An introduction to network inference and mining - TP

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An introduction to network inference and mining - TP

Nathalie Villa-Vialaneix -nathalie.villa@toulouse.inra.fr http://www.nathalievilla.org

INRA, UR 0875 MIAT

Formation INRA , Niveau 3

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Packages in R

is provided with basic functions but more than 3,000 packages are available on theCRAN (Comprehensive R Archive Network) for additionnal functions (see also the projectBioconductor).

• Installing new packages(has to be done only once) with the command line or the menu (Windows or Mac OS X or RStudio)

i n s t a l l.p a c k a g e s(c( " huge " , " i g r a p h " ,

" m i x O m i c s " ))

• Loading a package(has to be done each time R is re-started)

l i b r a r y( i g r a p h )

• Be sure you properly set the working directory (directory in which you put the data files) before you start

Formation INRA (Niveau 3) Network (TP) Nathalie Villa-Vialaneix 2 / 40

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Outline

1 Network inference Data description Inference with glasso Basic mining

2 Network mining

Building the graph with igraph Global characteristics

Visualization

Individual characteristics Clustering

3 Use gephi

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Network inference

Outline

2 Network mining

Visualization

3 Use gephi

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Network inference Data description

Use case description

Data in the R package mixOmics

microarray data: expression of 120 selected genes potentially involved in nutritional problems on 40 mice. These data come from a nutrigenomic study [Martin et al., 2007].

data( n u t r i m o u s e ) s u m m a r y( n u t r i m o u s e ) expr <- n u t r i m o u s e$gene

r o w n a m e s( expr ) <- p a s t e(1:nrow( expr ) ,

n u t r i m o u s e$genotype , n u t r i m o u s e$diet , sep = " - " )

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Data distribution

b o x p l o t( expr , n a m e s= NULL )

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Gene correlations and clustering

expr .c <- s c a l e( expr )

h e a t m a p (as.m a t r i x( expr .c))

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Hierarchical clustering from raw data

h c l u s t . tree <- h c l u s t ( dist (t( expr ))) plot( h c l u s t . tree )

rect. h c l u s t ( h c l u s t . tree , k =7 , b o r d e r =r a i n b o w(7))

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Save gene clusters

h c l u s t . g r o u p s <- c u t r e e ( h c l u s t . tree , k =7) t a b l e( h c l u s t . g r o u p s )

h c l u s t . g r o u p s

# 1 2 3 4 5 6 7

# 1 8 4 2 0 5 2 1 7 6 3

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Network inference Inference with glasso

Sparse linear regression by Maximum Likelihood

Estimation: [Friedman et al., 2008] Gaussien framework allows us to use ML optimizationwith a sparse penalization

L(S|X)+pen=

n

X

i=1





p

X

j=1

logP(X_i^j|X_i^−j, S_j)



−λkSk₁

g l a s s o . res <- huge (as.m a t r i x( expr ) , m e t h o d = " g l a s s o " ) g l a s s o . res

# M o d e l : g r a p h i c a l l a s s o ( g l a s s o )

# I n p u t : T h e D a t a M a t r i x

# P a t h l e n g t h : 1 0

# G r a p h d i m e n s i o n : 1 2 0

# S p a r s i t y l e v e l : 0 - - - > 0 . 2 1 2 8 8 5 2

estimates of the concentration matrixS are in glasso.res$icov[[1]], ..., glasso.res$icov[[10]], each one corresponding to a different λ

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Select λ for a targeted density with the StARS method [Liu et al., 2010]

g l a s s o . sel <- huge . s e l e c t ( g l a s s o . res ,

c r i t e r i o n = " s t a r s " ) plot( g l a s s o . sel )

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Using igraph to create the graph

From the binary adjacency matrix:

bin .mat <- as.m a t r i x( g l a s s o . sel$opt . icov )! =0 c o l n a m e s( bin .mat) <- c o l n a m e s( expr )

Create an undirected simple graph from the matrix:

n u t r i m o u s e . net <- s i m p l i f y ( g r a p h . a d j a c e n c y ( bin .mat, mode= " max " ))

n u t r i m o u s e . net

# I G R A P H UN - - 1 2 0 3 9 2 - -

# + a t t r : n a m e ( v/c )

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Network inference Basic mining

Connected components

The resulting network is not connected:

is. c o n n e c t e d ( n u t r i m o u s e . net )

# [ 1 ] F A L S E

Connected components are extracted by:

c o m p o n e n t s . n u t r i m o u s e <- c l u s t e r s ( n u t r i m o u s e . net ) c o m p o n e n t s . n u t r i m o u s e

# [ 1 ] 1 2 3 2 2 4 5 2 2 2 6 2 7 2

# . . .

#

# $c s i z e

# [ 1 ] 7 6 7 1 6 2 1 1 1 1 1 1 1 1 2

# . . .

#

# $n o

# [ 1 ] 4 0

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Working on a connected subgraph

The largest connected component (with 99 nodes) can be extracted with:

n u t r i m o u s e . lcc <- i n d u c e d . s u b g r a p h ( n u t r i m o u s e . net , c o m p o n e n t s . n u t r i m o u s e$m e m b e r s h i p ==

w h i c h.max( c o m p o n e n t s . n u t r i m o u s e$c s i z e )) n u t r i m o u s e . lcc

# I G R A P H UN - - 6 7 3 7 5 - -

# + a t t r : n a m e ( v/c ) and visualized with:

n u t r i m o u s e . lcc$ l a y o u t <- l a y o u t. k a m a d a . k a w a i ( n u t r i m o u s e . lcc )

plot( n u t r i m o u s e . lcc , v e r t e x . size =2 , v e r t e x . c o l o r = " l i g h t y e l l o w " ,

v e r t e x .f r a m e. c o l o r = " l i g h t y e l l o w " , v e r t e x . l a b e l . c o l o r = " b l a c k " ,

v e r t e x . l a b e l . cex = 0 . 7 )

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Resulting network

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Node clustering (compared to raw clustering)

Using one of the clustering function available in igraph:

set. seed ( 1 2 1 9 )

c l u s t e r s . n u t r i m o u s e <- s p i n g l a s s . c o m m u n i t y ( n u t r i m o u s e . lcc )

c l u s t e r s . n u t r i m o u s e

t a b l e( c l u s t e r s . n u t r i m o u s e$m e m b e r s h i p )

# 1 2 3 4

# 1 5 2 5 1 7 1 0

The hierarchical clustering for nodes in the largest connected component is obtained with:

i n d u c e d . h c l u s t . g r o u p s <- h c l u s t . g r o u p s [ c o m p o n e n t s . n u t r i m o u s e$m e m b e r s h i p ==

w h i c h.max( c o m p o n e n t s . n u t r i m o u s e$c s i z e )]

t a b l e( i n d u c e d . h c l u s t . g r o u p s )

# 1 3 4 5 6

# 6 1 7 4 2 1 1

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Visual comparison

par( m f r o w =c(1 ,2)) par( mar =rep(1 ,4))

plot( n u t r i m o u s e . lcc , v e r t e x . size =5 ,

v e r t e x . c o l o r =r a i n b o w(6)[ i n d u c e d . h c l u s t . g r o u p s ] , v e r t e x .f r a m e. c o l o r =

r a i n b o w(6)[ i n d u c e d . h c l u s t . g r o u p s ] , v e r t e x . l a b e l = NA ,

main = " H i e r a r c h i c a l c l u s t e r i n g " ) plot( n u t r i m o u s e . lcc , v e r t e x . size =5 ,

v e r t e x . c o l o r =r a i n b o w(4)[

c l u s t e r s . n u t r i m o u s e$m e m b e r s h i p ] , v e r t e x .f r a m e. c o l o r =r a i n b o w(4)[

c l u s t e r s . n u t r i m o u s e$m e m b e r s h i p ] ,

v e r t e x . l a b e l = NA , main = " G r a p h c l u s t e r i n g " )

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Visual comparison

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Numeric comparison

c o m p a r e . c o m m u n i t i e s ( i n d u c e d . h c l u s t . groups ,

c l u s t e r s . n u t r i m o u s e$m e m b e r s h i p , m e t h o d = " nmi " )

# [ 1 ] 0 . 5 0 9 1 5 6 8

m o d u l a r i t y ( n u t r i m o u s e . lcc , i n d u c e d . h c l u s t . g r o u p s )

# [ 1 ] 0 . 2 3 6 8 4 6 2

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Network mining

Outline

2 Network mining

Visualization

3 Use gephi

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Network mining Building the graph with igraph

Use case description

Data are Natty’s facebook network¹

• fbnet-el.txt is the edge list;

• fbnet-name.txt are the nodes’ initials.

e d g e l i s t <- as.m a t r i x(read.t a b l e( " fbnet - el . txt " )) v n a m e s <- read.t a b l e( " fbnet - name . txt " )

v n a m e s <- as.c h a r a c t e r( v n a m e s [ ,1])

The graph is built with:

# w i t h ‘ g r a p h . e d g e l i s t ’

f b n e t 0 <- g r a p h . e d g e l i s t ( edgelist , d i r e c t e d = F A L S E ) f b n e t 0

# I G R A P H U - - - 1 5 2 5 5 1 - -

See also help(graph.edgelist)for more graph constructors

1Do it with yours: http://shiny.nathalievilla.org/fbs

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Vertexes, vertex attributes

The graph’s vertexes are accessed and counted with:

V ( f b n e t 0 )

v c o u n t ( f b n e t 0 )

Vertexes can be described by attributes:

# a d d a n a t t r i b u t e f o r v e r t i c e s V ( f b n e t 0 )$i n i t i a l s <- v n a m e s f b n e t 0

# I G R A P H U - - - 1 5 2 5 5 1 - -

# + a t t r : i n i t i a l s ( v/x )

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Edges, edge attributes

The graph’s edges are accessed and counted with:

E ( f b n e t 0 )

# [ 1 ] 1 1 - - 1

# [ 2 ] 4 1 - - 1

# [ 3 ] 5 2 - - 1

# [ 4 ] 6 9 - - 1

# [ 5 ] 7 4 - - 1

# [ 6 ] 7 5 - - 1

# . . .

e c o u n t ( f b n e t 0 )

# 5 5 1

igraph can also handle edge attributes (and also graph attributes).

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Network mining Global characteristics

Connected components

is. c o n n e c t e d ( f b n e t 0 )

# [ 1 ] F A L S E

\end{ R c o d e }

As this n e t w o r k is not c o n n e c t e d , the c o n n e c t e d c o m p o n e n t s can be e x t r a c t e d :

\ b e g i n { R c o d e }

fb . c o m p o n e n t s <- c l u s t e r s ( f b n e t 0 ) n a m e s( fb . c o m p o n e n t s )

# [ 1 ] " m e m b e r s h i p " " c s i z e " " n o "

head ( fb . c o m p o n e n t s$m e m b e r s h i p , 10)

# [ 1 ] 1 1 2 2 1 1 1 1 3 1

fb . c o m p o n e n t s$c s i z e

# [ 1 ] 1 2 2 5 1 1 2 1 1 1 2 1

# [ 1 1 ] 1 2 1 1 2 3 1 1 1 1

# [ 2 1 ] 1

fb . c o m p o n e n t s$no

# [ 1 ] 2 1

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Network mining Global characteristics

Largest connected component

f b n e t . lcc <- i n d u c e d . s u b g r a p h ( fbnet0 , fb . c o m p o n e n t s$m e m b e r s h i p ==

w h i c h.max( fb . c o m p o n e n t s$c s i z e ))

# m a i n c h a r a c t e r i s t i c s o f t h e L C C f b n e t . lcc

# I G R A P H U - - - 1 2 2 5 3 5 - -

# + a t t r : i n i t i a l s ( v/x ) is. c o n n e c t e d ( f b n e t . lcc )

# [ 1 ] T R U E

and global characteristics

g r a p h .d e n s i t y( f b n e t . lcc )

# [ 1 ] 0 . 0 7 2 4 8 3 4

t r a n s i t i v i t y ( f b n e t . lcc )

# [ 1 ] 0 . 5 6 0 4 5 2 4

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Network mining Visualization

Network visualization

Different layouts are implemented in igraph to visualize the graph:

plot( f b n e t . lcc , l a y o u t=l a y o u t. random , main = " r a n d o m l a y o u t " , v e r t e x . size =3 ,

v e r t e x . c o l o r = " pink " , v e r t e x .f r a m e. c o l o r = " pink " , v e r t e x . l a b e l . c o l o r = " d a r k r e d " ,

edge . c o l o r = " grey " ,

v e r t e x . l a b e l = V ( f b n e t . lcc )$i n i t i a l s ) Try also layout.circle,layout.kamada.kawai,

layout.fruchterman.reingold... Network are generated with some randomness. See also help(igraph.plotting)for more information on network visualization

igraph integrates a pre-defined graph attribute layout:

V ( f b n e t . lcc )$l a b e l <- V ( f b n e t . lcc )$i n i t i a l s plot( f b n e t . lcc )

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Network mining Visualization

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Network mining Individual characteristics

Degree and betweenness

f b n e t . d e g r e e s <- d e g r e e ( f b n e t . lcc ) s u m m a r y( f b n e t . d e g r e e s )

# M i n . 1 s t Q u . M e d i a n M e a n 3 r d Q u . M a x .

# 1 . 0 0 2 . 0 0 6 . 0 0 8 . 7 7 1 5 . 0 0 3 1 . 0 0

f b n e t . b e t w e e n <- b e t w e e n n e s s ( f b n e t . lcc ) s u m m a r y( f b n e t . b e t w e e n )

# M i n . 1 s t Q u . M e d i a n M e a n 3 r d Q u . M a x .

# 0 . 0 0 0 . 0 0 1 4 . 0 3 3 0 1 . 7 0 1 2 3 . 1 0 3 4 3 9 . 0 0 and their distributions:

par( m f r o w =c(1 ,2))

plot(d e n s i t y( f b n e t . d e g r e e s ) , lwd =2 ,

main = " D e g r e e d i s t r i b u t i o n " , xlab = " D e g r e e " , ylab = " D e n s i t y " )

plot(d e n s i t y( f b n e t . b e t w e e n ) , lwd =2 , main = " B e t w e e n n e s s d i s t r i b u t i o n " , xlab = " B e t w e e n n e s s " , ylab = " D e n s i t y " )

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Degree and betweenness distribution

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Combine visualization and individual characteristics

par( mar =rep(1 ,4))

# s e t n o d e a t t r i b u t e ‘ s i z e ’ w i t h d e g r e e V ( f b n e t . lcc )$size <- 2* sqrt( f b n e t . d e g r e e s )

# s e t n o d e a t t r i b u t e ‘ c o l o r ’ w i t h b e t w e e n n e s s bet .col <- cut(log( f b n e t . b e t w e e n +1) ,10 ,

l a b e l s= F A L S E )

V ( f b n e t . lcc )$c o l o r <- heat.c o l o r s(10)[11 - bet .col] plot( f b n e t . lcc , main = " D e g r e e and b e t w e e n n e s s " ,

v e r t e x .f r a m e. c o l o r =heat.c o l o r s( 1 0 ) [ bet .col] , v e r t e x . l a b e l = NA , edge . c o l o r = " grey " )

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Network mining Clustering

Node clustering

One of the function to perform node clustering is spinglass.community (that prossibly produces different results each time it is used since it is based on a stochastic process):

f b n e t . c l u s t e r s <- s p i n g l a s s . c o m m u n i t y ( f b n e t . lcc ) f b n e t . c l u s t e r s

# G r a p h c o m m u n i t y s t r u c t u r e c a l c u l a t e d w i t h

# t h e s p i n g l a s s a l g o r i t h m

# N u m b e r o f c o m m u n i t i e s : 9

# M o d u l a r i t y : 0 . 5 6 5 4 1 3 6

# M e m b e r s h i p v e c t o r :

# [ 1 ] 9 5 6 5 5 9 1 9 1 1 4 9 9 6 2 7 2 7 2 7 5

# . . .

t a b l e( f b n e t . c l u s t e r s$m e m b e r s h i p )

# 1 2 3 4 5 6 7 8 9

# 8 7 8 3 2 1 4 7 1 8 2 2 6

See help(communities)for more information.

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Combine clustering and visualization

# c r e a t e a n e w a t t r i b u t e

V ( f b n e t . lcc )$c o m m u n i t y <- f b n e t . c l u s t e r s$m e m b e r s h i p f b n e t . lcc

# I G R A P H U - - - 1 2 2 5 3 5 - -

# + a t t r : l a y o u t ( g/n ) , i n i t i a l s ( v/c ) ,

# l a b e l ( v/c ) , s i z e ( v/n ) , c o l o r ( v/c ) ,

# c o m m u n i t y ( v/n ) Display the clustering:

par( m f r o w =c(1 ,1)) par( mar =rep(1 ,4))

plot( f b n e t . lcc , main = " C o m m u n i t i e s " , v e r t e x .f r a m e. c o l o r =

r a i n b o w(9)[ f b n e t . c l u s t e r s$m e m b e r s h i p ] , v e r t e x . c o l o r =

r a i n b o w(9)[ f b n e t . c l u s t e r s$m e m b e r s h i p ] , v e r t e x . l a b e l = NA , edge . c o l o r = " grey " )

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Combine clustering and visualization

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Export the graph

Thegraphml format can be used to export the graph (it can be read by most of the graph visualization programs and includes information on node and edge attributes)

w r i t e. g r a p h ( f b n e t . lcc , file= " f b l c c . g r a p h m l " , f o r m a t= " g r a p h m l " )

seehelp(write.graph)for more information of graph exportation formats

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Use gephi

Outline

2 Network mining

Visualization

3 Use gephi

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Use gephi

Import data

Start and select “new project”.

• Create a graph from an edge list: filefbnet-el.txt

File / Open Graph type: “undirected”

• Create a graph (with nodes an edges attributes) from a GraphML file: filefblcc.graphmlpreviously created with igraph

On the right part of the screen, the number of nodes and edges are indicated.

• Check nodes attributes and define nodes labels

Data lab

Copy data to a column: initials Copy to: Label

Other nodes or edges attributes can be imported from a csv file with

import file

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Use gephi

Import data

Data lab

import file

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Use gephi

Import data

Data lab

import file

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Use gephi

Visualization

• Visualize the graph with Fruchterman & Reingold algorithm

Bottom left of panel “Global view”

Spatialization: Choose “Fruchterman and Reingold”

Area: 800 - Gravity: 1 Click on “Stop” when stabilized

• Customize the view:

• zoom or de-zoom with the mouse

• change link width (bottom toolbox)

• display labels and change labels size and color (bottom toolbox)

• with the “select” tool, visualize a node neighbors (top left toolbox)

• with the “move” tool, move a node (top left toolbox)

• Use the view to understand the graph(delete labels before)

• Color a node’s neighbors (middle left toolbox)

• Visualize the shortest path between two nodes (middle left toolbox)

• Visualize the distances from a given node to all the other nodes by nodes coloring (middle left toolbox)

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Use gephi

Visualization

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Use gephi

Visualization

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Use gephi

Graph mining

• Node characteristics

Window / Statistics

On the bottom right panel, Degree: run Check on Data Lab

On the top left panel, Clustering / Nodes / Size: Choose a clustering parameter:

Degree

Size: Min size:10, Max size: 50, Apply On the bottom right panel, Shortest path: run Color: Choose a clustering parameter: Betweenness centrality

Default: choose a palette, Apply

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Use gephi

Node clustering

On the bottom right panel, Modularity: run Check on Data Lab

On the top left panel, Clustering / Nodes / Label color: Choose a clustering parameter: Modularity class

Color: Default: choose a palette, Apply

• Export a view

Preview / Default with straight links / Refresh / Export (bottom left)

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Use gephi

Node clustering

On the bottom right panel, Modularity: run Check on Data Lab

On the top left panel, Clustering / Nodes / Label color: Choose a clustering parameter: Modularity class

Color: Default: choose a palette, Apply

• Export a view

Preview / Default with straight links / Refresh / Export (bottom left)

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Use gephi

Friedman, J., Hastie, T., and Tibshirani, R. (2008).

Sparse inverse covariance estimation with the graphical lasso.

Biostatistics, 9(3):432–441.

Liu, H., Roeber, K., and Wasserman, L. (2010).

Stability approach to regularization selection for high dimensional graphical models.

InProceedings of Neural Information Processing Systems (NIPS 2010), pages 1432–1440, Vancouver, Canada.

Martin, P., Guillou, H., Lasserre, F., Déjean, S., Lan, A., Pascussi, J., San Cristobal, M., Legrand, P., Besse, P., and Pineau, T. (2007).

Novel aspects of PPARα-mediated regulation of lipid and xenobiotic metabolism revealed through a multrigenomic study.

Hepatology, 54:767–777.