Effective indexing and searching with dimensionality reduction in high-dimensional space

Abstract

In multimedia information retrieval, multimedia data are represented as vectors in high-dimensional space. Performance of many indexing methods maintaining these vectors dramatically degrades with increasing dimensionality, which is known as the dimensionality curse. To resolve this dimensionality curse, dimensionality reduction methods which map vectors in high-dimensional space into those in low-dimensional space before the data are indexed have been proposed. This paper addresses indexing and searching issues for low-dimensional data vectors which are reduced by a dimensionality reduction method. This method maps high-dimensional vectors into low-dimensional ones by using their norms and approximated angles. However, in indexing such data using the R*-tree, which is a traditional multi-dimensional index structure, there several problems appear. In this paper, we first identify the problems associated with indexing and searching of low-dimensional vectors and then propose an approach to solve these problems. We formally prove that the proposed approach does not incur false dismissal in searching. Finally, we verify the superiority of the proposed approach via extensive experiments with synthetic and real-life data sets.