1. Dimension reduction : PCA and Clustering by Agnieszka S. Juncker
Part of the slides is adapted from Chris Workman

2. Advanced Data Analysis
The DNA Array Analysis Pipeline
Question
Experimental Design
Array design
Probe design
Sample Preparation
Hybridization
Buy Chip/Array
Image analysis
Normalization
Expression Index
Calculation
Comparable
Gene Expression Data
Statistical Analysis
Fit to Model (time series)
Advanced Data Analysis
Clustering PCA Classification Promoter Analysis
Meta analysis Survival analysis Regulatory Network

3. Motivation: Multidimensional data
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4. Dimension reduction methods
Principal component analysis (PCA)
Cluster analysis
Multidimensional scaling
Correspondance analysis
Singular value decomposition

5. Principal Component Analysis (PCA)
used for visualization of complex data
developed to capture as much of the variation in data as possible

6. Principal components 1. principal component (PC1)
the direction along which there is greatest variation
2. principal component (PC2)
the direction with maximum variation left in data, orthogonal to the 1. PC

7. Principal components General about principal components
summary variables
linear combinations of the original variables
uncorrelated with each other
capture as much of the original variance as possible

8. Principal components

9. PCA - example

10. PCA on all Genes Leukemia data, precursor B and T
Plot of 34 patients, dimension of 8973 genes reduced to 2

11. PCA of genes (Leukemia data)
Plot of 8973 genes, dimension of 34 patients reduced to 2

12. Principal components - Variance

13. Clustering methods Hierarchical Partitioning agglomerative (buttom-up)
eg. UPGMA
divisive
(top-down)
Partitioning
eg. K-means clustering

14. Hierarchical clustering
Representation of all pairwise distances
Parameters: none (distance measure)
Results:
in one large cluster
hierarchical tree (dendrogram)
Deterministic

15. Hierarchical clustering – UPGMA Algorithm
Assign each item to its own cluster
Join the nearest clusters
Reestimate the distance between clusters
Repeat for 1 to n

16. Hierarchical clustering

17. Hierarchical clustering
Data with clustering order
and distances
Dendrogram representation

18. Leukemia data - clustering of patients

19. Leukemia data - clustering of patients on top 100 significant genes

20. Leukemia data - clustering of genes

21. K-means clustering Partition data into K clusters
Parameter: Number of clusters (K) must be chosen
Randomilized initialization:
different clusters each time

22. K-means - Algorithm Assign each item a class in 1 to K (randomly)
For each class 1 to K
Calculate the centroid (one of the K-means)
Calculate distance from centroid to each item
Assign each item to the nearest centroid
Repeat until no items are re-assigned (convergence)

23. K-mean clustering, K=3

24. K-mean clustering, K=3

25. K-mean clustering, K=3

26. K-means clustering of Leukemia data

27. Self Organizing Maps (SOM)
Partitioning method
(similar to the K-means method)
Clusters are organized in a two-dimensional grid
Size of grid is specified
(eg. 2x2 or 3x3)
SOM algoritm finds the optimal organization of data in the grid

28. SOM - example

29. Comparison of clustering methods
Hierarchical clustering
Distances between all variables
Timeconsuming with a large number of gene
Advantage to cluster on selected genes
K-means clustering
Faster algorithm
Does only show relations between all variables
SOM
more advanced algorithm

30. Distance measures Euclidian distance Vector angle distance
Pearsons distance

31. Comparison of distance measures

32. Summary Dimension reduction important to visualize data Methods:
Principal Component Analysis
Clustering
Hierarchical
K-means
Self organizing maps
(distance measure important)

33. Next: Exercises in PCA and clustering
Coffee break
Next: Exercises in PCA and clustering