使用R树进行k-NN搜索

在地理信息系统中经常要做k-NN搜索，进行这些查询用到的算法与位置和范围查询的算法不同，需要专门进行研究，介绍了一种分支界限遍历R树算法，并将该算法概括为k-NN算法。文中讨论了两种方法。对R树进行结点内MBR的排序以及剪枝过程，以减少搜索空间中需访问结点的数量，有效地进行k-NN搜索。     

不确定数据上范围受限的最近邻查询算法

不确定数据的查询处理是数据库领域近年来的热点研究课题.提出一种不确定数据上的范围受限的最近邻查询.给定不确定数据集D={o1,o2,…,on},范围约束R是一个简单多边形,q为一固定的查询点,范围受限的最近邻查询返回的是在数据集D中,既满足范围约束R,又能成为查询点q的最近邻的对象集合.为处理该查询,提出了范围受限的最近邻核心集的概念和范围受限的最近邻核心集的查找算法.并提出一种计算范围受限的最近邻候选集的优化方法,降低了查询代价.最后通过实验验证了该算法的有效性.     

面向存在不确定对象的组最近邻查询方法

组最近邻查询是空间对象查询领域的一类重要查询,通过该查询可找到距离给定查询点集最近的空间对象.由于图像分辨率或解析度的限制等因素,空间对象的存在不确定性广泛存在于某些涉及图像处理的查询应用中.这些对象位置数据的存在不确定性会对组最近邻查询结果产生影响.本文给出面向存在不确定对象的概率阈值组最近邻查询定义,设计了高效的查询处理机制,通过剪枝优化等手段提高概率阈值组最近邻查询效率,并进一步提出了高效概率阈值组最近邻查询算法.采用多个真实数据集对概率阈值组最近邻算法进行了实验验证,结果表明所提算法具有良好的查询效率.     

Efficient processing of probabilistic reverse nearest neighbor queries over uncertain data

Reverse nearest neighbor (RNN) search is very crucial in many real applications. In particular, given a database and a query object, an RNN query retrieves all the data objects in the database that have the query object as their nearest neighbors. Often, due to limitation of measurement devices, environmental disturbance, or characteristics of applications (for example, monitoring moving objects), data obtained from the real world are uncertain (imprecise). Therefore, previous approaches proposed for answering an RNN query over exact (precise) database cannot be directly applied to the uncertain scenario. In this paper, we re-define the RNN query in the context of uncertain databases, namely probabilistic reverse nearest neighbor (PRNN) query, which obtains data objects with probabilities of being RNNs greater than or equal to a user-specified threshold. Since the retrieval of a PRNN query requires accessing all the objects in the database, which is quite costly, we also propose an effective pruning method, called geometric pruning (GP), that significantly reduces the PRNN search space yet without introducing any false dismissals. Furthermore, we present an efficient PRNN query procedure that seamlessly integrates our pruning method. Extensive experiments have demonstrated the efficiency and effectiveness of our proposed GP-based PRNN query processing approach, under various experimental settings.     

时空数据库中多个最近邻对象的查询算法

在时空数据库中，最近邻查询用于对某个查询对象，在被查询对象中找出离它最近的一个或多个对象。该文在TPR树这一时空索引的基础上，提出了一种高效的最近邻查询算法，能够支持移动对象的多个最近邻对象的查询，并在性能上也有所提高。     

面向移动对象的高效组最近邻居查询方法

组最近邻居查询是移动对象数据库重要的查询类型之一。本文提出了一种基于网格索引结构的剪枝搜索策略,将空间区域划分为网格,通过对象点的网格单元标识减少组最近邻居查询所需要的节点访问代价。用步长迭代法得到查询对象集的质心,提出了一种移动对象组最近邻居查询MOGNN算法,采用更精确的裁剪搜索空间准则,减少了查询所需要访问的节点数目。实验结果与分析表明,基于网格索引的MOGNN查询算法具有良好的查询性能。     

移动对象的动态反向k最近邻研究

反向最近邻查询是空间数据库中最重要的算法之一。传统的反向最近邻查询方法主要是针对静态对象的查询,随着无线通讯和定位技术的快速发展,移动对象发出的查询请求成为新的研究热点。该文将TPR-tree作为算法的索引结构,并提出了基于矩形框的对角线的修剪策略,将半平面修剪策略进行改进,给出了移动对象的动态反向k最近邻的查询方案。     

Range nearest-neighbor query

A range nearest-neighbor (RNN) query retrieves the nearest neighbor (NN) for every point in a range. It is a natural generalization of point and continuous nearest-neighbor queries and has many applications. In this paper, we consider the ranges as (hyper)rectangles and propose efficient in-memory processing and secondary memory pruning techniques for RNN queries in both 2D and high-dimensional spaces. These techniques are generalized for kRNN queries, which return the k nearest neighbors for every point in the range. In addition, we devise an auxiliary solution-based index EXO-tree to speed up any type of NN query. EXO-tree is orthogonal to any existing NN processing algorithm and, thus, can be transparently integrated. An extensive empirical study was conducted to evaluate the CPU and I/O performance of these techniques, and the study showed that they are efficient and robust under various data sets, query ranges, numbers of nearest neighbors, dimensions, and cache sizes.     

路网中双色数据集上连续反向k近邻查询处理的研究

近年来,反向最近邻查询(RNN)算法研究得到了普遍的关注,成为了数据库领域的一个研究热点。欧氏空 间中提出了较多的高效算法,而路网中的反向最近邻处理方面所做的工作不够,有关这方面的成果较少。路网中查询 点和数据对象之间以及不同数据对象之间的距离受到路网连通性的影响,欧氏空间中的反向最近部方法在路网中不 适用。反向最近部查询有两种类型:单色反向最近部查询(Monochromatic RNN, MRNN)和双色反向最近部查询(13i- chromatic RNN,13RNN)。到目前为止,仍然没有有效的算法来处理路网中双色数据集上的连续反向k近部查询。因 此,研究路网中双色数据集上连续反向k近部查询是很有意义的。     

Distributed Processing of Similarity Queries

Many modern applications in diverse fields demand the efficient manipulation of very large multidimensional datasets. It is evident, that efficient and effective query processing techniques need to be developed, in order to provide acceptable response times in query processing. In this paper, we study the processing of similarity nearest neighbor queries in large distributed multidimensional databases, where objects are represented as vectors in a vector space, and are distributed in a multi-computer environment. The departure from the centralized case embodies a number of advantages and (unfortunately) a number of difficulties that need to be successfully overcome. In this perspective, four query evaluation strategies are presented, namely Concurrent Processing (CP), Selective Processing (SP), Two-Phase Processing (2PP) and Probabilistic Processing (PRP). The proposed techniques are compared analytically and experimentally, in order to discover the advantages of each one, as well as the best cases where each one should be applied. Experimental results are presented, demonstrating the performance of each method under different parameters values. Also, we investigate the impact of derived data that should be maintained in order to process similarity queries efficiently.     

K-nearest neighbor finding using MaxNearestDist

Similarity searching often reduces to finding the k nearest neighbors to a query object. Finding the k nearest neighbors is achieved by applying either a depth- first or a best-first algorithm to the search hierarchy containing the data. These algorithms are generally applicable to any index based on hierarchical clustering. The idea is that the data is partitioned into clusters which are aggregated to form other clusters, with the total aggregation being represented as a tree. These algorithms have traditionally used a lower bound corresponding to the minimum distance at which a nearest neighbor can be found (termed MinDist) to prune the search process by avoiding the processing of some of the clusters as well as individual objects when they can be shown to be farther from the query object q than all of the current k nearest neighbors of q. An alternative pruning technique that uses an upper bound corresponding to the maximum possible distance at which a nearest neighbor is guaranteed to be found (termed MaxNearestDist) is described. The MaxNearestDist upper bound is adapted to enable its use for finding the k nearest neighbors instead of just the nearest neighbor (i.e., k=1) as in its previous uses. Both the depth-first and best-first k-nearest neighbor algorithms are modified to use MaxNearestDist, which is shown to enhance both algorithms by overcoming their shortcomings. In particular, for the depth-first algorithm, the number of clusters in the search hierarchy that must be examined is not increased thereby potentially lowering its execution time, while for the best-first algorithm, the number of clusters in the search hierarchy that must be retained in the priority queue used to control the ordering of processing of the clusters is also not increased, thereby potentially lowering its storage requirements.     

基于平面线段的反向最近邻查询

反向最近邻查询是空间数据库空间查询的研究热点。目前反向最近邻查询的查询粒度都是基于一维的点．在一些空间物体不能抽象为点的情况下将其抽象为点进行反向最近邻查询,查询结果不能达到一定的精度。该文在分析基于平面线段的最近邻查询和R树结构的基础上提出了一种改进的R树－Rcd树,并给出了基于Rcd树的平面线段反向最近邻查询算法．该方法能实现平面线段的反向最近邻查询。     

空间对象的反最近邻查询处理技术研究

空间数据库中反最近邻查询的研究是空间查询的研究热点。在对现有的反最近邻查询技术进行分析比较的基础上,针对提高动态数据集的查询效率问题,给出了基于R树索引结构的反最近邻查询方案。通过实验结果的分析比较,可以看出该方案能够有效地解决动态数据集的查询问题。     

空间数据库中的线段k近邻查询研究

K近邻查询是空间数据库中的重要查询之一,k近邻查询在内容的相似性检索、模式识别、地理信息系统中有重要应用。针对现有k近邻查询都是基于点查询的情况,提出基于平面线段的k近邻查询,查找线段集中给定查询点的k个最近线段。给出基于Voronoi图的线段k近邻查询算法及给出相关定理和证明。该算法通过线段Voronoi图的邻接特性找到一个候选集,然后从中找到最终结果。通过随机数据的实验证明,所提算法明显优于线性扫描算法和基于R树的k近邻查询算法。     

路网上的单色和双色反k最远邻查询

传统的路网上的反最远邻查询是直接找出查询点的反最远邻,这种方法不但效率不高,而且需要大量内存资源进行预计算。为了更有效地解决基于路网的单色和双色反k最远邻查询问题,提高反k最远邻查询的效率,提出了从反最近邻的角度来分析反最远邻查询问题,把反最远邻查询转化为反最近邻问题。根据这一理论,提出了一种有效的基于路网的单色和双色的反k最远邻查询算法。通过实验与实验分析表明,该方法具有良好的实用价值。     

距离-关键字相似度约束的双色反k近邻查询方法

针对空间关键字双色反k近邻查询返回结果质量较低的问题,提出了基于距离-关键字相似度约束的双色反k近邻查询方法。首先,通过设置一个阈值将查询结果中质量较低的用户给过滤掉,从而避免了查询结果中出现空间距离相对较远的用户,保证了查询结果质量;然后,为支持该查询,提出了一种关键字多分辨率网格矩形树（KMG-Tree）索引来管理数据;最后,提出了基于Six-region算法的Six-region-optimize算法来提高查询处理效率。Six-region-optimize算法的查询效率相较baseline和Six-region算法分别平均提高了约85.71%和23.45%。基于真实时空数据进行实验测试和分析,实验结果验证了Six-region-optimize算法的有效性和高效性。     

Fast and versatile algorithm for nearest neighbor search based on a lower bound tree

In this paper, we present a fast and versatile algorithm which can rapidly perform a variety of nearest neighbor searches. Efficiency improvement is achieved by utilizing the distance lower bound to avoid the calculation of the distance itself if the lower bound is already larger than the global minimum distance. At the preprocessing stage, the proposed algorithm constructs a lower bound tree (LB-tree) by agglomeratively clustering all the sample points to be searched. Given a query point, the lower bound of its distance to each sample point can be calculated by using the internal node of the LB-tree. To reduce the amount of lower bounds actually calculated, the winner-update search strategy is used for traversing the tree. For further efficiency improvement, data transformation can be applied to the sample and the query points. In addition to finding the nearest neighbor, the proposed algorithm can also (i) provide the k-nearest neighbors progressively; (ii) find the nearest neighbors within a specified distance threshold; and (iii) identify neighbors whose distances to the query are sufficiently close to the minimum distance of the nearest neighbor. Our experiments have shown that the proposed algorithm can save substantial computation, particularly when the distance of the query point to its nearest neighbor is relatively small compared with its distance to most other samples (which is the case for many object recognition problems).     

空间数据库引擎的R树索引

介绍了空间数据库引擎(SDBE)的R树索引结构，给出系统使用R树索引的方式，并描述了利用R树索引实现最近邻居查询的分支—限界算法，包括代价函数及其上、下界函数的定义，以及算法的伪码形式。     

Visible Reverse k-Nearest Neighbor Query Processing in Spatial Databases

Reverse nearest neighbor (RNN) queries have a broad application base such as decision support, profile-based marketing, resource allocation, etc. Previous work on RNN search does not take obstacles into consideration. In the real world, however, there are many physical obstacles (e.g., buildings) and their presence may affect the visibility between objects. In this paper, we introduce a novel variant of RNN queries, namely, visible reverse nearest neighbor (VRNN) search, which considers the impact of obstacles on the visibility of objects. Given a data set P, an obstacle set O, and a query point q in a 2D space, a VRNN query retrieves the points in P that have q as their visible nearest neighbor. We propose an efficient algorithm for VRNN query processing, assuming that P and O are indexed by R-trees. Our techniques do not require any preprocessing and employ half-plane property and visibility check to prune the search space. In addition, we extend our solution to several variations of VRNN queries, including: 1) visible reverse k-nearest neighbor (VRkNN) search, which finds the points in P that have q as one of their k visible nearest neighbors; 2) delta-VRkNN search, which handles VRkNN retrieval with the maximum visible distance delta constraint; and 3) constrained VRkNN (CVRkNN) search, which tackles the VRkNN query with region constraint. Extensive experiments on both real and synthetic data sets have been conducted to demonstrate the efficiency and effectiveness of our proposed algorithms under various experimental settings.     

Top-n query processing in spatial databases considering bi-chromatic reverse k-nearest neighbors

A reverse k-nearest neighbor (RkNN) query retrieves the data points which regard the query point as one of their respective k nearest neighbors. A bi-chromatic reverse k-nearest neighbor (BRkNN) query is a variant of the RkNN query, considering two types of data. Given two types of data G and C, a BRkNN query regarding a data point q in G retrieves the data points from C that regard q as one of their respective k-nearest neighbors among the data points in G. Many existing approaches answer either the RkNN query or the BRkNN query. Different from these approaches, in this paper, we make the first attempt to propose a top-n query based on the concept of BRkNN queries, which ranks the data points in G and retrieves the top-n points according to the cardinalities of the corresponding BRkNN answer sets. For efficiently answering this top-n query, we construct the Voronoi Diagram of G to index the data points in G and C. From the information associated with the Voronoi Diagram of G, the upper bound of the cardinality of the BRkNN answer sets for each data point in G can be quickly computed. Moreover, based on an existing approach to answering the RkNN query and the characteristics of the Voronoi Diagram of G, we propose a method to find the candidate region regarding a BRkNN query, which tightens the corresponding search space. Finally, based on the triangle inequality, we propose an efficient refinement algorithm for finding the exact BRkNN answers from the candidate regions. To evaluate our approach on answering the top-n query, it is compared with an approach which applies a state-of-the-art algorithm for answering the BRkNN query to each data point in G. The experiment results reveal that our approach has a much better performance.