Databases Reference
In-Depth Information
2.2
The set of the semantic projections
Π
v
The projection
P
λi
is defined as follows:
Projection to the eigenspace corresponding to the eigenvalue
λ
i
,
The set of the semantic projections
Π
v
is defined as follows:
The number of the elements of
v
is 2
v
, and accordingly it implies that 2
v
different
contexts can be expressed by this formulation.
Π
2.3
Semantic operator
The correlations between each context word and each semantic element are
computed by this process. The context word is used to represent the user's
impression and the image's contents for images to be extracted. A sequence
of
l
context words and a positive real number
are given, the semantic
operator
S
p
constitutes a semantic projection
, according to the context.
That is,
where
T
l
is the set of sequences of
l
words and . Note that the
set {
u
1
,
u
2
, …,
u
l
} must be a subset of the words defined in the matrix M.
The constitution of the operator
S
p
consists of the following processes:
1.
Fourier expansion
of is computed as the inner product of
u
i
and
q
j
u
ij
,
i.e.
is defined as
This is the mapping of the context word
u
i
to the
MDS
.
