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plantationscarfΤεχνίτη Νοημοσύνη και Ρομποτική

25 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

79 εμφανίσεις

December 2002
Estimate
Forecast to
November 2003
Completed
Ongoing
Not started
( | ~ (,,)) ( | target + noise)
( )
( | ~ (,)) ( | noise)
P Y J Y G n p T P J
J
P Z J Z G n p P J

  

Process structured, linked data on
multiple entity and link types
Detect terrorist activities via
likelihood ratio on random graphs
Track, forecast & develop course of action
via terrorist enterprise model
December 2002
Estimate
Forecast to
November 2003
Completed
Ongoing
Not started
( | ~ (,,)) ( | target + noise)
( )
( | ~ (,)) ( | noise)
P Y J Y G n p T P J
J
P Z J Z G n p P J

  

Process structured, linked data on
multiple entity and link types
Detect terrorist activities via
likelihood ratio on random graphs
Track, forecast & develop course of action
via terrorist enterprise model
[
]
[
]
(
)
(
)
(
)
1
( )
cr( )
var
,;


H
i i
i V H
H
X
B T T d O n
X
p
p
-
Î
Î
= +
å
Õ
E
(
)
(
)
Aut cr( ) Aut cr( )
/
H H
c
p

H

cr(
H
)

Applied Mathematics

Operations Research

Simulation Science

Computer Science

© 2010
All Rights Reserved

Who Are We?


Small, established scientific consulting firm


~150 employees


Founded in 1982


Headquarters in Reston, Virginia


20 miles from Washington, D.C.


Employing many mathematicians


Ph.D. and undergraduate


To solve challenging, technical problems


For clients in the Defense and Intelligence communities

Metron Proprietary


2

2

© 2010
All Rights Reserved

What kind of undergraduate background
is useful for working at Metron?


Computer skills


Java or C++


Writing skills


Mathematics


Linear algebra


Probability and statistics


Any course that contributes to mathematical
maturity

© 2010
All Rights Reserved

Exposing Terrorist Networks


Use ideas from classical detection theory

to determine presence of terrorist

cells in a network


Metron Proprietary


4

Noise
Process

Signal + Noise

Process

Likelihood Ratio
: optimal statistic for
deciding whether a graph
J

arose from
signal + noise process or noise only


H
(
J
)

=

P
(
J
|

)

P
(
J
|

+

)

© 2010
All Rights Reserved

Network Detection: A Sample Theorem

Metron Proprietary


5









m


movies”

n


actors”

Unipartite Projection:
who’s acted with whom

independent links,
average of

m

per actor

instance
of

B

*

Random Collaboration Model:
B

*
(
n
,
m
,
m
)



Kevin Bacon game: connect “actors” in same “movie”



Yields realistic network model (high clustering coefficient, etc.)


)

)

)
( )
( )
1
( ) 1
1
1
*
1
i
b
v H
c H
H
i
s
r H
r H
s
i
H n
E X
b
O
s
X K m
m
B
m
m





 
 
 
 
 
 
 
 
 


Theorem [Lo, Ferry]:
For
m
,
n




with
constant

m

,
the expected number of subgraphs of
B

*
(
n
,
m
,
m
)

isomorphic to
H


is given by




H

represents a threat activity obscured by noise model
B

*



Formula used to detect whether
H

arises by chance or by design

Example of Theorem

Let
H

be

v
´
(
H
)

=
8

= number of non
-
isolated vertices of
H

r
(
H
)

=
7

= rank of
H

c
(
H
)

=
2

= number of cut vertices of
H

Break
H

into
blocks at cut
vertices

3
1 2
1
3
1 3
s
s
s
m m m


 
  
 
 

Stirling numbers
count partitions
of
b
i

blocks into
s

“movies”

Ratio of expected to
possible number of
H

’s is


)

)

)

)

)
8 2
8
7
*
1 3 1
H
H n
E X
O m
X K m
B
m m m m

  
 
 
 
b
1
= 3

b
2
= 2

1
m

i
b
s
 
 
 
© 2010
All Rights Reserved

Pattern Analysis and Link Discovery Tool for Networks
(PALADIN) Components

Metron Proprietary


6


Customize extraction of entities and
links, with attributes, from data


Statistical analyses of numerous
social network metrics to
discover entities and groups
with anomalous properties


Subgraph
matching to
discover threat
signatures


Connect related
signatures to
detect
organized
threat networks
and activities

Entity
-
Link Extractor

Network Anomaly Detector

Network Pattern Matcher

Network Visualization and Exploration Tool


Drill
-
down into
and compare
discovered
networks


Functions and
features to
control display
layout and
information
fidelity

Group Detector


Hierarchical clustering algorithms to
detect groups of interconnected entities