Kernel-Based Adaptive Image Retrieval Methods - Multimedia Database Retrieval: Technology and Applications - page 38

2.4.3.2 Integrating Elliptic Basis Function

The basic RBF version of the ARBFN discussed in Eq. ( 2.52 ) is based on the
assumption that the feature space is uniformly weighted in all directions. However,
image feature variables tend to exhibit different degrees of importance which
heavily depend on the nature of the query and the relevant images defined [ 16 ].
This leads to the adoption of an elliptic basis function (EBF):

t M

x − z i M =( x − z i ) ( x − z i ) (2.57)

where

M = Diag [ ʱ 1 ,..., ʱ j ,..., ʱ P ] (2.58)

So, the parameter P represents the relevance weights which are

derived from the variance of the positive samples in

ʱ j , j = 1 ,...,

N p
i

x i } x i ∈ R

P

{

1 ,

as follows:

=

1

, ʶ p = 0

ʱ j = (2.59)

1

ʶ j ,

Otherwise

where

1
N p −

2

2

N p
i = 1 ( x ij − x j )

ʶ j = (2.60)

1

N p
i = 1 x ij

1
N p

x j = (2.61)

ʱ j assign a
specific weight to each input coordinate, determining the degree of the relevance of
the features. The weight

The matrix M is a symmetrical M P × P , whose diagonal elements

ʱ j is inversely proportional to ʶ j , the standard deviation of

N p
i =

x ij }

the j -th feature component of the positive samples,

1 . If a particular feature
is relevant, then all positive samples should have a very similar value to this feature,
i.e., the sample variance in the positive set is small [ 17 ].

{

2.4.3.3 Shifting RBF Centers

The possibility of moving the expansion centers is useful for improving the
representativeness of the centers. Recall that, in a given training set, both positive
and negative samples are presented, which are ranked results from the previous
search operation. For all negative samples in this set, the similarity scores from the
previous search indicate that their clusters are close to the positive samples retrieved.