Dimensionality reduction for similarity search with the Euclidean distance in high-dimensional applications

Abstract

In multimedia information retrieval, multimedia data are represented as vectors in high-dimensional space. To search these vectors efficiently, a variety of indexing methods have been proposed. However, the performance of these indexing methods degrades dramatically with increasing dimensionality, which is known as the dimensionality curse. To resolve the dimensionality curse, dimensionality reduction methods have been proposed. They map feature vectors in high-dimensional space into vectors in low-dimensional space before the data are indexed. This paper proposes a novel method for dimensionality reduction based on a function that approximates the Euclidean distance based on the norm and angle components of a vector. First, we identify the causes of, and discuss basic solutions to, errors in angle approximation during the approximation of the Euclidean distance. Then, this paper propose a new method for dimensionality reduction that extracts a set of subvectors from a feature vector and maintains only the norm and the approximated angle for every subvector. The selection of a good reference vector is crucial for accurate approximation of the angle component. We present criteria for being a good reference vector, and propose a method that chooses a good reference vector. Also, we define a novel distance function using the norm and angle components, and formally prove that the distance function consistently lower-bounds the Euclidean distance. This implies information retrieval with this function does not incur any false dismissals. Finally, the superiority of the proposed approach is verified via extensive experiments with synthetic and real-life data sets.