Processing Incomplete k Nearest Neighbor Search

Given a set S of multidimensional objects and a query object q, a k nearest neighbor (kNN) query finds from S the k closest objects to q. This query is a fundamental problem in database, data mining, and information retrieval research. It plays an important role in a wide spectrum of real applications such as image recognition and location-based services. However, due to the failure of data transmission devices, improper storage, and accidental loss, incomplete data exist widely in those applications, where some dimensional values of data items are missing. In this paper, we systematically study incomplete k nearest neighbor (IkNN) search, which aims at the kNNquery for incomplete data. We formalize this problem and propose an efficient lattice partition algorithm using our newly developed L alpha B index to support exact IkNN retrieval, with the help of two pruning heuristics, i.e., a value pruning and partial distance pruning. Furthermore, we propose an approximate algorithm, namely histogram approximate, to support approximate IkNN search with improved search efficiency and guaranteed error bound. Extensive experiments using both real and synthetic datasets demonstrate the effectiveness of newly designed indexes and pruning heuristics, as well as the performance of our presented algorithms under a variety of experimental settings.