This section examines one model revision algorithm [5] to illustrate the process of revising the feature space using feedback from the user and the ground truth results. In this algorithm, a linear transform of the features is modified by the user's feedback. A gradient (steepest descent) method is employed to ensure rapid convergence, which makes the approach suitable for an interactive query environment.
We assume that an image database consists of a set of N feature vectors. Each feature vector has n dimensions. The feature vectors potentially represent a combination of color, texture and shape information.
The user starts a query by selecting a particular query image, region, or object. The corresponding feature vector is extracted from the example, and the K best matches are retrieved using a Euclidean metric. The K results whose feature vectors are closest to the target feature vectors are then returned to the user for visual inspection or further processing.
The user specifies a refinement by selecting
of the K matches that
are most similar to the desired
match and reissuing the query.
Based upon this feedback, the linear or nonlinear
transform matrix is modified to better approximate
the user's evaluation of similarity.
A second set of matches is found and
returned to the user.
The user selects the 
best matches and again
reissues the query.
This process is repeated until either the result set
converges, or the user stops the process.
If the set of the feature vectors selected by the user up to step (i-1)
is denoted as 
, then
where 
is the set of feature vectors selected during step i.
The vectors that are NOT selected up to step i-1 is 
, then
where 
is the set of feature vectors rejected during step i.
Algorithm The algorithm [5] for iterative refinement using nonlinear multidimensional scaling is as follows:
and 
to those vectors which are considered to
be similar. Also initialize 
and 
to those vectors that
are not considered to be similar.
If the number of vectors is less than a prescribed
threshold, set 
, where 
is a fixed increment.
Return to step 1.
and 
where
include all the vectors that are considered similar,
while include all the vectors that are considered to be no similar
(or irrelevant). Consequently, the class label for is 1, while
the class label for is 2. containing similar (or relevant)
results or to set containing dissimilar (or irrelevant) results. and as follows
if the difference between and is less than a prescribed
threshold, a equilibrium has been reached and exit.
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