OUTLINE

Microarrays Processing Microarray Data

– K- Means Clustering– Hierarchical Clustering– SOM

Microarrays

Gene Expression:– We see difference between cels because of

differential gene expression,– Gene is expressed by transcribing DNA intosingle-

stranded mRNA,– mRNA is later translated into a protein,– Microarrays measure the level of mRNA

expression

Microarrays

Gene Expression:– mRNA expression represents dynamic aspects of

cell,– mRNA is isolated and labeled using a fluorescent

material,– mRNA is hybridized to the target; level of

hybridization corresponds to light emission which is measured with a laser

Microarrays

Microarrays

Microarrays

Microarrays

Microarrays

Animation (by A. Malcolm Campbell):

– http://www.bio.davidson.edu/Courses/genomics/chip/chip.html

Microarrays

Sample Application (oncotypeDX):

http://www.oncotypedx.com/en-US/Breast.aspx

Microarrays

Sample Application (oncotypeDX):

– VIDEO

http://www.oncotypedx.com/en-US/Breast.aspx

Processing Microarray Data

Problems:– Extract data from microarrays,– Analyze the meaning of the multiple arrays.

Processing Microarray Data

Processing Microarray Data

Differentiating gene expression:

– R = G not differentiated

– R > G up-regulated

– R < G down regulated

Processing Microarray Data

Problems:– Extract data from microarrays,– Analyze the meaning of the multiple arrays.

Processing Microarray Data

Characteristics of microarray data:– Experiment = (gene1, gene2,…, geneN )– Gene = (experiment1, experiment2, …, experimentM)– N is often on the order of 104

– M is often on the order of 101

Processing Microarray Data

Microarray data:

Processing Microarray Data

Data Analysis:– Clustering:

What genes have similar functions, Subdivide genes or experiments into meaningful classes.

– Classification: Can we correctly classify an unknown experiment or gene

into a known class? FOR EXAMPLE: Can we make better treatment decisions for

a cancer patient based on gene expression profile?

Processing Microarray Data

Clustering:– Find classes in the data,– Identify new classes,– Identify gene correlations,– Methods:

K-means clustering, Hierarchical clustering, Self Organizing Maps (SOM)

Processing Microarray Data

Distance Measures:– Euclidean Distance:

– Manhattan Distance:

Processing Microarray Data

K-means Clustering:– Break the data into K clusters,– Start with random partitioning,– Improve it by iterating.

Processing Microarray Data

K-means Clustering:– Select # of clusters, say k,– Repeat

Select k random centroids, {m1, m2,…, mk}, Assign points (genes in this case) to the cluster of closest

centroid by using a distance measure, Compute new centroids, {m1, m2,…, mk},

– until no change to any centroid.

Processing Microarray Data

K-means Clustering:

Processing Microarray Data

K-means Clustering:– Select # of clusters, say k,

Therea are some methods to determine the optimum k, Assume k is given.

Processing Microarray Data

K-means Clustering:– Select k random centroids, {m1, m2,…, mk},

Just randomly assign the centroids.

Processing Microarray Data

K-means Clustering:– Assign points (genes in this case) to the cluster of closest

centroid by using a distance measure, Use the following formula to find the closest centroid to the

gene gi:

Then assign gene gi to the closest centroid.

),(min ijj gmd

Processing Microarray Data

K-means Clustering:– Compute new centroids, {m1, m2,…, mk},

Find the average in the cluster:

Where:– mc: centroid of the cluster c,– Nc: the number of points in cluster c,– gi: the points in cluster c.

cN

ii

cc g

Nm

1

1

Processing Microarray Data

K-means Clustering:– Repeat until no change to any centroid.

Centroids are in the proper places, We can not observe any other improvement in centroids, Therefore STOP.

Processing Microarray Data

K-means Clustering DEMO:– Our points:

Processing Microarray Data

K-means Clustering DEMO:– Centroids (4 centroids, squares):

Processing Microarray Data

K-means Clustering DEMO:– Assign each point to the closest centroid:

Processing Microarray Data

K-means Clustering DEMO:– Re evaluate the centroids:

Processing Microarray Data

K-means Clustering DEMO:– Iterate until no change.

Processing Microarray Data

K-means Clustering DEMO 2:

Processing Microarray Data

Hierarchical Clustering:– Similar to costruction of phylogenetic tree,– A distance matrix for all genes are constructed based

on distances between their expression profiles.– Neighbor-joining or UPGMA can be applied on this

matrix to get a hierarchical cluster.– Single linkage, complete linkage, average linkage

clustering

Processing Microarray Data

Hierarchical Clustering:– Single linkage: the distance between two clusters is

given by the value of the shortest link between the clusters

Processing Microarray Data

Hierarchical Clustering:– Complete linkage: the distance between two clusters

is given by the value of the longest link between the clusters

Processing Microarray Data

Hierarchical Clustering:– Average linkage: the distance between two clusters is

defined as the average of distances between all pairs of objects

– like UPGMA

Processing Microarray Data

Hierarchical Clustering:– Linkage Criteria:

Processing Microarray Data

Agglomerative Hierarchical Clustering:

Processing Microarray Data

Agglomerative Hierarchical Clustering:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering DEMO:

Processing Microarray Data

Agglomerative Hierarchical Clustering:

Processing Microarray Data

Agglomerative Hierarchical Clustering:

Processing Microarray Data

Self-Organizing Feature Maps:– by Teuvo Kohonen, – a data visualization technique which helps to

understand high dimensional data by reducing the dimensions of data to a map.

Processing Microarray Data

Self-Organizing Feature Maps:– humans simply cannot visualize high dimensional data

as is,– SOM help us understand this high dimensional data.

Processing Microarray Data

Self-Organizing Feature Maps:– Based on competitive learning,– SOM helps us by producing a map of usually 1 or 2

dimensions,– SOM plot the similarities of the data by grouping– similar data items together.

Processing Microarray Data

Self-Organizing Feature Maps:

Processing Microarray Data

Self-Organizing Feature Maps: Input vector, synaptic weight vector

x = [x1, x2, …, xm]T

wj=[wj1, wj2, …, wjm]T, j = 1, 2,3, l

Best matching, winning neuroni(x) = arg min ||x-wj||, j =1,2,3,..,l

Weights wi are updated.

Processing Microarray Data

Self-Organizing Feature Maps (EXAMPLE):– Assume that we want to cluster the countries

according to their economic potential,– Countries has N properties (like export - import

amounts, population …)

Processing Microarray Data

Self-Organizing Feature Maps (EXAMPLE):– Each country is a point in N dimension,– It means each country is a vetor of size N,– We want to cluster the countries according to the

similarities in economical potential.

Processing Microarray Data

Self-Organizing Feature Maps (EXAMPLE):

Processing Microarray Data

Self-Organizing Feature Maps (EXAMPLE):

Processing Microarray Data

Self-Organizing Feature Maps:– Similarly SOM is used to analyze microarray data,– Similar genes can be observed easily by this way.

References

M. Zvelebil, J. O. Baum, “Understanding Bioinformatics”, 2008, Garland Science

Andreas D. Baxevanis, B.F. Francis Ouellette, “Bioinformatics: A practical guide to the analysis of genes and proteins”, 2001, Wiley.

Barbara Resch, “Hidden Markov Models - A Tutorial for the Course Computational Intelligence”, 2010.

Pattern Classification (2nd ed) by R. O. Duda, P. E. Hart and D. G. Stork, John Wiley & Sons, 2000