Databases Reference
In-Depth Information
2.1
Creation of a metadata space
The semantic associative search for images is created by using our mathematical
model of meaning
4,
7)
. For the metadata items for space creation, a data matrix
M
is created. When
m
data items for space creation are given, each data item is
characterized by n features (
f
1
,
f
2
, …,
f
n
). For given
d
i
(
i
=1, …,
m
), the data matrix
M
is defined as the
m
×
n
matrix whose
i
-th row is
d
i
. Then, each column of the
matrix is normalized by the 2-norm in order to create the matrix M.
Figure 1 shows the matrix M. That is
M
=(
d
1
,
d
2
,
d
3
,…,
d
n
)
T
.
Figure 1: Representation of metadata items by matrix M
1.
The correlation matrix
M
T
M
of
M
is computed, where
M
T
represents the
transpose of
M
.
2.
The eigenvalue decomposition of
M
T
M
is computed.
The orthogonal matrix
Q
is defined by
where
q
i
's are the normalized eigenvectors of
M
T
M
. We call the eigenvectors
“semantic elements” hereafter. Here, all the eigenvalues are real and all the
eigenvectors are mutually orthogonal because the matrix
M
T
M
is symmetric.
3.
Defining the metadata space
MDS
.
which is a linear space generated by linear combinations of {
q
1
, …,
q
v
}. We
note that {
q
1
, …,
q
v
} is an orthonormal basis of
MDS
.
