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.

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Numeric Vector

Heatmap

Expression Vectors As Points in ‘Expression Space’

Experiment 1

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Experiment 3

Similar Expression

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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

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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

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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)

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Idea: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares.

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Self-Organizing Maps (SOMs)

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IDEA: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares.

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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

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Self-organizing Maps (SOMs)

Self-organizing Maps (SOMS)

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Genes , , and1 16 5

Genes and 6 14Genes and 9 13

Genes and 4, 7 2Genes 3

Gene 15 Genes 8

Genes 10

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G en e s

The Gene Expression Dynamics Inspector – GEDI

Group A

Group B

Group C

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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

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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

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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