# here

Τεχνίτη Νοημοσύνη και Ρομποτική

25 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

106 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

  

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

  

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

Who Are We?

Small, established scientific consulting firm

~150 employees

Founded in 1982

20 miles from Washington, D.C.

Employing many mathematicians

To solve challenging, technical problems

For clients in the Defense and Intelligence communities

Metron Proprietary

2

2

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

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
|

+

)

Network Detection: A Sample Theorem

Metron Proprietary

5

m

movies”

n

actors”

Unipartite Projection:
who’s acted with whom

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
 
 
 

Pattern Analysis and Link Discovery Tool for Networks

Metron Proprietary

6

Customize extraction of entities and

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
-

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