Kernel-Based Adaptive Image Retrieval Methods - Multimedia Database Retrieval: Technology and Applications - page 43

∑ i is the d i -by- d i covariance matrix

μ i is the d i -component mean vector and

where

∑ − i are its determinant and inverse,
respectively. These variables can be estimated using the positive training vectors
in the positive class

| ∑ i | for the i -th feature vector, and and

X + ,

N p
j = 1 v ji

1
N p

μ i = (2.77)

N p

j = 1 v ji − μ i v ji − μ i t

1

i =

∑

(2.78)

( N p − 1 )

where v ji is the i -th sub-vector of j -th positive sample, and N p is the number
of positive samples. For simplicity we abbreviate Eq. ( 2.76 )as P v ji |X + ) ∼

(

( μ i , ∑ i ) N . Similarly, the probability density function for the negative class is

given by: P

∑ i is the
covariance matrix for the i -th feature vector, which can be estimated using the
negative training vectors in the negative class

( μ i , ∑ i ) v ji |X − ) ∼ μ i is the mean vector and ( N where

X − .
After the desired output y j of the fuzzy sample is estimated, the gradient-descent
procedure of Eqs. ( 2.69 )-( 2.71 ) are applied to construct the learning parameters of
the RBF network.

2.4.6 Experimental Result

The Corel database was used in the experiments reported in Sect. 2.3.3 . All 40,000
images in the database were used, each of which was characterized by a multi-
feature representation (explained in Table 2.7 ). This section begins by implementing
the RBF network using the ARBFN leaning method and comparing its performance
with two other learning strategies. This is followed by examining the ARBFN and
the single-class learning methods discussed in Sects. 2.2 - 2.3 .
The first objective is to verify that the ARBFN is able to meet the demands of
adaptive retrieval applications; in particular, where there is a small set of training
samples with a high level of correlation between the samples. A learning session
with this condition may be observed in Fig. 2.3 d, where the top sixteen retrieved
images are returned to the user who provides relevance feedback. It is seen that
at later iterations the learning system can improve the result sets, which means
that the more times the interactive retrieval is implemented, the higher the level
of correlation retrieved images.
The ARBFN method was compared with two learning strategies that have been
successfully used in other situations to construct the RBF network. Table 2.12
summarizes the methods being compared. The first learning method, the orthogonal
least square (OLS) learning procedure described in [ 44 ], was used to identify
a RBF network model. In the second learning method [ 43 ], each vector in a