Database Reference
In-Depth Information
f
e
c
h
a
d
g
b
Fig. 4.1 Decomposing a set of instances in a VP-tree.
L
(
o
|
LN
(
o
,
C
, σ ))
, where L
(
o
|
LN
(
o
,
C
, σ )
is the likelihood of o given objects
LN
.
The following result uses local simple typicality to approximate the simple typi-
cality with a quality guarantee.
(
o
,
C
, σ )
Final winner:
e
Center(N6)=e
Radius(N6)=dist(e,f)
Neighborhood(N6)={N6,N7,c}
Winner(N6)=e
N1
c
e
N2
N3
e
b
c
h
N4
N5
N6
N7
g
ab c
d
e
f
h
Fig. 4.2 Computing the approximate most typical instance.
Theorem 4.1 (Local typicality approximation). Given an uncertain object O,
neighborhood threshold
, σ ) }
be the instance in C having the largest local simple typicality value, and o
σ
, and a subset C
O, let
o
=
arg max o 1 C {
LT
(
o 1 ,
C
,
O
=
arg max o 2 C {
T
(
o 2
,
O
) }
be the instance in C having the largest simple typicality
value. Then,
e σ 2
1
h 2
T
(
o
,
O
)
T
(
o
,
O
)
(4.2)
2 h 2
π
Moreover, for any object x
C,
1
h 2
e σ 2
1
h 2
T
(
x
,
O
)
LT
(
x
,
C
,
O
, σ ) <
(4.3)
2 h 2
π
π
 
Search WWH ::




Custom Search