On k-Nearest Neighbor Searching in Non-Ordered Discrete Data Spaces ∗

A k-nearest neighbor (k-NN) query retrieves k objects from a database that are considered to be the closest to a given query point. Numerous techniques have been proposed in the past for supporting efficient k-NN searches in continuous data spaces. No such work has been reported in the literature for k-NN searches in a non-ordered discrete data space (NDDS). Performing k-NN searches 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 large set of candidate solutions, creating a high degree of nondeterminism for the query result. We propose a new distance measure, called Granularity-Enhanced Hamming (GEH) distance, that effectively reduces the number of candidate solutions for a query. We have also considered using multidimensional database indexing for implementing k-NN searches in NDDSs. Our experiments on synthetic and genomic data sets demonstrate that our index-based k-NN algorithm is effective and efficient in finding k-NNs in NDDSs.

Efficient k-Nearest Neighbor Searching in Non-Ordered Discrete Data Spaces

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 non-ordered 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 non-determinism for the query result. We propose a new distance measure, called Granularity-Enhanced Hamming (GEH) distance, that 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 new 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 non-uniform data sets in NDDSs and that our heuristics are effective in improving the performance of such queries