1. Microarray Clustering
Xiaole Shirley Liu
STAT115/215

2. Profiles Heat map display
Gene expression profile refers to individual rows or columns as profiles
Row is profile of a gene
Column is profile of a sample / condition
Tongji 2009

3. Clustering Can cluster genes or samples
Genes: have similar expression profile over different samples or conditions
Samples: have similar expression profile over all the genes

4. Clustering Motivation for clustering: Clustering quality:
Visualizing data
Understand general characteristics of data
Make generalizations about gene behavior
Classify samples
Clustering quality:
“Distance”: 1 – corr
Maximize inter (between)-cluster distance
Minimize intra (within)-cluster distance

5. Cluster Stability
Mask out some data (e.g. only sample a subset of genes or samples) to perform clustering
Introduce a little noise to the data, then perform clustering
May select only diff expr genes for clustering, or use genes on the same pathway, etc.

6. Missing Value Estimation
Missing values affects clustering
E.g. when calculating distances
Naïve solution:
Ignore gene/sample, fill in 0 or Avg
K nearest neighbors
Gene i has missing value at sample j
Calculate corr between gene i and all other genes using all samples except j
Find k genes (e.g. 10) with highest corr to i
Calculate k genes’ avg expression at sample j

7. Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8

8. Hierarchical Clustering
Gene 1
Gene 2
Gene 3
Gene 4
Gene 5
Gene 6
Gene 7
Gene 8

9. Hierarchical Clustering
Gene 7
Gene 1
Gene 2
Gene 4
Gene 5
Gene 3
Gene 8
Gene 6

10. Hierarchical Clustering
Repeatedly
Merge two nodes (either a gene or a cluster) that are closest to each other
Re-calculate the distance from newly formed node to all other nodes
Branch length represents distance
Linkage: distance from newly formed node to all other nodes
Tongji 2009

11. Hierarchical Clustering Linkage
Single Complete
Average: pairwise distances

12. Some Brain Teasers If we have n data points
How many internal nodes are in the H-cluster?
How many possible ways to draw the H-cluster
Break

13. Partitional Clustering
Disjoint groups
From hierarchical clustering:
Cut a line from hierarchical clustering
By varying the cut height, we could produce arbitrary number of clusters

14. K-means Algorithm Choose K centroids at random Expression in Sample1
Iteration = 0

15. K-means Algorithm Choose K centroids at random
Assign object i to closest centroid
Iteration = 1

16. K-means Algorithm Choose K centroids at random
Assign object i to closest centroid
Recalculate centroid based on current cluster assignment
Iteration = 2

17. K-means Algorithm Choose K centroids at random
Assign object i to closest centroid
Recalculate centroid based on current cluster assignment
Repeat until assignment stabilize
Iteration = 3

18. K-means Algorithm Example
Assign each objects to most similar center 1 2 3 4 5 6 7 8 9 10
Update the cluster means 1 2 3 4 5 6 7 8 9 10
K=2
Arbitrarily choose K object as initial cluster center
reassign
reassign
Update the cluster means

19. K-means Algorithm Deterministic method
Initial cluster centers important
Can be trapped in local optimal
How to pick initial cluster centers
Run hierarchical cluster, find cut line
Random start many times with different initial centers
Not tolerant to outliers or noise

20. Problem With Outliers x1 x2 x3

21. Partition Around Medoids
Pick one real data point (closest to all) instead of average as the centroid of the cluster
More robust in the presence of noise and outliers

22. How to Pick K K = 2, gradually increase
Improvement: reduce within cluster distance and increase between cluster distance
Cost: cost with each increase in K
Compare the cost with improvement, stop when not worth it

23. How to Pick K W(k) = total sum of squares within clusters
B(k) = sum of squares between cluster means
n = total number of data points
Calinski & Harabasz, 1974
Hartigan, 1975
stop when H(k) < 10

24. How to Pick K

25. Practical Considerations
Only cluster genes that are variable across samples
The magic of 7!
Break

26. Batch Effect Removal

27. Motivation Batch Effect: Non-biological variation
Make samples not directly comparable
Caused by differences:
Array platform
Lab protocol or experimenter
Time of day or hybridization
Atmospheric ozone level (Rhodes et al. 2004)

28. Example of Batch Effect
Knock down expression using different cells and different siRNA in 3 batches

29. Batch vs Normalization
Shouldn’t normalization take care of this?
NO!
Normalization and expression indexing procedures only adjust sample and probe effects
Usually these are orthogonal to the batch effects, so batch effects are left in the data

30. Importance of Experimental Design
Record run date, labs, personnel, environmental variables, etc.
When possible, balance groups of interests, at least include some controls in each batch
Avoid “perfect confounding” when batch and group are perfectly correlated. E.g.
Treatments in one batch, controls in another
Treatment 1 in Batch 1, Treatment 2 in Batch 2

31. Decomposing Data Heterogeneity
Primary variables (T & C)
Random variations
(Error)
Baseline
expression
Samples
Genes =

32. Decomposing Data Heterogeneity
Primary variables (T & C)
Dependence variables
(Batch)
Independent variations
(Error)
Baseline
expression
Samples
Genes =
Intuitively similar to LIMMA’s linear model, consider batch as some kind of treatment
Break

33. Gene Ontology

34. Gene Annotation
How to report differentially expressed genes or gene clusters?
Enriched for certain pathways, certain functions, or proteins localized in the same complex, etc?
Gene Ontology Consortium
Ashburner et al 1998
Annotate gene function in the human genome
Now extended to many model organisms
Why do we care?
Effectively communicate biomedical knowledge
Organize and summarize annotations in structured way
Allow effective and meaningful computation on gene annotations

35. GO Categories Molecular function Biological process Cellular component
Describe gene’s jobs or abilities
E.g. transporters, transcription factor
Biological process
Events or pathways
E.g. cell differentiation, maturation, development
Cellular component
Describe locations (subcellular structures, macromolecular complexes)
E.g. nucleus, cell membrane, protein complexes

36. GO

37. GO Relationships: Same term could be annotated at multiple branches
Subclass: Is_a
Membership: Part_of
Topological: adjacent_to; Derivation: derives_from
E.g. 5_prime_UTR is part_of a transcript, and mRNA is_a kind of transcript
Same term could be annotated at multiple branches
Directed acyclic graph

38. Evaluate Differentially Expressed Genes
NetAffx mapped GO terms for all probesets
Whole genome Up genes
GO term X
Total 20K
Statistical significance?
Binomial proportional test
p = 100 / 20 K = 0.005
Check z table

39. Evaluate Differentially Expressed Genes
Whole genome Up genes
GO term X
Total 20K
Chi sq test or Fisher’s exact test:
Up !Up Total
GO: 80 (1) 20 (99) 100
!GO: 120 (199) 20K-120 (19701) 20K-100
Total: K K
Check Chi-sq table

40. GO Tools for Microarray Analysis
Hundreds
DAVID

41. Summary Clustering by distance Missing value estimation
Hierarchical clustering, linkage
K-mean clustering, how to determine K
Batch effect considerations
COMBAT for batch effect removal
GO categories, directed acyclic
GO enrichment statistics