Giri Narasimhan. CAP 5510: Introduction to Bioinformatics. ECS 254; Phone: x3748
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1 CAP 5510: Introduction to Bioinformatics Giri Narasimhan ECS 254; Phone: x /3/08 CAP5510 1
2 Gene g Probe 1 Probe 2 Probe N 3/3/08 CAP5510 2
3 Microarray Data Gene Expression Level Gene1 Gene2 Gene3 3/3/08 CAP5510 3
4 Study effect of treatment over time Sample Treated Sample(t1) Expt 1 Treated Sample(t2) Expt 2 Treated Sample(t3) Expt 3 Treated Sample(tn) Expt n 3/3/08 CAP5510 4
5 3/3/08 CAP
6 How to compare 2 cell samples with Two-Color Microarrays? mrna from sample 1 is extracted and labeled with a red fluorescent dye. mrna from sample 2 is extracted and labeled with a green fluorescent dye. Mix the samples and apply it to every spot on the microarray. Hybridize sample mixture to probes. Use optical detector to measure the amount of green and red fluorescence at each spot. 3/3/08 CAP5510 6
7 Sources of Variations & Experimental Errors Variations in cells/individuals Variations in mrna extraction, isolation, introduction of dye, variation in dye incorporation, dye interference Variations in probe concentration, probe amounts, substrate surface characteristics Variations in hybridization conditions and kinetics Variations in optical measurements, spot misalignments, discretization effects, noise due to scanner lens and laser irregularities Cross-hybridization of sequences with high sequence identity Limit of factor 2 in precision of results Variation changes with intensity: larger variation at low or high expression levels Need to Normalize data 3/3/08 CAP5510 7
8 Clustering Clustering is a general method to study patterns in gene expressions. Several known methods: Hierarchical Clustering (Bottom-Up Approach) K-means Clustering (Top-Down Approach) Self-Organizing Maps (SOM) 3/3/08 CAP5510 8
9 Hierarchical Clustering: Example /3/08 CAP5510 9
10 A Dendrogram 3/3/08 CAP
11 Hierarchical Clustering [Johnson, SC, 1967] Given n points in R d, compute the distance between every pair of points While (not done) Pick closest pair of points s i and s j and make them part of the same cluster. Replace the pair by an average of the two s ij Try the applet at: 3/3/08 CAP
12 3/3/08 CAP Distance Metrics For clustering, define a distance function: Euclidean distance metrics Pearson correlation coefficient k=2: Euclidean Distance k d i k i i k Y X Y X D 1/ 1 ) ( ), ( = = = = y i x i d i xy Y Y X X d xy 1
13 3/3/08 CAP
14 Clustering of gene expressions Represent each gene as a vector or a point in d- space where d is the number of arrays or experiments being analyzed. 3/3/08 CAP
15 Clustering Random vs. Biological Data From Eisen MB, et al, PNAS (25): /3/08 CAP
16 K-Means Clustering: Example Example from Andrew Moore s tutorial on Clustering. 3/3/08 CAP
17 Start 3/3/08 CAP
18 3/3/08 CAP
19 3/3/08 CAP
20 Start End 3/3/08 CAP
21 K-Means Clustering [McQueen 67] Repeat Start with randomly chosen cluster centers Assign points to give greatest increase in score Recompute cluster centers Reassign points until (no changes) Try the applet at: 3/3/08 CAP
22 Hierarchical clustering Comparisons Number of clusters not preset. Complete hierarchy of clusters Not very robust, not very efficient. K-Means Need definition of a mean. Categorical data? More efficient and often finds optimum clustering. 3/3/08 CAP
23 Functionally related genes behave similarly across experiments 3/3/08 CAP
24 Self-Organizing Maps [Kohonen] Kind of neural network. Clusters data and find complex relationships between clusters. Helps reduce the dimensionality of the data. Map of 1 or 2 dimensions produced. Unsupervised Clustering Like K-Means, except for visualization 3/3/08 CAP
25 SOM Architectures 2-D Grid 3-D Grid Hexagonal Grid 3/3/08 CAP
26 SOM Algorithm Select SOM architecture, and initialize weight vectors and other parameters. While (stopping condition not satisfied) do for each input point x winning node q has weight vector closest to x. Update weight vector of q and its neighbors. Reduce neighborhood size and learning rate. 3/3/08 CAP
27 SOM Algorithm Details Distance between x and weight vector: x wi Winning node: q( x) = min Weight update function (for neighbors): wi( k + 1) = wi( k) + μ( k, x, i)[ x( k) wi( k)] i x w i Learning rate: μ( k, x, i) 0( k)exp ri rq( x) = 2 2 3/3/08 CAP
28 World Bank Statistics Data: World Bank statistics of countries in indicators considered e.g., health, nutrition, educational services, etc. The complex joint effect of these factors can can be visualized by organizing the countries using the self-organizing map. 3/3/08 CAP
29 World Poverty PCA 3/3/08 CAP
30 World Poverty SOM 3/3/08 CAP
31 World Poverty Map 3/3/08 CAP
32 3/3/08 CAP
33 3/3/08 CAP
34 Viewing SOM Clusters on PCA axes 3/3/08 CAP
35 SOM Example [Xiao-rui He] /3/08 CAP
36 Neural Networks Synaptic Weights W Bias Input X ƒ( ) Output y 3/3/08 CAP
37 Learning NN 1 Weights W Input X Adaptive Algorithm Error + Desired Response 3/3/08 CAP
38 Types of NNs Recurrent NN Feed-forward NN Layered Hidden layers possible Other issues Different activation functions possible 3/3/08 CAP
39 Application: Secondary Structure Prediction 3/3/08 CAP
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