1. Microarray Data Preprocessing and Clustering Analysis
Spotted Microarray Workshop
Microarray Data Preprocessing and Clustering Analysis
Liangjiang (LJ) Wang
KSU Bioinformatics Center, Biology Division
June, 2005

2. Outline Overview of microarray data analysis.
Microarray data preprocessing.
Statistical inference of significant genes.
Clustering analysis and visualization.
Microarray databases and standards.

3. Spotted Microarray Gene expression matrix (ratios) Samples Genes
Reference Cells
Experimental Cells
Samples
Gene
expression
matrix (ratios)
Extract mRNA
Genes
Make and label cDNA
Array image data
Hybridize
Probes

4. Overview of Microarray Data Analysis
Microarray experiment
Image analysis and data normalization
Sample classification
Statistical inference of significant genes
Clustering analysis of co-expressed genes
List of significant or co-expressed genes
Promoter analysis, gene function prediction, and pathway analysis

5. Microarray Image Analysis
Spot finding: place a grid to identify spot locations.
Segmentation: separate each spot (foreground) from the background.
Spot intensity extraction: often use mean or median intensity of all the pixels within a spot.
Background subtraction: may subtract local background or globally estimated background.

6. Microarray Data Normalization
To remove the systemic bias in the data so that meaningful biological comparisons can be made:
Unequal quantities of starting RNA.
Differences in labeling (e.g., Cy3 versus Cy5).
Different detection efficiencies between the dyes.
Differences in hybridization and washing.
Other experimental variations.
Normalization is based on some assumptions:
A subset of genes (housekeeping genes) is assumed to be constant.
The total intensity or overall intensity distributions between the two channels are comparable.

7. Global Normalization Total intensity normalization:
A normalization factor is calculated by summing the measured intensities in both channels and then taking the ratio:
All the intensities in one channel are multiplied by the normalization factor:
A subset of genes (housekeeping genes) may be also used for the global normalization.

8. Scatter Plot of Cy3 vs Cy5 Intensities
Intensities from “self-self” hybridization
After normalization
Before normalization
(Quackenbush, 2001)

9. Lowess Normalization
Probably the most widely used approach for spotted microarray normalization.
A locally weighted linear repression is used to estimate the systematic bias in the data.
Ratio-Intensity (R-I) plot (also called MA plot)
Raw data
log ratio, log2(R / G)
(Quackenbush, 2001)
After lowess
log ratio, log2(R / G)
(Quackenbush, 2001)

10. Why Log Transformation?
Log 2 (R / G) treats up-regulated and down-regulated genes in a similar fashion:
If R / G = 4, log 2 (R / G) = 2.
If R / G = 1/4 = 0.25, log 2 (1/4) = -2.
Log normalizes distribution.

11. Finding Significant Genes
Fold change: uses a single fold change threshold to select genes; does not take into account the biological and experimental variability.
Statistical tests: t test, SAM and ANOVA; require a number of replicates for each condition.

12. Volcano Plot Statistical significance → high
(Wolfinger et al., 2001)
Larger fold changes does not necessarily mean higher significance levels.

13. Student’s t Test
To test whether there is a significant difference in gene expression measurements between two conditions (A and B):
H0: no difference in gene expression,
H1: the gene is differentially expressed,
Test statistic:
Calculate the probability (p value) of the t statistic with degree of freedom, df = nA + nB - 2.
Assume a 95% confidence level (i.e., 5% false positive rate). If p ≤ 0.05, reject the null hypothesis.

14. Problem of Multiple Testing
Suppose that you have 5,000 genes on your microarray, and you select the genes with p ≤ 0.05 (i.e., 5% false positive rate). Because you have applied 5,000 times of the t test, you may have 5,000 x 0.05 = 250 false positives!

15. Correction for Multiple Testing
Bonferroni correction:
Set the significance cutoff, p' = α / N, where α is the false positive rate, and N is the number of genes.
For example, if you have 5,000 genes in your microarray, and you expect 5% of false positives, the significance cutoff, p' = 0.05 / 5000 = 1.0 E -5.
False Discovery Rate (FDR):
Rank all the genes by significance (p value) so that the top gene has the most significant p value.
Start from the top of the list, and accept the genes if
i: the rank of the gene in the list.
N: the number of genes in the array.
q: the desired FDR.

16. SAM: Significance Analysis of Microarrays
SAM ( is a modified t test.
The observed d statistic is computed from the data, and the expected d statistic is assessed by permutation.
With a user-defined FDR, SAM derives the significance cutoffs for selecting up- and down-regulated genes.
Down-regulated
Up-regulated
Expected d statistic
Observed d statistic
SAM Plot
Observed d = expected d
Significance cutoffs

17. ANOVA
ANalysis Of VAriance (ANOVA) is used to find significant genes in more than two conditions:
For each gene, compute the F statistic.
Calculate the p value for the F statistic.
Adjust the significance cutoff for multiple testing.
Gene
Disease A
Disease B
Disease C A1 A2 A3 B1 B2 B3 C1 C2 C3 g1
0.9
1.1
1.4
1.9
2.1
2.5
3.1
2.9
2.6 g2
4.2
3.9
3.5
5.1
4.6
4.3
1.8
2.4
1.5 g3
0.7
1.2
0.6
0.8 g4
2.0
1.7
4.0
3.2
2.8
6.3
5.7
∙ ∙ ∙

18. Clustering Analysis
Clustering analysis is to partition a dataset into a few groups (clusters) such that:
Homogeneity: objects in the same
cluster are similar to each other.
Separation: dissimilar objects are
placed in different clusters.
In microarray data analysis, this
means to find groups of genes (or samples) with similar gene expression patterns.
Two key questions:
How to measure similarity of gene expression?
How to find these gene clusters?

19. Distance Metrics
Expression vector: each gene can be represented as a vector in the N-dimensional
hyperspace, where N is the
number of samples.
Euclidean distance:
Vector angle:
Pearson correlation coefficient:
Sample 1
Sample 2 A a2 a1 B b2 b1 d α

20. Z Transformation
If Euclidean distance is used for clustering analysis, z transformation of the gene expression matrix may be necessary.
For each gene, calculate the z scores of the expression values:
Log (ratio)
Samples
— Gene A
— Gene B
dAB = 3.58
Z score
Samples
— Gene A
— Gene B
dAB = 0.36

21. Hierarchical Clustering
Initialization: each object is a cluster
Iteration
Merge two clusters which are most similar to each other
Until all objects are merged into a single cluster b d c e a
Step 0
Step 1
Step 2
Step 3
Step 4
a b
a b c d e
c d e
d e
Agglomerative approach

22. Hierarchical Clustering (Cont’d)
Calculating distances between clusters:
Single linkage: takes the shortest
distance between two clusters.
Complete linkage: uses the largest
Average linkage: uses the average
The clustering results are visualized using a tree (called dendrogram) with color-coded gene expression levels.
Hierarchical clustering can be applied to genes, samples, or both. CL SL AL

23. Sample Clustering
Alizadeh, et al., Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature, 403:

24. k-Means Clustering Initialization User-defined k (# clusters)
Randomly place k vectors
(called centroids) in the
data space
Iteration
Each object is assigned to
its closest centroid
Re-compute each centroid
by taking the mean of
data vectors currently
assigned to the cluster
Until the cluster centroids no longer change
Iteration 0: 1: 2: 3:
k = 2

25. Self-Organizing Map (SOM)
The user defines an initial geometry of nodes (reference vectors) for the partitions such as a 3 x 2 rectangular grid.
During the iterative “training” process, the nodes migrate to fit the gene expression data.
The genes are mapped to the most similar reference vector.

26. k-means SOM 237 genes 194 genes
Clustering analysis of a yeast cell cycle time-series dataset
k-means
SOM
237 genes
194 genes

27. Tools for Microarray Data Analysis
GenePix ( commercial software for microarray image analysis.
GeneSpring ( commercial software for microarray data analysis.
TIGR MeV ( free software for clustering, visualization, classification and statistical analysis of microarray data.
Bioconductor ( open source, free software for the analysis of genomic data. For microarray data analysis, most of the statistical methods are implemented in R.

28. Microarray Databases
Gene Expression Omnibus (GEO) at NCBI ( a public repository for high throughput gene expression data.
ArrayExpress at EBI ( a public repository for microarray gene expression data; MIAME compliant.
Stanford Microarray Database (SMD at stores raw and normalized microarray data; provides data retrieval and online data processing.

29. The MIAME Standard
MIAME (Minimum Information About a Microarray Experiment) is a microarray data standard proposed by the Microarray Gene Expression Database group (MGED,
MIAME ( is needed to interpret the results from a microarray experiment and potentially to reproduce the microarray experiment.
MIAME checklist helps authors, reviewers and editors of scientific journals to meet the MIAME requirements and to make microarray data available to the community in a useful way.

30. Summary
Image analysis and data normalization are important preprocessing steps for microarray data analysis.
Statistical methods are available for selecting significantly up- or down-regulated genes.
Clustering analysis is widely used to explore and visualize microarray data.
The resulting significant or co-expressed genes can be further investigated using Gene Ontology annotation and promoter analysis.