Dimensionality reduction using magnitude and shape approximations

• Authors: Ümit Y. Ogras;Hakan Ferhatosmanoglu
• Venue: CIKM '03 Proceedings of the twelfth international conference on Information and knowledge management
• Year: 2003

High dimensional data sets are encountered in many modern database applications. The usual approach is to construct a summary of the data set through a lossy compression technique, and use this lower dimensional synopsis to provide fast, approximate answers to the queries. In this paper, we develop a novel dimensionality reduction technique based on partitioning the high dimensional vector space into orthogonal subspaces. First, we find a relation between the Euclidian distance of two n-dimensional vectors and the Euclidian distances of their projections on the orthogonal subspaces. Then, based on this relation we develop a method to approximate the Euclidian distance using novel inner product approximation. This process allows us to incorporate the shape information of the vectors to this approximation. While the inner product approximation is symmetric, i.e., captures only the magnitude information of the data, the proposed method takes both the magnitude and shape information of the original vectors into account through partitioning. In the experiments, we demonstrate the effectiveness of our technique by comparing it with commonly used methods.