GMM-KNN: A method for processing continuous k-NN queries based on the Gaussian mixture model

Abstract

For a given set of moving objects and a k nearest neighbor query q, the processing of Continuous K Nearest Neighbor (CKNN) query refers to search the k nearest objects for q and continuously monitor its result in real-time when the objects and the queries are constantly moving. Most existing works about processing CKNN queries usually exist some flaws about the index maintenance, updates of results, and the query cost, which makes them hardly can perfectly settle this issue. To address these challenges, we propose GMM-KNN, an incremental search algorithm based on a Gaussian Mixture Model to handle CKNN queries over a tremendous volume of moving objects. In particularly, our approach adopts the grid index to maintain the moving objects in real-time, and introduces a Gaussian Mixture Model to simulate the distribution of moving objects in this grid index. For a given query q, we first employs YPK-CNN algorithm to compute the initial result of q. Once the query point occurs a movement, we no longer recompute its k nearest neighbors with YPK-CNN algorithm, but endeavor to rapidly estimate an appropriate search region that guarantees covering k nearest neighbors of q based on its previous search scope. In this step, the Gaussian Mixture Model plays a significant role in computing the appropriate search space for the moving query because it can help us avoid iteratively enlarging the search region, which can greatly enhance the search efficiency. Finally, we conduct extensive experiments to fully evaluate the performance of our proposal.