Dimensionality Reduction in High-Dimensional Space for Multimedia Information Retrieval

Abstract

This paper proposes a novel method for dimensionality reduction based on a function approximating the Euclidean distance, which makes use of the norm and angle components of a vector. First, we identify the causes of errors in angle estimation for approximating the Euclidean distance, and discuss basic solutions to reduce those errors. Then, we propose a new method for dimensionality reduction that composes a set of subvectors from a feature vector and maintains only the norm and the estimated angle for every subvector. The selection of a good reference vector is important for accurate estimation of the angle component. We present criteria for being a good reference vector, and propose a method that chooses a good reference vector by using the Levenberg-Marquardt algorithm. Also, we define a novel distance function, and formally prove that the distance function consistently lower-bounds the Euclidean distance. This implies that our approach does not incur any false dismissals in reducing the dimensionality. Finally, we verify the superiority of the proposed approach via performance evaluation with extensive experiments.