A Family of Contextual Measures of Similarity between Distributions with Application to Image Retrieval
Résumé
We introduce a novel family of contextual measures of
similarity between distributions: the similarity between two
distributions q and p is measured in the context of a third
distribution u. In our framework any traditional measure of
similarity / dissimilarity has its contextual counterpart. We
show that for two important families of divergences (Bregman
and Csisz´ar), the contextual similarity computation
consists in solving a convex optimization problem. We focus
on the case of multinomials and explain how to compute in
practice the similarity for several well-known measures.
These contextual measures are then applied to the image
retrieval problem. In such a case, the context u is estimated
from the neighbors of a query q. One of the main benefits
of our approach lies in the fact that using different contexts,
and especially contexts at multiple scales (i.e. broad and
narrow contexts), provides different views on the same problem.
Combining the different views can improve retrieval
accuracy. We will show on two very different datasets (one
of photographs, the other of document images) that the proposed
measures have a relatively small positive impact on
macro Average Precision (which measures purely ranking)
and a large positive impact on micro Average Precision
(which measures both ranking and consistency of the scores
across multiple queries).