Kernel-Based Adaptive Image Retrieval Methods - Multimedia Database Retrieval: Technology and Applications - page 18

Table 2.1 Summary of the adaptive retrieval algorithm

Input: Query vector = x q

Set of vectors to be searched in the database

= x n , n = ,···, T

1

Output: The final retrieval set, containing k -relevant samples = S k ( x q )

Computation:

P

2

2

∑ i x qi − x ni

d ( x q , x n )=

, n = , ,..., T ,

1 2

)= x )

S k ( x q | d ( x q , x ) ≤ d ( x q , x k

where S k ( x q ) is the set of nearest neighbors, and x k is the k -th nearest neighbor

of x q .

N
i

Repeat: Obtain training sample: { x i } ₐ S k ( x q )

= 1

User selects class label: l i
Calculate model parameters of the mapping function f q
Calculate f q ( x n ) ,for n = 1 , 2 ,..., T , and obtain

)= x ) S k ( x q | f q ( x ) ≥ f q ( x k

Until: User is satisfied with the retrieval result.

2.2.2 Query Adaptation Method

Among the early attempts to conduct adaptive retrieval, Rui et al. [ 11 , 12 ]imple-
mented the query modification strategy, and the mapping function takes the form of
the following linear function:

x · x q

x q

f q ( x )= (2.5)

x

K x x q

∝ , (2.6)

where K is the linear kernel function:
K x x q ≡ x x q ≡

, , x · x q (2.7)

x q denotes the Euclidean inner product, x q = x q 1 ,..., x qP t and x · is the modified

query vector, and is the Euclidean norm. The linear kernel function represents

the similarity metric for a pair of vectors, x and x q . The two vectors, x and x q

·