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8/8/2019 Visualisation of Social Networks
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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
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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
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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
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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
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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
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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
8/8/2019 Visualisation of Social Networks
http://slidepdf.com/reader/full/visualisation-of-social-networks 7/7
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) .
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