Efficient k-nearest neighbor searching in nonordered discrete data spaces

Abstract

Numerous techniques have been proposed in the past for supporting efficient k -nearest neighbor ( k -NN) queries in continuous data spaces. Limited work has been reported in the literature for k -NN queries in a nonordered discrete data space (NDDS). Performing k -NN queries in an NDDS raises new challenges. The Hamming distance is usually used to measure the distance between two vectors (objects) in an NDDS. Due to the coarse granularity of the Hamming distance, a k -NN query in an NDDS may lead to a high degree of nondeterminism for the query result. We propose a new distance measure, called Granularity-Enhanced Hamming (GEH) distance, which effectively reduces the number of candidate solutions for a query. We have also implemented k -NN queries using multidimensional database indexing in NDDSs. Further, we use the properties of our multidimensional NDDS index to derive the probability of encountering valid neighbors within specific regions of the index. This probability is used to develop a new search ordering heuristic. Our experiments on synthetic and genomic data sets demonstrate that our index-based k -NN algorithm is efficient in finding k -NNs in both uniform and nonuniform data sets in NDDSs and that our heuristics are effective in improving the performance of such queries.