Center-Based Indexing in Vector and Metric Spaces

The paper addresses the problem of indexing data for k nearest neighbors (k-nn) search. Given a collection of data objects and a similarity measure the searching goal is to find quickly the k most similar objects to a given query object. We present a top-down indexing method that employs a widely used scheme of indexing algorithms. It starts with the whole set of objects at the root of an indexing tree and iteratively splits data at each level of indexing hierarchy. In the paper two different data models are considered. In the first, objects are represented by vectors from a multi-dimensional vector space. The second, more general, is based on an assumption that objects satisfy only the axioms of a metric space. We propose an iterative k-means algorithm for tree node splitting in case of a vector space and an iterative k-approximate-centers algorithm in case when only a metric space is provided. The experiments show that the iterative k-means splitting procedure accelerates significantly k-nn searching over the one-step procedure used in other indexing structures such as GNAT, SS-tree and M-tree and that the relevant representation of a tree node is an important issue for the performance of the search process. We also combine different search pruning criteria used in BST, GHT nad GNAT structures into one and show that such a combination outperforms significantly each single pruning criterion. The experiments are performed for benchmark data sets of the size up to several hundreds of thousands of objects. The indexing tree with the k-means splitting procedure and the combined search criteria is particularly effective for the largest tested data sets for which this tree accelerates searching up to several thousands times.