Extending High-Dimensional Indexing Techniques Pyramid and iMinMax(θ): Lessons Learned

Abstract

Pyramid Technique and iMinMax(θ) are two popular high-dimensional indexing approaches that map points in a high-dimensional space to a single-dimensional index. In this work, we perform the first independent experimental evaluation of Pyramid Technique and iMinMax(θ), and discuss in detail promising extensions for testing k-Nearest Neighbor (kNN) and range queries. For datasets with skewed distributions, the parameters of these algorithms must be tuned to maintain balanced partitions. We show that, by using the medians of the distribution we can optimize these parameters. For the Pyramid Technique, different approximate median methods on data space partitioning are experimentally compared using kNN queries. For the iMinMax(θ), the default parameter setting and parameters tuned using the distribution median are experimentally compared using range queries. Also, as proposed in the iMinMax(θ) paper, we investigated the benefit of maintaining a parameter to account for the skewness of each dimension separately instead of a single parameter over all the dimensions.