This document discusses analyzing and visualizing gene expression data. It defines key terms like genes and gene expression data. It also describes clustering gene expression data using k-means clustering to group genes based on similarity in a dataset of yeast cell cycle genes. Finally, it discusses visualizing gene expression data using techniques like vector fusion, nMDS, and PCA to project high-dimensional gene expression datasets into 2D or 3D spaces.

1. Analysis of
Gene Expression Data
_______________________
Jhoirene B. Clemente
Algorithms and Complexity Lab
University of the Philippines Diliman

2. Overview
● Definitions
● Clustering of Gene Expression Data
● Visualizations of Gene Expression Data

3. Definitions
Gene
Basic unit of heredity in a living organism.
It is normally a stretch of DNA that codes
for a type of protein or for an RNA chain
that has a function in the organism.
Gene Expression Data
Expression level of genes in an individual
that is measured through Microarray

4. Definitions

5. Definitions

6. Definitions
Gene Expression Data
Gene Gene
Expression
a
b
c
...
n

7. Definitions
Gene Expression Data 1 Sample
Gene Gene
Expression
a
b
n
Samples c
...
n

8. Definitions
(n x m) Data Matrix m Samples
Gene Sample Sample ..... Sample
1 1 m
a
b
n
Samples c
...
n

9. Definitions
(n x m) Data Matrix m Samples
Gene Sample Sample ..... Sample
1 1 m
a
b
n
Samples c
...
n

10. Clustering
Clustering is the unsupervised classification of
patterns including observations, data sets and
feature vectors into groups called clusters,
such that objects in the same cluster are similar to
each other while objects in different clusters are
dissimilar as possible.

11. Clustering
Clustering is the unsupervised classification of
patterns including observations, data sets and
feature vectors into groups called clusters,
such that objects in the same cluster are similar to
each other while objects in different clusters are
dissimilar as possible.

12. Cluster Analysis
Preprocessing
● Filtering
● Normalization
Clustering
Analysis

13. Clustering
Partitional
● K-means Algorithm
● X-means Algorithm
Hierarchical

14. Clustering
Given the (n x m) data matrix, we can
● Cluster the set of genes
● Cluster the set of samples
● Cluster the set of genes and samples
simultaneously.

15. Data Set
Data set is a time series gene expression data from
a synchronized population of yeast.

16. Data Set
Data set is a time series gene expression data from
a synchronized population of yeast.

17. Preprocessing
Filtering
● Removed genes not involved in cell cycle
regulation
● Removed genes belonging to more than one
group
Normalization
● All gene expression values range from -1.0 to
1.0.

18. Data Set
Data matrix (384 genes and 17 samples) with 5
classifications.
Groupings based from cell cycle phase activation.

19. Data Set
Group 1: Resting Phase

20. Data Set
Group 2: First Growth Phase

21. Data Set
Group 3: Synthesis Phase

22. Data Set
Group 4: Second Growth Phase

23. Data Set
Group 5: Cell Division

24. Clustering of genes
K-means Algorithm
Given n data points in Rd
1. Assign k initial centers of the k clusters
2. Assign all the data points to the nearest cluster
(Euclidean distance, Manhattan distance, etc.)
3. Adjust the k centers
4. Repeat steps 2 and 3 until convergence

25. Clustering of genes
K-means Algorithm
Given n data points in Rd
1. Assign k initial centers of the k clusters
2. Assign all the data points to the nearest cluster
(Euclidean distance, Manhattan distance, etc.)
3. Adjust the k centers
4. Repeat steps 2 and 3 until convergence
k =5
since we want to approximate the 5

26. Clustering of genes
Initialization
1. Choose the first k centers that will maximize the
distance between the clusters
2. Sort the distances between all the data points
and then choose the k initial points at constant
intervals from the sorted list
3. Use the first k points in the data set as the first k
centers

27. Clustering of genes
Using k-means clustering, with k =5

28. Clustering of genes
● Clustering may suggest possible roles for genes
with unknown functions
● Clustering the samples or experiments may shed
light on new subtypes of diseases.
● Identify which type of treatment is suited for a
specific type of cancer.
● Building genetic networks

29. visualization
Vector Fusion
Non-metric Multidimensional Scaling (nMDS)
Principal Components Analysis (PCA)

30. Vector fusion
Visualization technique that uses the Single point
broken line parallel algorithm

31. nMDS visualization
Input (Dissimilarity Matrix=|ij|) actual distance
● In nMDS, only the rank order of entries is
assumed to contain the significant information.
● Thus, the purpose of the non-metric MDS
algorithm is to find a configuration of points
whose distances reflect as closely as possible
the rank order of the data.
● The transformation is by using a non parametric
function f. (monotone regression)
dij= f(dij) pseudo-distance

32. PCA

33. vector fusion
visualization

34. nmds visualization

35. nmds visualization

36. nmds visualization

37. nmds visualization

38. nmds visualization

39. nmds visualization

40. nmds visualization

41. References
2010: "Non-Metric Multidimensional Scaling and Vector
Fusion Visualization of Cell Cycle Independent Gene
Expressions for Gene Function Analysis", Clemente J.,
Salido J.A., (2010), Published in the conference
proceedings of National Conference on Information
Technology for Education(NCITE) 2010 and Philippine IT
Journal Feb 2011 Issue.
2010: "Cluster Analysis for Identifying Genes Highly
Correlated with a Phenotype", Clemente J.,
Undergraduate thesis, Department of Computer Science,
University of the Philippines Diliman

42. Thank you for
Listening