1. CSCE555 Bioinformatics Lecture 14 Cluster analysis for microarray data
Meeting: MW 4:00PM-5:15PM SWGN2A21
Instructor: Dr. Jianjun Hu Course page:
University of South Carolina
Department of Computer Science and Engineering
2008

2. Outline Why microarray data analysis Understanding Microarray Data
Clustering in microarray analysis
Project proposals and Group
11/27/2018

3. Functional Genomics – Why?
You can’t learn everything from DNA sequence
Levels of organization contain different information
Want to know how a whole cell works
May not know a priori which pieces of information are going to be the most valuable to solve a particular problem
Need to know both analytical tools and biology
What are the great questions?
What techniques are available to answer them?
What computational/stasticial techniques can get you what you want?
Start with whole genome, annotated so you know where most of the genes are
Make probes to 3’ ends of genes generally

4. Microarrays Extract RNA and incorporate label Combine Scanned image
Hybridize

5. Types of Microarrays For measuring mRNA
Affymetrix, Nimblegen, Illumina (short oligos made on the slide)
Oligonucleotides (short DNA – typically 70-mers)
For identifying where proteins bind DNA and non-coding or other RNAs
Tiling arrays
For identifying SNPs
There are even protein arrays!

6. Why microarrays?
You can get a great deal of data – multiplexed, uses very little reagent, can use standard detection devices
Similar techniques are used for working with RNA and DNA and similar attachment chemistries
Can carry out enzyme reactions on the arrays for sequencing and other analyses

7. Microarray experiments have multiple steps each step introduces some variability
Cell harvest
Slide Manufacture
RNA preparation
Slide Post-processing
Labeling reaction
Pre-hybridization
Hybridization
Washing
Scanning
Data Analysis

8. What questions are you asking?
First of all – you are measuring mRNA abundance – so questions are about gene expression at the mRNA level
What are the levels of all mRNAs?
How do they change?
Are there interesting changes or groups that provide insight into some process or state?

9. Design and analysis Experimental design is critical Analysis tools:
Hierarchical clustering
Gene lists based on expression
Time course analysis
Statistics
Gene Ontology
Pathway analysis
Classifiers – to identify biomarkers

10. Aim of clustering: Group objects according to their similarity
a set of objects
that are similar
to each other
and separated
from the other
objects.
Example: green/
red data points
were generated
from two different
normal distributions

11. Clustering microarray data
Genes and experiments/samples are given as the row and column vectors of a gene expression data matrix.
Clustering may be applied either to genes or experiments (regarded as vectors in Rp or Rn).
gene expression data matrix
n experiments
p genes

12. Why cluster genes?
Identify groups of possibly co-regulated genes (e.g. in conjunction with sequence data).
Identify typical temporal or spatial gene expression patterns (e.g. cell cycle data).
Arrange a set of genes in a linear order that is at least not totally meaningless.

13. Why cluster experiments/samples?
Quality control: Detect experimental artifacts/bad hybridizations
Check whether samples are grouped according to known categories (though this might be better addressed using a supervised approach: statistical tests, classification)
Identify new classes of biological samples (e.g. tumor subtypes)

14. Alizadeh et al., Nature 403:503-11, 2000

15. Cluster analysis
Generally, cluster analysis is based on two ingredients:
Distance measure: Quantification of (dis-)similarity of objects.
Cluster algorithm: A procedure to group objects. Aim: small within-cluster distances, large between-cluster distances.

16. Some distance measures
Given vectors x = (x1, …, xn), y = (y1, …, yn)
Euclidean distance:
Manhattan distance:
Correlation
distance:

17. Which distance measure to use?
The choice of distance measure should be based on the application area. What sort of similarities would you like to detect?
Correlation distance dc measures trends/relative differences:
dc(x, y)= dc(ax+b, y) if a > 0.
x = (1, 1, 1.5, 1.5)
y = (2.5, 2.5, 3.5, 3.5) = 2x + 0.5
z = (1.5, 1.5, 1, 1)
dc(x, y) = 0, dc(x, z) = 2.
dE(x, z) = 1, dE(x, y) ~ 3.54.

18. Which distance measure to use?
Euclidean and Manhattan distance both measure absolute differences between vectors. Manhattan distance is more robust against outliers.
May apply standardization to the observations:
Subtract mean and divide by standard deviation:
After standardization, Euclidean and correlation distance are equivalent:

19. K-means clustering Input: N objects given as data points in Rp
Specify the number k of clusters.
Initialize k cluster centers. Iterate until convergence:
- Assign each object to the cluster with the closest center (wrt Euclidean distance).
- The centroids/mean vectors of the obtained clusters are taken as new cluster centers.
K-means can be seen as an optimization problem:
Minimize the sum of squared within-cluster distances,
Results depend on the initialization. Use several starting points and choose the “best” solution (with minimal W(C)).

20. K-means/PAM: How to choose K (the number of clusters)?
There is no easy answer.
Many heuristic approaches try to compare the quality of clustering results for different values of K (for an overview see Dudoit/Fridlyand 2002).
The problem can be better addressed in model-based clustering, where each cluster represents a probability distribution, and a likelihood-based framework can be used.

21. Self-organizing maps Neural Network
K = r*s clusters are arranged as nodes of a two-dimensional grid. Nodes represent cluster centers/prototype vectors.
This allows to represent similarity between clusters.
Algorithm:
Initialize nodes at random positions. Iterate:
- Randomly pick one data point (gene) x.
- Move nodes towards x, the closest node most, remote nodes (in terms of the grid) less. Decrease amount of movements with no. of iterations.
from Tamayo et al. 1999

22. Self-organizing maps
from Tamayo
et al. 1999
(yeast cell
cycle data)

23. Agglomerative hierarchical clustering
Bottom-up algorithm (top-down (divisive) methods are less common).
Start with the objects as clusters.
In each iteration, merge the two clusters with the minimal distance from each other - until you are left with a single cluster comprising all objects.
But what is the distance between two clusters?

24. Distances between clusters used for hierarchical clustering
Calculation of the distance between two clusters is based on the pairwise distances between members of the clusters.
Complete linkage: largest distance
Average linkage: average distance
Single linkage: smallest distance
Complete linkage gives preference to compact/spherical
clusters. Single linkage can produce long stretched clusters.

25. Hierarchical clustering
Golub data: different types of leukemia. Clustering based on the 150 genes with highest variance across all samples.
The height of a node in the dendrogram represents the distance of the two children clusters.
Loss of information: n objects have n(n-1)/2 pairwise distances, tree has n-1 inner nodes.
The ordering of the leaves is not uniquely defined by the dendrogram: 2n-2 possible choices.

26. Alternative: direct visualization of similarity/distance matrices
Array batch 1
Array batch 2
Useful if one wants to investigate a specific factor (advantage: no loss of information). Sort experiments according to that factor.

27. Clustering of time course data
Suppose we have expression data from different time points t1, …, tn, and want to identify typical temporal expression profiles by clustering the genes.
Usual clustering methods/distance measures don’t take the ordering of the time points into account – the result would be the same if the time points were permuted.
Simple modification: Consider the difference xi(j+1) – xij between consecutive timepoints as an additional observation yij. Then apply a clustering algorithm such as K-means to the augmented data matrix.

28. Biclustering
Usual clustering algorithms are based on global similarities of rows or columns of an expression data matrix.
But the similarity of the expression profiles of a group of genes may be restricted to certain experimental conditions.
Goal of biclustering: identify “homogeneous” submatrices.
Difficulties: computational complexity, assessing the statistical significance of results
Example: Tanay et al

29. The role of feature selection
Sometimes, people first select genes that appear to be differentially expressed between groups of samples. Then they cluster the samples based on the expression levels of these genes. Is it remarkable if the samples then cluster into the two groups?
No, this doesn’t prove anything, because the genes were selected with respect to the two groups! Such effects can even be obtained with a matrix of i.i.d. random numbers.

30. Conclusions
Clustering has been very popular in the analysis of microarray data. However, many typical questions in microarray studies (e.g. identifying expression signatures of tumor types) are better addressed by other methods (classification, statistical tests).
Clustering algorithms are easy to apply (you cannot really do it wrong), and they are useful for exploratory analysis. But it is difficult to assess the validity/significance of the results. Even “random” data with no structure can yield clusters or exhibit interesting looking patterns.

31. Final Project Proposal
Aims: investigate a bioinformatics problem
Group: one or two person
Proposal: one page
Problem description
Data sources
Algorithms
Expected results
Test: presentation and final report

32. Acknowledgement
Anja von Heydebreck