Unsupervised analysis of gene expression data Bing Zhang Department of Biomedical Informatics Vanderbilt University
[email protected]
Overall workflow of a microarray study Biological question Experiment design Microarray experiment Image analysis Pre-processing Data Analysis
Experimental verification 2
Hypothesis
Applied Bioinformatics, Spring 2011
Three major goals of gene expression studies
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Class comparison (supervised analysis)
e.g. disease biomarker discovery
Differential expression analysis
Input: gene expression data, class label of the samples
Output: differentially expressed genes
Class detection (unsupervised analysis)
e.g. patient subgroup detection
Clustering analysis
Input: gene expression data
Output: groups of similar samples or genes
Class prediction (supervised learning)
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e.g. disease diagnosis and prognosis
Machine learning techniques
Input: gene expression data, class label of the samples (training data)
Output: prediction model Applied Bioinformatics, Spring 2011
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What is clustering
Clustering algorithms are methods to divide a set of n objects (genes or samples) into g groups so that within group similarities are larger than between group similarities
Unsupervised techniques that do not require sample annotation in the process Samples
Genes
Sample_1 Sample_2 Sample_3 Sample_4 Sample_5
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TNNC1 DKK4 ZNF185 CHST3 FABP3 MGST1 DEFA5 VIL1 AKAP12 HS3ST1 ……
14.82 10.71 15.20 13.40 15.87 12.76 10.63 11.47 18.26 10.61 ……
14.46 10.37 14.96 13.18 15.80 12.80 10.47 11.69 18.10 10.67 ……
14.76 11.23 15.07 13.15 15.85 12.67 10.54 11.87 18.50 10.50 ……
11.22 19.74 12.57 11.18 13.16 14.92 15.52 13.94 15.60 12.44 ……
Applied Bioinformatics, Spring 2011
11.55 19.73 12.37 10.99 12.99 15.02 15.52 14.01 15.69 12.23 ……
…… …… …… …… …… …… …… …… …… …… …… ……
Why clustering?
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Exploratory data analysis, providing rough maps and suggesting directions for further study
Representing distances among high-dimensional expression profiles in a concise, visually effective way, such as a tree or dendrogram
Identify candidate subgroups in complex data. e.g. identification of novel sub-types in cancer, identification of co-expressed genes
Functional annotation based on guilt by association
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Clustering methods
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Hierarchical clustering: generate a hierarchy of clusters going from 1 cluster to n clusters
Partitioning: divide the data into g groups using some reallocation algorithms, e.g. K-means
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Hierarchical clustering
Agglomerative clustering (bottom-up)
At each step of the algorithm, the pair of clusters with the shortest distance are combined into a single cluster. The algorithm stops when all sample units are combined into a single cluster of size n.
Divisive clustering (top-down)
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Start out with all sample units in n clusters of size 1.
Start out with all sample units in a single cluster of size n. At each step of the algorithm, clusters are partitioned into a pair of daughter clusters, selected to maximize the distance between each daughter. The algorithm stops when sample units are partitioned into n clusters of size 1.
Applied Bioinformatics, Spring 2011
Agglomerative clustering
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Require distance measurement
Between two objects
Between clusters
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Between objects distance measurement
Euclidean distance
#( x
i " yi )
Parametric, normally distributed and follow the linear regression model !
Focus on the expression profile shape
Non-parametric, no assumption
!
Less sensitive but more robust than Pearson
Applied Bioinformatics, Spring 2011
2
i=1 n
Focus on the expression profile shape !
Spearman correlation coefficient
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Focus on the absolute expression value
d=
Pearson correlation coefficient
n
r=
# (x i=1
#
n i=1
d =1" r
i
" x )(y i " y )
(x i " x ) 2
#
n i=1
(y i " y ) 2
Different measurement, different distance
Most similar profile to GeneA (blue) based on different distance measurement: Euclidean: GeneB (pink) Pearson: GeneC (green) Spearman: GeneD (red)
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Gene expression level (log2)
6 5 4
GeneA
3
GeneB GeneC
2
GeneD
1 0 1
2
3
4
5
Time (hr)
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6
7
Between cluster distance measurement
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Single linkage: the smallest distance of all pairwise distances
Complete linkage: the maximum distance of all pairwise distances
Average linkage: the average distance of all pairwise distances
Applied Bioinformatics, Spring 2011
Visualization and interpretation of hierarchical clustering results
Dendrogram
Tree structure with the genes or samples as the leaves The height of the join indicates the distance between the left branch and the right branch
Heat map
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Output of a hierarchical clustering
Graphical representation of data where the values are represented as colors.
Applied Bioinformatics, Spring 2011
Partitioning
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General idea
Select the number of groups, g
Randomly divide the objects into g Group
Iteratively rearrange the objects until a stop condition
Representative methods
K-means
Self Organizing Map (SOM)
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K-means
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Define k = number of clusters
Randomly initialize a seed vector for each cluster
Go through all objects, and assign each object to the cluster witch it is most similar to
Recalculate all seed vectors as means of patterns of each cluster
Repeat 3 & 4 until a stop condition (e.g. Until all objects get assigned to the same partition twice in a row)
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K-means seed vector 1 Randomly initialize seeds Objects join with closest seed seed vector 2
Recaculate seeds Reassign objects Recaculate seeds Reassign objects
Seeds become stable: final clusters 15
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Cool animations
Hierarchical clustering
K-means
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http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/AppletH.html
http://animation.yihui.name/mvstat:k-means_cluster_algorithm
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Resources
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Data source
Gene Expression Omnibus (GEO): http://www.ncbi.nlm.nih.gov/geo/
ArrayExpress: http://www.ebi.ac.uk/arrayexpress/
Microarray data analysis tools
Bioconductor: http://www.bioconductor.org/
Expression profiler: http://www.ebi.ac.uk/expressionprofiler/
Applied Bioinformatics, Spring 2011
Summary
Agglomerative clustering
Bottom-up
Between objects distance measurement
Euclidean distance
Pearson’s correlation coefficient Spearman’s correlation coefficient
Single linkage
Complete linkage
Average linkage
Visualization
Dendrogram
Heat map
k-means clustering
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Between cluster distance measurement
Partitioning Applied Bioinformatics, Spring 2011
Exercise
Data set: evan_deneris_2010_5ht_top500diff.txt
500 selected probe sets
Four groups (Rostral_5ht, Rostral_non5ht, Caudal_5ht, Caudal_non5ht)
No missing value; Already normalized; Already log transformed
Use hierarchical clustering in Expression profiler (http://www.ebi.ac.uk/expressionprofiler) to generate a heat map
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Applied Bioinformatics, Spring 2011