Databases are increasingly being used to store multi-media objects such as maps, images, audio and video. Storage and retrieval of these objects is accomplished using multi-dimensional index structures such as R$^*$-trees and SS-trees. As dimensionality increases, query performance in these index structures degrades. This phenomenon, generally referred to as the dimensionality curse, can be circumvented by reducing the dimensionality of the data. Such a reduction is however accompanied by a loss of precision of query results. Current techniques such as QBIC use SVD transform-based dimensionality reduction to ensure high query precision. The drawback of this approach is that SVD is expensive to compute, and therefore not readily applicable to dynamic databases. In this paper, we propose novel techniques for performing SVD-based dimensionality reduction in dynamic databases. When the data distribution changes considerably so as to degrade query precision, we recompute the SVD transform and incorporate it in the existing index structure. For recomputing the SVD-transform, we propose a novel technique that uses aggregate data from the existing index rather than the entire data. This technique reduces the SVD-computation time without compromising query precision. We then explore efficient ways to incorporate the recomputed SVD-transform in the existing index structure without degrading subsequent query response times. These techniques reduce the computation time by a factor of 20 in experiments on color and texture image vectors. The error due to approximate computation of SVD is less than 10\%.
Keywords: Dimensionality Curse, Similarity Searching, Dimensionality Reduction, SVD, Multi-dimensional Indexing