information visualization using graphs algorithms symeonidis alkiviadis [email protected]...
TRANSCRIPT
Contents
Preliminaries
Gene clustering
Graph extraction from biological data
Graph visualization
Open issues
Discussion
Preliminaries
Visualize clusters of genes produced by clustering over gene expressions
Gene expression:
set of values of genes over a set of patients
Preliminaries
Graph G(V,E) : set of vertices, with edges joining vertices
Each vertex represents a gene
Each edge represents strong correlation
Clustering => groups of vertices
Contents
Preliminaries
Gene clustering
Graph extraction from biological data
Graph visualization
Open issues
Discussion
Gene clustering
Correlation
Compute Pearson's correlation coefficient for every pair of genes
Ny
yNx
x
Nxy
xyr
22
22
Gene clustering
Greedy clustering
for every unclassified gene x
create a cluster which includes it
add all genes y
with correlation > threshold
Cost: O(|genes|2)
Contents
Preliminaries
Gene clustering
Graph extraction from biological data
Graph visualization
Open issues
Discussion
Graph extraction from biological data
In-cluster relationMean value of correlation coefficients for all
genes in a cluster
All pairs of genes with correlation higher than threshold* mean are considered highly correlated
Edge meaning: (Very) strong correlation
Graph extraction from biological data
Inter-cluster relationMean value of correlation coefficients for
each cluster
All pairs of genes with correlation higher than threshold* (mean1+mean2)/2 are considered highly correlated
Edge meaning: Possibly wrong classification
Graph extraction from biological data
Genes → vertices ۷
Clusters→ groups ۷
Edges ۷ all highly correlated pairs of genes
Contents
Preliminaries
Gene clustering
Graph extraction from biological data
Graph visualization
Open issues
Discussion
Graph visualization
Gene → Vertex → circle
High correlation → Edge → line
Cluster → Group → Circle with respective genes - vertices on its periphery
Graph visualizationDetermine ordering of vertices in group(tree)
Tree
depth first search discovery time
Graph visualizationDetermine ordering of vertices in group(bicon)
Biconnected graph:
Remains connected after removing one(any) vertex/edge
Graph visualizationDetermine ordering of vertices in group(bicon)
For every node u identify triangles
or create them
Store (v,w)
Remove u
u v
wu v
w
Graph visualizationDetermine ordering of vertices in group(bicon)
Restore graphRemove all stored edgesPerform dfs, compute longest path
and place it
Graph visualizationDetermine ordering of vertices in group(bicon)
Place any remaining verticesNext to 2 neighborsNext to 1 neighborNext to 0 neighbors
Graph visualizationDetermine ordering of vertices in group(n-bic)
Non-biconnected graph … under development
There is a vertex whose removal disconnects the graph
Decompose into bicon. components
get articulation points
vertices responsible for non-biconnectivity
Graph visualizationDetermine ordering of vertices in group(n-bic)
Decompose into bicon. components biconnected subgraphs
get articulation pointsvertices responsible for non-biconnectivity
Graph visualizationDetermine ordering of vertices in group(n-bic)
Articulation points
+ biconnected components
------------------------------------------
Block - cut - point tree
-Dfs on block cut point=> relative ordering of components
- For each biconnected component act as before
Graph visualizationDetermine ordering of vertices in group
CostTree:
dfs: O(|E|+\V|)=O(|E|)Biconnected graph
Dominated by dfs O(|E|) Non- biconnected graph
Dominated by extracting block-cut tree O(|E|)
Graph visualizationedge coloring
Each edge is assigned a weight
weight(xnode ,ynode )= r(xgene ,ygene)The color of each edge reflects its weight
brighter color → stronger correlation
In- group edges have different color than inter-group edges