Fast adaptive Mahalanobis distance-based search and retrieval in image databases

Motivated by the need to efficiently leverage user relevance feedback in content-based retrieval from image databases, we propose a fast, clustering-based indexing technique for exact nearest-neighbor search that adapts to the Mahalanobis distance with a varying weight matrix. We derive a basic property of point-to-hyperplane Mahalanobis distance, which enables efficient recalculation of such distances as the Mahalanobis weight matrix is varied. This property is exploited to recalculate bounds on query-cluster distances via projection on known separating hyperplanes (available from the underlying clustering procedure), to effectively eliminate noncompetitive clusters from the search and to retrieve clusters in increasing order of (the appropriate) distance from the query. We compare performance with an existing variant of VA-File indexing designed for relevance feedback, and observe considerable gains.