data in an efficient manner.
Visualization of data can help you review the data quality.
Assumption: Guilt by association – similar gene expression patterns may indicate a biological relationship.
Expression 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
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1 2 3 4 5 6 7 8Line Graph
-2 2
Numeric Vector
Heatmap
Expression Vectors As Points in ‘Expression Space’
Experiment 1
Experiment 2
Experiment 3
Similar Expression
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G1
G2
G3
G4
G5
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Distance and Similarity -the ability to calculate a distance (or similarity, it’s inverse) between two expression vectors is fundamental to clustering algorithms
-distance between vectors is the basis upon which decisions are made when grouping similar patterns of expression
-selection of a distance metric defines the concept of distance
Distance: a measure of similarity between gene expression.
Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 Exp 6
Gene A
Gene B
x1A x2A x3A x4A x5A x6A
x1B x2B x3B x4B x5B x6B
Some distances: (MeV provides 11 metrics)
1. Euclidean: i = 1 (xiA - xiB)26
2. Manhattan: i = 1 |xiA – xiB|6
3. Pearson correlation
p0
p1
Clustering Algorithms
Clustering Algorithms
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.
Hierarchical Clustering
(HCL-1)
• IDEA: Iteratively combines genes into groups based on similar patterns of observed expression
• By combining genes with genes OR genes with groups algorithm produces a dendrogram of the hierarchy of relationships.
• Display the data as a heatmap and dendrogram
• Cluster genes, samples or both
Hierarchical ClusteringGene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical ClusteringGene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical ClusteringGene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8
Hierarchical Clustering
H L
Hierarchical Clustering
The Leaf Ordering Problem:• Find ‘optimal’ layout of branches for a given dendrogram architecture• 2N-1 possible orderings of the branches• For a small microarray dataset of 500 genes there are 1.6*E150 branch configurations
SamplesG
enes
Hierarchical ClusteringThe Leaf Ordering Problem:
Hierarchical Clustering
Pros:– Commonly used algorithm– Simple and quick to calculate
Cons:– Real genes probably do not have a
hierarchical organization
Self-Organizing Maps (SOMs)
a dbc
Idea: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares.
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D
B
C
Self-Organizing Maps (SOMs)
a dbc
IDEA: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares.
A
D
B
C
Gene 1Gene 2Gene 3Gene 4Gene 5Gene 6Gene 7Gene 8Gene 9Gene 10-Gene 11Gene 12Gene 13Gene 14Gene 15Gene 16
a_1hr a_2hr a_3hr b_1hr b_2hr b_3hr1 2 4 5 7 92 3 7 7 6 34 4 5 5 4 43 4 3 4 3 31 2 3 4 5 68 7 7 6 5 34 4 4 4 5 45 6 5 4 3 23 3 1 3 6 82 4 8 5 4 21 5 6 9 8 71 3 5 8 8 64 3 3 4 5 69 7 5 3 2 11 2 2 3 4 41 2 5 7 8 9
A
B
C
D
E
F
G
H
I
A
B
C
D
E
F
G
H
I
A
B
C
D
E
F
G
H
I
A
B
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D
E
F
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H
I A
B
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D
E
F
G
H
I
Self-organizing Maps (SOMs)
Self-organizing Maps (SOMS)
A
B
C
D
E
F
G
H
I
Genes , , and1 16 5
Genes and 6 14Genes and 9 13
Genes and 4, 7 2Genes 3
Gene 15 Genes 8
Genes 10
Genes and 11 12
G en e s
The Gene Expression Dynamics Inspector – GEDI
Group A
Group B
Group C
1.5 1.4 1.7 1.2 .85 .65 .50 .55 2.5 2.8 2.7 2.1
.78 .95 .75 .45 1.1 1.2 1.0 1.3 .56 .62 .78 .89
.45 .23 .15 .05 .82 .71 .62 .49 .11 .16 .11 .95
2.2 4.5 6.7 6.2 2.2 2.5 2.8 2.9 .48 .90 1.5 1.8
2.1 2.0 1.9 1.6 4.2 4.8 5.2 5.5 2.5 2.6 2.0 1.9
1.2 1.1 1.6 2.9 1.1 1.8 1.9 1.4 1.7 1.2 1.1 1.6
Gene 1Gene 2Gene 3Gene 4Gene 5Gene 6
…
Group A
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2
Group B Group C
C3 C4} } }S a m p l e s
G en e s
1 2 3 4
H
L
Grou
p A
Grou
p B
Grou
p C
GEDI’s Features:•Allows for simultaneous analysis or several time courses or datasets
•Displays the data in an intuitive and comparable mathematically driven visualization
•The same genes maps to the same tiles
Software Demonstrations
MeV available at http://www.tigr.org/software/tm4/mev.html
GEDI available at http://www.chip.org/~ge/gedihome.htm
Comparison of GEDI vs. Hierarchical ClusteringHierarchical clustering of random data
(GIGO)
From: CreateGEP_Journal.wpd, random_A
G.E.D.I. allows the direct visual assessment of the quality of conventional cluster analysis
Questions