Visualisation of Social Networks

8/8/2019 Visualisation of Social Networks

http://slidepdf.com/reader/full/visualisation-of-social-networks 1/7

V i s u a l i sa t i o n o f S o c i a l N e t w o r k s u s i n g C A V A L I E R

A n t h o n y D e k k er

C 3 R e s e a r c h C e n t r e

D e f e n c e S c i e n c e T e c h n o l o g y O r g a n i s a t i o n ( D S T O )

F e r n h i l l P a r k , D e p a r t m e n t o f D e f e n c e

C a n b e r r a A C T 2 6 0 0 , A u s t r a l i a

d e k k e r @ A C M , o r g

A b s t r a c t

S o c i a l N e t w o r k A n a l y s i s i s a n a p p r o a c h t o a n a l y s i n g

o r g a n i s a t i o n s f o c u s i n g o n r e l a t i o n s h i p s a s t h e m o s t

i m p o r t a n t a s p e c t. I n th i s p a p e r w e d i s c u s s v i s u a l i s a t i o n

t e c h n i q u es f o r S o c i a l N e t w o r k A n a l y s i s , i n c l u d i n g

s p r i n g - e m b e d d i n g a n d s i m u l a t e d a n n e a l i n g t e c h n i q u e s.

W e i n t r o d u c e a v i s u a l is a t i o n t e c h n i q u e b a s e d o n K o h o n e n

n e u r al n e t w o r k s , a n d a l s o i n t r o d u c e s o c i a l f l o w d i a g r a m s

f o r d e m o n s t r a t i n g t h e r e l a t i o n s h i p b e t w e e n t w o f o r m s o f

c o n c e p t u a l d i s t a n c e .

Keywords: Social network analysis, Kohonen neural networks.

1 Soc ia l Ne tw ork Analy s i s : I ntroduct ion

S o c i a l N e t w o r k A n a l y s i s ( W a s s e r m a n a n d F a u s t 1 9 94 ) i s

a n a p p r o a c h t o a n a l y s i n g o r g a n i s a t i o n s f o c u s i n g o n t h e

relationships b e t w e e n p e o p l e a n d / o r g r o u p s a s t h e m o s t

i m p o r t a n t a s p e c t. G o i n g b a c k t o t h e 1 9 5 0 ' s a n d b e f o r e , it

i s c h a r a c t e r i s e d b y a d o p t i n g m a t h e m a t i c a l t e c h n i q u e s

e s p e c i a l l y f r o m graph theory ( G i b b o n s 1 9 8 5 , K r a c k h a r d t

1 9 94 ). I t h a s a p p l i c a t io n s i n o r g a n i s a t i o n a l p s y c h o l o g y ,

s o c i o l o g y a n d a n t h r o p o l o g y .

T h e f i r s t g o a l o f S o c i a l N e t w o r k A n a l y s i s i s t o visualisec o m m u n i c a t i o n a n d o t h e r r e l a t i o n s h i p s b e t w e e n p e o p l e

a n d / o r g r o u p s b y m e a n s o f d i a g r a m s . V i s u a l i s a t i o n o fS o c i a l N e t w o r k s h a s a l o n g t r a d i t io n , a n d a n e x c e l l e n t

h i s t o r ic a l s u r v e y is g i v e n i n F r e e m a n ( 2 0 00 ) . T h e

i m p o r t a n c e o f v i s u a l i s a t i o n i n t h i s f i e l d l i e s i n t h e

c o m p l e x i t y o f o r g a n i sa t i o n a l s t ru c t u r e, a n d t h e n e e d f o r

g o o d v i s u a l r e p r e s e n t a t io n s o f h o w a n o r g a n i s a t i o n

func t ions .

T h e s e c o n d g o a l i s t o s t u d y t h e fac tors which in f luencerelationships ( f o r e x a m p l e t h e a g e , b a c k g r o u n d , a n d

t r a i n in g o f t h e p e o p l e i n v o l v e d ) a n d t o s t u d y t h e

correlations b e t w e e n re l a t i o n s h i p s . T h i s c a n b e d o n e

us ing t rad i t iona l s ta t i s t ica l techn iques such as cor re la t io n ,

a n a l y s i s o f v a r i a n c e , a n d f a c t o r a n a l y s i s ( C o h e n e t a l

1996) , bu t a lso requ i res appropr ia te v isua l i sa t ion

techn iques .

T h e t h i r d g o a l o f S o c i a l N e t w o r k A n a l y s i s i s t o d r a w o u t

implications o f t h e r e l a t i o n a l d a t a , i n c l u d i n g b o t t l e n e c k s

Copyright © 2001, DSTO Australia. This paper appeared at theAustralian Symposium on Information Visualisation, Sydney,December 200 1. Conferences in Research and Practice inInformation Technology, Vol. 9. Peter Eades and Tim Pattison,Eds . Reproduction for academic, not-for profit purposespermitted provided this text is included.

w h e r e m u l t i p l e i n f o r m a t i o n f l o w s f u n n e l t h r o u g h o n e

p e r s o n o r s e c t i o n ( s l o w i n g d o w n w o r k p r o c e s s e s ) a n d

s i t u a ti o n s w h e r e i n f o r m a t i o n f l o w s d o e s n o t m a t c h f o r m a l

group s t ruc tu re .

T h e f o u r t h a n d m o s t i m p o r t a n t g o a l o f S o c i a l N e t w o r k

A n a l y s i s i s t o m a k e recommendat ions t o i m p r o v e

c o m m u n i c a t i o n a n d w o r k f l o w i n a n o r g a n i s a t i o n , a n d ( i n

m i l i t a r y te r m s ) t o s p e e d u p t h e o b s e r v e - o r i e n t - d e c i d e - a c t

( O O D A ) l o o p o r d e c i s i o n c y c l e ( A l l a r d 1 9 9 6 ) .

V i s u a l i s a t i o n i s c r i t i c a l l y i m p o r t a n t i n p r e s e n t i n g t h e s e

r e c o m m e n d a t i o n s t o c l i e n ts .I n p r e v i o u s w o r k , w e h a v e a p p l i e d S o c i a l N e t w o r k

A n a l y s i s to m i l i t a r y o r g a n i s a t i o n s ( D e k k e r 2 0 0 0 ) . I n t h i s

p a p e r w e p r e s e n t a n u m b e r o f v i s u a l i s a t i o n t e c h n i q u e s

t h a t w e h a v e d e v e l o p e d i n t h e c o u r s e o f t h i s w o r k . W e

h a v e c o n s t r u c t e d a J a v a - b a s e d t o o l s u i t e c a l l e d

C A V A L I E R ( C o m m u n i c a t i o n a n d A c t i v i t y

V i s u A L I s a t i o n f o r t h e E n t e R p r i s e ) , t o c a r r y o u t S o c i a l

N e t w o r k A n a l y s i s , a n d t h e v i s u a l i s a t i o n t e c h n i q u e s t h a t

w e d e s c r i b e a r e i n c o r p o r a t e d w i t h i n t h a t t o o l.

2 S p r i n g E m b e d d i n g

O n e o f t h e m o s t c o m m o n t e c h n i q u e s f o r v i s u a l i s i n g

S o c i a l N e t w o r k s i s s p r i n g - e m b e d d i n g ( F r e e m a n 2 0 0 0 ) . A

s p r i n g - e m b e d d i n g l a y o u t a l g o r i t h m a s s u m e s t h a t l i n k sb e t w e e n n o d e s b e h a v e p h y s i c a l l y l i k e s p r i n g s , w i t h a n

i d e a l s p r i n g length ( t h a t c o r r e s p o n d s t o s o m e k i n d o f

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

strength ( b e s t r e s u l ts a r e o b t a i n e d w h e n t h i s d e c r e a s e s a s

the idea l sp r ing leng th increases) . The nodes can be

a s s i g n e d t o p o i n t s i n t w o - d i m e n s i o n a l o r t h r e e -

d i m e n s i o n a l s p a c e b y m o v i n g t h e m i n a w a y w h i c h

m i n i m i s e s t h e t o t a l s t r e s s i n t h e c n t i r c c o l l e c t i o n o f

s t r ings , us ing s t ra igh t fo rward phys ics .

T h e m a j o r c a s e s t u d y w e u s e i n t h i s p a p e r ( i l l u s t ra t e d in

f i g u r es 1 to 4 ) i n v o l v e d a m i l i t a r y C 3 I - r e l a t e d

o r g a n i s a t i o n s e e k i n g s c i e n t i f i c a l l y b a s e d a d v i c e t o a

r e o r g a n i s a t i o n p r o c e s s . D a t a w a s c o l l e c t e d d u r i n g

M a r c h / A p r i l 2 0 0 0 u s i n g e l e c t r o n i c q u e s t i o n n a i r e s w h i c hi n c l u d e d q u e s t i o n s o n c o m m u n i c a t i o n a n d a r e a s o f s t a f f

i n t er e s t . W e h a v e a l s o c o n d u c t e d s i m i l a r s tu d i e s i n o t h e r

organ isa t ions .

F i g u r e 1 v i s u a l i s e s c o m m u n i c a t i o n b e t w e e n p e o p l e i n t h a t

o r g a n i s a t i o n , u s i n g s p r in g - e m b e d d i n g . T h e o r g a n i s a t i o n

c o n s i s t e d o f s i x m a i n s u b - u n i t s ( l a b e l l e d " A " t o " F " i n t h e

f i g u r e ) a s w e l l a s a n u m b e r o f s p e c i a l e x e c u t i v e a n d

l i a i so n s t a f f ( l a b e l l e d " G " i n th e f i g u re ) . E x t e n s i v e

c o m m u n i c a t i o n t o o k p l a c e b e t w e e n a l l g r o u p s , h u t t h e

s t r o n g e s t c o m m u n i c a t i o n l i n k s w e r e b e t w e e n t h e t h r e e

4



g r o u p s " A , " " E " a n d " F . " M o d e r a t e l y s t r o n g l i n k s a l s o

e x i s t e d b e t w e e n t h e f o u r g r o u p s " C , " " D , " " E " a n d " F . "

W e a k e r , b u t s t i l l s i g n i f i c a n t , l i n k s w e r e " A - B , " " A ~ C "

a n d " A - D . " C o m m u n i c a t io n b e t w e e n p e o p le w a s c o d e d

p s e u d o - l o g a r i t h m i c a l l y a s f o l l o w s :

1 .0 = t h r e e o r m o r e t i m e s p e r d a y

0 . 8 = o n c e p e r d a y

0 . 6 = t h re e o r m o r e t i m e s p e r w e e k0 . 4 = o n c e p e r w e e k

0 . 2 = o n c e p e r f o r t n i g h t

0 . 0 = l e s s t h a n o n c e p e r f o r t n i g h t

T h e 1 8 0 - d e g r e e c o m m u n i c a t i o n c o r r e l a t i o n (i .e .

c o r r e la t i o n b e t w e e n r e p o rt e d c o m m u n i c a t i o n to a n d f ro )

was r = 0.61 ( r 2 = 0 . 3 7 ) , w h i c h i s t y p i c a l f o r s u r v e y s o f

t h i s k i n d ( s i n c e p e o p l e h a v e d i f f e r e n t r e c o l l e c t i o n s o f t h e

a m o u n t o f c o m m u n i c a t i o n b e tw e e n t h em ) .

W e t a k e t h e s i n g l e -l i n k d i s t a n c e b e t w e e n t w o p e o p l e t o

b e t h e r e c i p r o c a l o f t h e l a r g e r o f th e t w o n u m b e r s

r e p o r t in g c o m m u n i c a t i o n b e t w e e n t h e m ( t hu s r a n g i n g

f r o m 1 t o i n f i n i ty ) . T h e c o n c e p t u a l d i s t a n c e b e t w e e n t w o

a r b i t r a r y p e o p l e i s t h e n t h e l e n g t h o f t h e s h o r t e s t p a t h

b e t w e e n t h e m ( r a n g i n g f r o m 1 t o 7 .2 5 i n t h i s c a s e ) .

T h i s d e f i n i t i o n o f c o n c e p t u a l d i s t a n c e b e t w e e n p e o p l e

d o e s n o t t a k e i n t o a c c o u n t t h e n u m b e r o f d i f f e r e n t p a t h s

b e t w e e n p e o p l e , b u t i t h a s a n u m b e r o f a d v a n t a g e s :

• I t c a n b e c o m p u t e d e f f i c i e n t l y .

• D i s t a n c e s d o n o t c h a n g e v e r y m u c h i f s o m e p e o p l e

f a i l t o c o m p l e t e s u r v e y f o r m s ( a s e r i o u s p r o b l e m

w h e n s u r v e y p a r t i c i p a t i o n i s v o l u n t a r y ) .

• I t c o r r e l a t e s e x t r e m e l y w e l l w i t h p h y s i c a l d i s t a n c e in

s p r i n g - e m b e d d i n g , a n d h e n c e i s e a s i l y v i su a l i s e d .

• I n s i m u l a t i o n e x p e r i m e n t s , i t c o r r e l a te s w e l l w i t h

i n f o r m a t i o n p r o p a g a t i o n t i m e ( t y p i c a l c o r r e l a t i o n s

a r e i n t h e r a n g e 0 . 7 t o 0 . 8 , w i t h r 2 i n t h e r a n g e 0 . 5 t o

o.7).

T h e r e s u l t i n g c o r r e l a t i o n b e t w e e n p h y s i c a l d i s t a n c e i n t h e

d i a g r a m a n d c o n c e p t u a l d i s t a n c e i s 0 . 8 5 ( r2 = 0 .72) .

F i g u r e 2 i s t h e r e s u l t o f s p r i n g - e m b e d d i n g i n t h r e e -

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

d e p i c t i o n o f c o n c e p t u a l d i s t a n c e . I n p a r t i c u l a r , t h e

c o r r e l a t i o n b e t w e e n p h y s i c a l d i s t a n c e i n t h e t h r e e -

d i m e n s i o n a l d i a g r a m a n d c o n c e p t u a l d i s ta n c e i s 0 . 93 ( rz =

0 . 8 6 ) . S u c h a t h r e e - d i m e n s i o n a l d i a g r a m c a n b e d i f f i c u l tt o i n te r p r e t , h o w e v e r , a n d m a n y p a r t i c i p a n t s i n o u r

s t u d i e s h a v e r e p o r t e d d i f f i c u l t y i n i n t e r p r e t i n g s u c h

d i a g ra m s . T h e i n c l u s i o n o f li n k s i n t h e d i a g r a m p r o v i d e s

a v a l u a b l e s e n s e o f p e r s p e c t i v e , b u t a l s o o b s c u r e s t h e

n o d e s i n t h e re a r . W e h a v e h a d g r e a t e r s u c c e s s w i t h

interactive t h r e e - d i m e n s i o n a l d i a g r a m s u s i n g V R M L

( V i r tu a l R e a l i t y M o d e l l i n g L a n g u a g e ) t e c h n o l o g y . T h e

a b i l it y to m a n i p u l a t e t h e t h r e e - d i m e n s i o n a l m o d e l

i n c r e a se s u n d e r s t a n d i n g o f i t s st r u ct u r e , a n d V R M L i s

e a s i ly d e p l o y e d u s in g W e b t e ch n o l o g i e s. V R M L a l so

a l l o w s e a s y l i n k i n g o f e x p l a n a t o r y t e x t t o n o d e s .

H o w e v e r , V R M L i s s o m e w h a t d i f f i c u l t f o r f i r s t - t i m e

u s e r s , a n d i n s t a l l i n g V R M L b r o w s e r s i s a l so d i f f i c u l t fo r

t h e i n e x p e r i e n c e d c o m p u t e r u s e r .

Figure 1 . Social Netwo rk for a Mi l i tary Organi sat ion :

S p r i n g - E m b ed d i n g L a y o u t

I n f i g u r e 1 , s p r i n g - e m b e d d i n g is u s e d w i t h i d e a l s p r i n g

l e n g t h s e q u a l t o t h e c o n c e p t u a l d i s t a n c e b e t w e e n p e o p l e .

Figure 2 . Social Netw ork for a Mi l i tary Organi sat ion :

T h ree - D i m en s i o n a l S p r i n g - E m b ed d i n g L a y o u t

3 A l t e r n a t i v e L a y o u t A l g o r i t h m s

B o t h t w o - d i m e n s i o n a l a n d t h r e e - d i m e n s i o n a l s p r in g -

e m b e d d i n g l a y o u t s s h a r e s o m e l i m i t a ti o n s fo r o u r

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

t o g e t h e r , w h i c h c r e a t e s d i f f i c u l t i e s w h e n t h e n o d e s m u s t

b e l a b e l l e d . A l s o , b y r e f l e c t i n g t h e c o n c e p t u a l d i s t a n c e

s o a c c u r a t e l y , t h e y c a n p a r a d o x i c a l l y o v e r - e m p h a s i s el a r g e c o n c e p t u a l d i s t a n c e s . F o r e x a m p l e , t h e n o d e s

l a b e l l e d " B " a t t h e b o t t o m o f f ig u r e 1 ( a l s o s h o w n a t t h e

t o p r i g h t o f f i g u re 2 ) a r e s e p a r a t e d s i g n i f i c a n t l y f r o m t h e

n o d e s r e p r e s e n t i n g t h e r e st o f t h e o r g a n i s a t i o n , a n d t h i s

c a u s e s a n i m m e d i a t e r e a c t i o n w h e n p r e s e n t e d t o c a s e

s t u d y p a r t i c i p a n t s . H o w e v e r , s u c h a n im m e d i a t e r e a c t i o n

( w h i c h m a y g o s o f a r a s to r e s u l t i n a r e s t r u c t u r i n g o f t h e

o r g a n i s a t i o n ) m a y b e i n a p p r o p r i a t e , s i n c e t h e l a r g e

c o n c e p t u a l d i s t a n c e s m a y r e f l e c t l i m i t a t i o n s i n t h e d a t a ,

o r s o m e n o n - o b v i o u s p h e n o m e n o n .

5 0



O n e s o l u t i o n t o t h e s e p r o b l e m s i s t o u s e s p r i n g -

e m b e d d i n g b a s e d o n a t r a n s f o r m a t i o n o f c o n c e p t u a l

d is tance , such as the square roo t , o r to use fo rce-based

l a y o u t t e c h n i q u e s ( B r a n d e s 20 0 1 ) . H o w e v e r , w e h a v e

a l s o i n v e s t i g a t e d a n u m b e r o f a l t e r n a ti v e l a y o u t

techn iques . In f igure 3 , s ta f f a re p laced in a c i rc le w i th

s e n i o r s t a f f c e n tr a l a n d j u n i o r s t a f f t o w a r d s t h e o u t s i d e .

S i m u l a t e d a n n e a l i n g (Hech t-N ie isen 1990) was used to

f i n d a c o n f i g u r a t io n w h i c h p l a c e d t o g e t h e r s t a f f w h oc o m m u n i c a t e d m o s t w i t h e a c h o t h e r. T h i s i s a p r o v e n

t e c h n i q u e f o r s o l v i n g v e r y d i f f i c u l t o p t i m i s a t i o n p r o b l e m s

( o r a t l e a s t o f f i n d i n g n e a r - p e r fe c t s o l u ti o n s ) . T h e o r i g i n

o f t h i s t e c h n iq u e l i e s i n m a t h e m a t i c a l a n a l y s i s o f m e t a l s

w h i c h a r e h e a t e d a n d v e r y s l o w l y c o o l e d , r e s u l t i n g i n a

n e a r - p e r f e c t c r y s t a l s t r u c tu r e . A p p l i c a t i o n s i n c l u d e

m o d e r n c h i p - d e s i g n s o f t w a r e , w h i c h u s e s s i m u l a t e d

a n n e a l i n g t o m i n i m i s e c h i p a r e a a n d m a x i m i s e c l o c k

speed .

Figure 3 . Social Netw ork for a Mi l i tary Organi sat ion:C i r c l e L a y o u t

T h e s i m u l a t e d a n n e a l i n g a l g o r i t h m w e u s e ( a l g o r i t h m 1 )

i s s h o w n b e l o w . I n p r o d u c i n g f i g u r e 3, i n i ti a l p o s i t i o n s

h a d r a d i i b a s e d o n s e n i o r i t y ( s m a l l f o r s e n i o r s t a f f a n d

l a r g e f o r j u n i o r s t a ff ) a n d a r b i t r a r y e v e n l y - s p a c e d a n g l e s

(w i th respec t to the cen t ra l po in t ) . The en ergy fac to r used

i n t h e a l g o r i t h m c a n b e t h e i n v e r s e o f t h e c o r r e l a t i o n

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

s i m i l a r q u a n t it y t h at d e c r e a s e s a s q u a l i t y in c r e a s e s . T h e

a l g o r i t h m a t t e m p t s t o m i n i m i s e t h i s e n e r g y b y r e p e a t e d

s w a p p i n g o p e r a t i o n s . I n th e c a s e o f f ig u r e 3 , s w a p p i n g

m e a n s e x c h a n g i n g a n g l e s w h i l e l e a v i n g r a d i i u n c h a n g e d .

T h e a l g o r i t h m i s a l s o e f f e c t i v e w h e r e i n i t i a l p o s i t i o n s a r e

a r r a n g e d i n a r e g u l a r g r i d , i n w h i c h c a s e s w a p p i n g i sin te rp re ted l i te ra l ly .

O u r v e r s i o n o f s i m u l a t e d a n n e a l i n g c o n v e r g e s f a i r l y

r a p i d l y , in c o n t r a s t t o s i m u l a t e d a n n e a l i n g b a s e d o n

r a n d o m p o s i t i o n a l c h a n g e s , w h i c h c o n v e r g e s m u c h m o r e

s l o w l y . H o w e v e r , o u r v e r s i o n s u ff e r s f ro m t h e l i m i t a t i o n

t h a t t h e r a n g e o f p o s s i b l e n o d e p o s i t i o n s i s l i m i t e d a

p r i o r i to a fa i r ly sm al l se t . Fo r the c i rc le layou t in f igure

3 , th is i s no t a severe l im i ta t ion , bu t fo r layou ts on a

r e g u l a r g r i d t h e l i m i t a t i o n i s m o r e s e r i o u s .

input: s e t o f n o d e s N o f s i z e n w i t h d i s t a n c e f u n c ti o n d

output: s p a t i a l l a y o u t o f N

T = Tmax;

E = energy;

whi le T > Train

r a n d o m l y c h o o se a p a i r o f n o d e s p a n d q ;

Eold = E;

s w a p p o s i t io n s o f p a n d q ;

E = energy;

if Eold < E then

w i t h p r o b a b i l i t y l - e x p ( ( E o l d - E ) / 7 ) u n d o s w a p ;

d e c r e a s e T ;

en d w h i l e

A l g o r i t h m 1 : A l g o r i t h m f o r S i m u l a t ed A n n e a l i n g

G ra p h L a y o u t

I n f i g u r e 3 , t h e c o r r e l a t i o n b e t w e e n p h y s i c a l d i s t a n c e i n

t h e d i a g r a m a n d c o n c e p t u a l d i s t a n c e i s o n l y 0 . 3 6 ( r 2 =

0 . 1 3 ), b u t t h e p l a c e m e n t o f g r o u p s ( g r o u p s " C , '" " D , " " E , "a n d " F " t o g e t h e r , " A " n e a r " E " a n d " F , " a n d " B " n e a r

" A " ) i s s i m i l a r to f i g u r e l , i .e . t o p o l o g y i s p r e s e r v e d e v e n

i f e x a c t d i s t a n c e s a r e n ot . T h i s d i a g r a m w a s f o u n d t o b e

qu i te he lp fu l in p resen t ing s tu dy resu l t s to the c l ien t .

4 L a y o u t u s i n g K o h o n e n N e u r a l N e t w o r k s

F i g u r e 4 i s p r o d u c e d u s i n g a s e l f - o r g a n i s i n g ( K o h o n e n )

n e u r a l n e t w o r k . K o h o n e n n e u r a l n e t w o r k s ( K o h o n e n

1989 , Hech t-N ie lsen 1990 , R i t te r e t a l 1992) are a form

o f s e l f - o r g a n i z i n g n e u r a l n e t w o r k w h i c h p r o d u c e

t o p o l o g i c a l m a p p i n g s . T h e y h a v e b e e n a p p l i e d to a r e a s

such as pa t te rn recogn i t io n (Koh onen 1990) , the lea rn ing

o f b a l l i s t i c m o v e m e n t s ( R i t t e r a n d S c h u l t e n 1 9 89 ),

m o d e l l i n g a e r o d y n a m i c f l o w ( H e c h t - N i e l s e n 1 9 88 ), a n d

i m a g e c o l o u r q u a n t i z a t io n ( D e k k e r 1 99 4 ).

!ii/! ,~i

Figure 4 . Social Netw ork for a Mi l i tary Organi sat ion:

K o h o n e n N e u r a l N e t w o r k L a y o u t

51



W e u s e a n a d a p t a ti o n o f th e b a s i c K o h o n e n n e u r a l

n e t w o r k p r e s e n t e d i n D e k k e r ( 1 9 9 4 ) . I n t h a t w o r k , o n e -

d i m e n s i o n a l n e t w o r k s a r e u s e d , b u t t h e e x t e n s i o n t o

a r b i t r a r y g r a p h s i s e a s y .

T h e b a s i c a l g o r i t h m ( a lg o r i t h m 2 ) is s h o w n b e l o w . T h e

a l g o r i t h m i s c o n t r o l l e d b y t w o p a r a m e t e r s : a f a c t o r a i n

t h e r a n g e 0 . . . 1 , a n d a r a d i u s r , b o t h o f w h i c h d e c r e a s e

w i t h ti m e . W e h a v e f o u n d t h a t th e a l g o r it h m w o r k s w e l li f t h e m a i n lo o p is r e p e a t e d 1 , 0 0 0 , 0 0 0 t i m e s . T h e

a l g o r i th m b e g i n s w i t h e a c h n o d e a s s i g n e d to a r a n d o m

p o s i t i o n . A t e a c h s t e p o f t h e a l g o r i th m , w e c h o o s e a

r a n d o m p o i n t w i t h i n th e r e g i o n t h a t w e w a n t t h e n e t w o r k

t o c o v e r ( i n t h e c a s e o f f i g u r e 4 , a r e c ta n g l e ) , a n d f i n d t h e

c l o s e s t n o d e ( i n t e r m s o f E u c l i d e a n d i s t a n c e ) t o t ha t

p o i n t. W e t h e n m o v e t h at n o d e t o w a rd s t h e r a n d o m p o i n t

b y t he f r a c t io n a o f t h e d is t a n c e. W e a l s o m o v e n e a r b y

n o d e s ( t h o s e w i t h c o n c e p t u a l d i s ta n c e w i t h i n t h e r a d i u s r )

b y a l e s s e r a m o u n t .

input: s e t o f n o d e s N o f s i z e n w i t h d i s t a n c e f u n c t i o n d

output : s p a t i a l l a y o u t o f N

r = 12 ;

~ = 1 ;

rep ea t m a n y t i m es

c h o o s e r a n d o m (x,y);

i = i n d e x o f c l o s e s t n o d e ;

m o v e n o d e i to w a r d s (x ,y ) b y a ;

m o v e n o d e s w i th d< r t o w a r d s (x ,y ) by ~zx( l~ /Z / r 2 ) ;

d e c r e a s e a a n d r ;

en d rep ea t

A l g o r i t h m 2 : B a s ic A l g o r i t h m f o r K o h o n e n N eu ra l

N e t w o r k L a y o u t

F i g u r e 5 i l l u s tr a t e s t h i s p r o c e d u r e a t a p o i n t w h e r e a =

0 . 6 6 6 6 a n d t h e r a d i u s r = 4 . D a r k c i r c l e s s h o w t h e

n e t w o r k b e f o r e u p d a t e , a n d l i g h t e r c i r c l e s s h o w t h e

u p d a t e d ne t w o r k . T h e r a n d o m p o i n t is sh o w n b y a

s q u a re . N u m b e r s s h o w c o n c e p t u a l d i s t a n c e s b e t w e e n

n o d e s .

K o h o n e n ( 1 9 8 9 ) s u g g e st s d e c r e a s in g a a n d r l i n e a r l y

o v e r t i m e , b u t w e h a v e f o u n d t h a t r e s u l t s a r e i m p r o v e d

a n d t h e r e q u i r e d i t e r a t i o n t i m e r e d u c e d i f b o t h a r e

d e c r e a s e d exponent ial ly, b y m u l t i p l y i n g b y 0 . 9 8 a t

r e g u l a r i n t e r v a l s d u r i n g t h e m a i n l o o p , s o t h a t t h e f i n a l

va lu es a r e a = 0 . 02 and r = 1 .

T h e i m p r o v e d a l g o r i t h m ( a l g o r i t h m 3 ) i n c o r p o r a t e s a

m o d i f i c a t i o n d u e t o D e s i e n o ( H e c h t - N i e l s e n 1 9 9 0, p 6 9 )

w h i c h s i g n i f i c a n t l y i m p r o v e s p e r f o r m a n c e . A b i a s f a c t o r

b [ j ] i s s u b t r a c t e d f r o m t h e d i s t a n c e s t o t h e r a n d o m p o i n t

a t e a c h s t e p , b a s e d o n a n e s t i m a t e o f t h e f r e q u e n c y w i t h

w h i c h n o d e s h a v e b e e n m o v e d i n t h e p a s t ( f [ j] i n t h e

a l g o r i t h m ) .

A g r a p h l a y o u t a l g o r i t h m s i m i l a r t o o u r a l g o r i t h m 2 w a s

i n t r o d u c e d b y M e y e r ( 1 9 9 8 ) . H o w e v e r i t i s s u b j e c t t o

" c l a s h e s " w h i c h t h e D e s i e n o m o d i f i c a ti o n h e l p s a v o i d .

~] R andompoint

~'~" ' , , Netw ork f ter uodate

1Closest node

inal network

W

F i g u re 5 . Up d a t e S t ep fo r K o h o n en N eu ra l N e t w o rk

L a y o u t A l g o r i t h m

T h e f i n a l r e s u l t o f th e a l g o r i t h m i s a p o s i t i o n i n g o f n o d e s

w h i c h b a l a n c e s t h e p l a c e m e n t o f c o n c e p t u a l l y c l o s e

n o d e s t o g e t h e r w i t h a n a p p r o x i m a t e l y e v e n l y - b a s e d

d i s t r i b u t i o n o f n o d e s w i t h i n th e s p e c i f i e d r e g i o n . T h e

l a t te r p r o p e r t y i s o f b e n e f i t w h e n t h e n o d e s a r e l a b e l l e d

w i t h n a m e s o f p e o p l e . I t i s a l s o p o s s i b l e t o c o n d u c t t h e

l e a r n i n g p r o c e s s w i t h r a n d o m p o i n t s d r a w n f r o m a n

a r b i t r a r y n o n - r e c t a n g u l a r sh a p e , a n d t h u s o v e r l a y a s o c i a l

f l e tw o r k o n e . g . a n o f f i c e b u i l d i n g l a y o u t .

input: s e t o f n o d e s N o f s i z e n w i t h d i s t a n c e f u n c t i o n d

output : s p a t i a l l a y o u t o f N

/3 = 0 . 001 ;

~, = 20 00 ;

b [ l . . . n ] = 0 ;

f [ 1 . . .n ] = 1/n;

invariant : f o r j ~ 1 . . .n , b [/ '] = ~, × ( ( l / n ) - f [ j ] )

r = 12;

a = l ;

rep ea t m a n y t i m es

c h o o s e r a n d o m ( x , y );

i = i n d e x o f n o d e w i t h m i n i m u m o f d i s ta n c e - b [ i ];

f o r j ~ 1 . . . n , b [ j ] = b [j ] + / 3 × ) ' × f [ / ] ;

f o r j ~ 1 . .. n , f O ' ] = f [ / ] - / 3 × f [ j ] ;

m o v e n o d e i t o w a r ds (x ,y ) b y a ;

m o v e n o d e s w i t h d< r t o w a r d s (x ,y ) b y a × ( 1 - d 2 / r 2 ) ;

b [i ] = b [ i ] - f i x 7 ;

f [ i ] = f [ i ] + ]3 ;

d e c r e a s e a a n d r ;

en d rep ea t

A l g o r i t h m 3 : I m p ro v ed A l g o r i t h m f o r Ko h o n e n

N e u r a l N e t w o r k L a y o u t

5 2



I n f i g u r e 4 , t h e c o r r e l a t i o n b e t w e e n p h y s i c a l d i s t a n c e i n

t h e d i a g r a m a n d c o n c e p t u a l d i s t a n c e i s 0 . 5 0 ( r2 = 0 .25),

which i s be t te r than the c i rc le layou t in f igure 3 . The

p l a c e m e n t o f g r o u p s i s s i m i l a r t o f i g u r e s I a n d 3 .

C o m p a r i n g f i g u r e s 1 a n d 4 s h o w s t h a t f i g u r e 4 i s v e r y

c lose to a topo log ica l (con t inuous) d is to r t ion o f f igure 1 .

T h i s i s d u e t o t h e f a c t t h a t K o h o n e n n e u r a l n e t w o r k s

c r e a t e t o p o l o g i c a l m a p p i n g s .

W e h a v e f o u n d t h i s k i n d o f d i a g r a m e x t r e m e l y u s ef u l ,

p a r t i c u l a r l y w h e n d o c u m e n t i n g t h e r e s u l ts o f a S o c i a l

N e t w o r k a n a l y s i s s u r v e y .

T h e d e c r e a s e w i t h i n t h e a l g o r i t h m o f t h e r a d i u s o v e r t i m e

m e a n s t h a t t h e a l g o r i t h m e f f e c t i v e l y m o v e s p r o g r e s s i v e l y

s m a l l e r " c h u n k s " o f t h e n e t w o r k t o g e t h e r, i . e . i t is

i n h e r e n t l y h i e r a r c h i c a l , b u t w i t h o u t e x p l i c i t l y s p e c i f y i n g

c lus te r ing as in Brocke nauer and Corne lsen (2001) . Th is

m a k e s t h e a l g o r i t h m h i g h l y e f f e c t i v e f o r v i s u a l i s i n g t r e e

s t r u c t u r e s . Figure 6 shows a t ree s t ruc tu re (an

organ isa t iona l char t ) la id ou t us ing the Kohonen

a l g o r i t h m .

(~). --(c)

( k) ( ~ )

~9 ~ z - W 0

Figure 6 . Koho nen N e u r a l N e t w o r k L a y o u t f o r a T r e e

S t r u c t u r e

Figure 7. Social Netw ork for a M i l i t a r y Organisat ion:

T h ree - D i m en s i o n a l F a c t o r L a y o u t

T h i s k i n d o f d i a g r a m w a s f o u n d t o b e q u i t e d e c e p t i v e i f

o n l y t w o f a c t o r s w e r e p r e s e n t e d ( i n a t w o - d i m e n s i o n a ld i a g r a m ) , s i n c e t h a t c o u l d p l a c e p e o p l e w i t h q u i t e

d i f f e r e n t i n t e r e st s t o g e t h e r. T w o - d i m e n s i o n a l d ia g r a m s

o f t h i s k i n d w e r e f r e q u e n t ly m i s u n d e r s t o o d b y c l i e n t s .

T h r e e - d i m e n s i o n a l d i a g r a m s l i k e f i g u r e 7 w e r e m o r e

s u c c e s s f u l ( p r o v i d e d t ha t t h e r e w e r e o n l y t h r e e m a j o r

f a c t o r s ) , b u t s u f f e r e d f r o m t h e s a m e p r o b l e m s n o t e d f o r

f i g u r e 2 a b o v e .

6 S o c i a l F l o w D i a g r a m s

F i g u r e 8 s h o w s a n e x a m p l e s o c i a l n e t w o r k d i a g r a m

p r o d u c e d b y t h e C A V A L I E R t o o l , b a s e d o n t h e g r o u n d

f o r c e s t r u ct u r e d u r i n g t h e G u l f W a r ( C l a n c y a n d F r a n k s

1999, Kha led and Sca le 1995). Boxes represen t d iv is ion-

leve l un i t s f rom par t ic ip a t ing coun tr ies ( in the case o f

Saud i , Kuwai t i , and Gulf s ta te un i t s , these a re no t iona l ) ,

w h i l e c i r c l e s r e p r e s e n t c o m m a n d e r s . U n i t s o n t h e r ig h t

w e r e u n d e r t h e c o n t r o l o f A m e r i c a n G e n e r a l N o r m a n

S c h w a r z k o p f , w h i l e t h o s e o n t h e l e f t w e r e u n d e r t h e

c o n t r o l o f S a u d i P r i n c e K h a l e d b i n S u l t a n .

5 C o n c e p t u a l S p a c e s

T h e e l e c t r o n i c q u c s t i o n n a i r e i n t h i s c a s e s t u d y i n c l u d e d

i n f o r m a t i o n a b o u t 1 5 t o p i c s o f i n t e r e st , m a n y o f w h i c h

w e r e f o u n d t o b e h i g h l y c o r r e l a t e d w i t h e a c h o t h e r .

F a c t o r a n a l y s i s ( p r i n c i p a l c o m p o n e n t a n a l y s i s ) o n t h e s et o p i c s f o u n d t h a t 4 m a i n f a c t o r s ( p r i n c i p a l c o m p o n e n t s )

exp la ine d 73 percen t o f the var ia t ion in da ta abou t

in te res ts . The f i r s t o f these fac to rs s im ply represen ted

p e o p l e ' s g e n e r a l l ev e l o f in t e r e s t in e v e r y t h in g . F i g u r e 7

i l l u s tr a t e s t h e o t h e r t h re e p r i n c i p a l c o m p o n e n t s - - p e o p l e

a r e l o c a t e d i n a t h r e e - d i m e n s i o n a l c o n c e p t u a l s p a c e

a c c o r d i n g t o t h e n u m e r i c a l v a l u e s o f t h e s e t h r e e p r i n c i p a l

c o m p o n e n t s . I n o t h e r w o r d s , t h e d i a g r a m p l a c e s p e o p l e

wi th s im i la r in te res t toge ther , and in m os t cases , these a re

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

~2 u~n~1 U ~ r i n e

F i g u re 8. S o c i a l N e t w o rk f o r Gu l f W a r G ro u n dF o rces: S p r i n g - E m b ed d i n g L a y o u t

5 3



Figure 8 is produced by a s pring-embedding layout

algorithm which attempts to balance two forms of

distance: cultural distance and command distance.

Cultural distances range from ~/8 for units from the same

country and service to 6 for the less than friendly

relationship between the US and Syria. Cultural

differences between the US Army and Marines are

reflected by a distance of '/2. Dark grey lines in the

figure show formal command relationships, and

command distance is measured by counting the mi nimum

number of these links. The light grey line between the

US VII Corps commander and the Egyptian Corps

commander represents an informal working relationship,

which we represent using a command distance of 2.

We are particularly interested in comparisons between

two or more distance relationships, such as occur in this

example. When all pairs of division-level units in figure

8 are considered, there is a statistical correlation of 0.58

(r2 = 0.33) between the cultural distance and command

distance. This indicates that the organisational structure

negotiated between the US and Saudi Arabia was fairly

successful in separating culturally different units.

F i g u r e 9 . S o c i a l F l o w D i a g r a m f o r G u l f W a r G r o u n d

F o r c e s

The relationship between these two distance concepts is

visualised in figure 9, which we call a soc ia l f lowdiagram. In this figure, each division-level unit is

represented by a pair of boxes (one white, one coioured)

linked by an arrow. As a result of the spring-embedding

layout algorithm, the physical distance between white

boxes closely indicates cultural distance (physical

distance has a 0.97 correlation with cultural distance),

while the physical distance between coloured boxesindicates command distance (somewhat less closely, with

a correlation of 0.86). The arrows indicate how culturally

similar units have been separated in some cases, and

culturally dissimilar units have been co mbined in others.

For example, in the lower left of the figure, the French

division, which was initially strongly opposed to being

under US control, has in fact been placed within the US

command structure. In the upper left, the US Marines

have separated themselves from their Army colleagues.

On the other hand, in spite of a somewhat deceptive long

arrow in the diagram, figure 9 shows that the UK forces

remained closely tied to the US Army.

Figure 10 uses spr ing-embedding to visualise a slightly

different definition of cultural distance between selected

countries. The defin ition of cultural distance used here

combines differences in religion, language, economics,

and military alliances such as NATO (the correlation with

physical distance is 0.85).

India

N0oo0c4~y

"~%o~ub,i0

O

R~ia

F i g u r e I 0 . C u l t u r a l D i s t a n c e s f o r S e l e ct e d C o u n t r i e s

Figure 11 is a social flow diagram which visualises the

change in this de finition of cultural distance after the end

of the Cold War. White boxes represent the situation

during the Cold War, while coioured circles represent the

present situation (also shown in figure 10). The

correlation with physical distance is 0.85 for the Cold

War situation, and 0.81 for the present. The top left of

the diagram shows how some former Communist

countries have moved closer to Western Europe, while

others have not.

R~ia

A~ia~e,~_and

~m~ In~.~ia S i ~

M~ia

F i g u r e I I . S o c i a l F l o w D i a g r a m f o r E n d o f C o l d W a r

54



We produce soc ia l f low diagrams us ing spr ing-

embedding, g iv ing the in t roduced a r rows a ve ry shor t

desired l eng th , but a ve ry low s t reng th , so tha t a wide

va r i a t ion in a r row l engths i s t o l e ra t ed by the spr ing-

embedding a lgor i thm.

We have found soc ia l f low diagrams to be ve ry e f f ec t ive

in v i sua l i s ing how conceptua l d i s t ance i s a f f ec t ed by

factors such a s s im ilar i ty of tasking, both in re la t ionshipsbe tween groups ( a s in f igure s 9 and 11) and in

re la t ionships betw een individual peop le .

7 C o n c l u s i o n

W e have d i scus sed the use o f vi sua li sa tion for Soc ia l

N e t w or k A na l ys i s w i t h i n t he C A V A L I E R

( C om m uni c a t i on a nd A c t i v i t y V i s uA L I s a t i on f o r t he

EnteRpr i se ) t ool sui t e , i nc luding spr ing-embedding and

s imula ted annea l ing t echniques . W e have in t roduced a

vi sua l i s a t ion t echnique based on Kohonen neura l

ne tworks , and we have a l so in t roduced s o c i a l f l o wd iagrams for dem onstra t in g the re la t ionship betw een two

forms of conceptua l d i st ance .

8 A c k n o w l e d g e m e n t s

Dawn Hayte r and Jon Rigte r provided va luable

sugges t ions on th is re sea rch projec t. The CA VA LIE R

sof tware inc luded the JAMA l inea r a lgebra module f rom

the US N a t iona l Ins t it u t e of Standa rds and Techn olog y

(NIST) which has been r e l ea sed to the publ i c doma in.

Figure s 2 and 7 were produced us ing the P e r s i s t e n c e o fVisionTM ( P O V - R a y M ve r s ion 3 .1) r ay- t r ac ing package .

T ha nks a l s o t o a n a nonym ous r e f e r e e w ho p r ov i de d

seve ral use ful comm ent s , i nc luding point ing out t he workof Me ye r (1998) .

9 R e f e r e n c e s

A L L A R D , K . (1 9 9 6 ): C o m m a n d , C o n t r o l , a n d t h e

Comm on Defense , rev ised ed i t ion , Nat iona l De fense

Unive r s i ty Pre s s, W ashington, D.C.

B R A N D E S, U . ( 2001 ) : D r a w i ng on Phys i c a l A na l og i e s .

In D r a w i n g G r a p h s : M e t h o d s a n d M o d e l s , 7 1 - 8 6 ,

K A U FM A N N , M . a nd W A G N E R , D . ( e ds ) , Sp r i nge r

V e r l a g L N C S 2025 .

B R O C K E N A U E R , R . an d C O R N E L S E N , S . ( 2 00 1 ):

Dra win g Clusters and Hierarchies . In D r a w i n g

Graphs: Methods a nd Mode ls , 193- 227 ,

K A U FM A N N , M . a nd W A G N E R , D . (e ds) , Sp r i nger

V e r l a g L N C S 2025 .

C L A N C Y , T . a n d F R A N K S , F . ( 19 9 9 ): Into the Storm: A

S t u d y i n C o m m a n d , Se dgw i c k a nd J a c kson .

C O H E N , R . J. , SW E R D L I K , M . E . a nd PH I L L I PS , S . M .

(1996) : Psycho log ica l Tes t ing an d Assessmen t , 3 aedition, Mayf ie ld .

D E K K E R , A . H . (1994 ) : K ohone n N e ur a l N e t w or ks f o r

Opt ima l Colour Quant iza t ion. Network : Computa t ion

in Neura l Sys tems 5: 351 -367, Inst it u te of Phys ic s

Pub l ishing. See a lso the associa ted web s ite a thttp://www.acm.or ~-dckkcr/NEUQUANT.HTML

DEKKER, A. H. (2000) : Soc ia l Ne twork Ana lys i s i n

M i l i t a r y H e a dqua r t e r s u s i ng C A V A L I E R . Proc. 5 h

In terna tiona l Comm and and Con tro l Research and

Techno logy Sympos ium, canbe r ra . Ava i l able a thttp://www.dodccrp.org/2000ICCRTS/cd/papcrs/Track6/O39.pdf

FREEMAN, L. C. (2000) : Vi sua l iz ing Soc ia l Ne tworks .

J our na l o f Soc ia l S truc ture I (1) . Ava i l able a thttp://www.heinz.cmu.cdu/proicct/1NSNA/joss/vsn.html

G I B B O N S, A . ( 1985 ) : Algor i thmic Graph Theory ,

Cam br idge Un ive r s i ty Pre s s.

H E C H T - N I E L SE N , R . ( 1988 ): N e u r oc om pu t i ng : p i c k ing

the human bra in . IEEE Spec trum 25 (3): 36--41.

H E C H T - N I E L S E N , R . ( 1 99 0 ): Neurocomput ing ,

A ddi s on W e s l ey .

K H A L E D B I N S U L T A N a n d S E A L E , P . ( 19 95 ): D e s e r t

W a r r io r : A P e r s o n a l V i ew o f t h e G u l f W a r b y t h e J o i n t

F o r c e s C o m m a n d e r , Harper Col l ins .

K O H O N E N , T . ( 1989 ) : Sel f -Organ iza t ion andAssoc ia t ive Memo ry , 3"a edition, Spr inge r -Ver l ag ,

Berlin.

K O H O N E N , T . ( 1990 ): Pa t te r n R e c ogn i t i on by t he Se l f-

O r ga n i z i ng M a p . Para l le l Arch i tec tures and Neur a l

Ne twork s : Th ird I ta lian Work shop , Vietr i sul Mare ,

Sa le rno, 13-18, C AIA NIE LL O, E. R. ( ed) , W or ld

Scient i f ic , Singapore .

K R A C K H A R D T , D . ( 1994 ) : G r a ph T he o r e t i c a l

Dim ens ions of Informa l Organiza tions. In

Computa t iona l Organ iza t ion Theory . 8 9 - 1 1 1 .

C A R L E Y , K . M . a nd PR I E T U L A , M . J . ( eds ).

Lawrence Erlbaum Associa tes , Hil lsdale , NJ.

MEYER, B (1998) : Se l f -Organiz ing Graphs : A Neura l

N e t w or k Pe r s pe ct i ve o f G r a ph L a you t . Proc. Graph

D r a w i n g ' 9 8 , Mont rea l , Canada , 246-262, Spr inge r

Ver l ag LN CS 1547. See a l so the a s soc ia t ed web s i te a thtlp://www.cssc.monash.cdu.au/-bcrndm/ISOM/indcx.html

R I T T E R , H . a nd SC H U L T E N , K . ( 1989 ) : E x t e nd i ng

K ohone n ' s Se l f - O r ga n i z i ng M a pp i ng A l go r i t hm t o

Lea rn Ba l l i s t i c Movement s . In N e u r a l C o m p u t e r s ,

3 9 3 - 4 0 6 , E C K M I L L E R , R . an d v .d . M A L S B U R G , C .

(eds) , Spr inger-Verlag, Berl in.

R I T T E R , H . , M A R T I N E T Z , T . a n d S C H U L T E N , K .

(1992) : Neu ra l Computa t ion and Se l f-Organ iz ing

Maps: An In troduc tion , A ddi s on - W e s l e y .

W A S S E R M A N , S . a n d F A U S T , K . ( 1 9 9 4 ) : Social

Ne tw ork Ana lys is : M ethods a nd App lica t ions ,Cam br idge Un ive r s i ty Pre s s.

55

Visualisation of Social Networks

Documents

Transcript of Visualisation of Social Networks