Characterizing the optimal pivots for efficient similarity searches in vector space databases with Minkowski distances

Pivot-based retrieval algorithms are commonly used to solve similarity queries in a number of application domains, such as multimedia retrieval, biomedical databases, time series and computer vision. The query performances of pivot-based index algorithms can be significantly improved by properly choosing the set of pivots that is able to narrow down the database elements to only those relevant to a query. While many other approaches in the literature rely on empirical studies or intuitive observations and assumptions to achieve effective pivot strategies, this paper addresses the problem by using a formal mathematical approach. We conclude in our study that the optimal set of pivots in vector databases with Lp metrics is a set of uniformly distributed points on the surface of an n-sphere defined by these metrics. To make the study mathematically tractable, a uniform distribution of data in the database is assumed, allowing us to outline the problem from a purely geometrical point of view. Then, we present experimental results demonstrating the usefulness of our characterization when applied to real databases in the (Rn,Lp) metric space. Our technique is shown to outperform comparable techniques in the literature. However, we do not propose a new pivot-selection technique but rather experiments that are designed exclusively to show the usefulness of such a characterization.