Search

The $$k$$ k -d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be successful in practice. We analyze three such schemes. We show that the probability that they fail to find the nearest neighbor, for any data set and any query point, is directly related to a simple potential function that captures the difficulty of the point configuration. We then bound this potential function in several situations of interest: when the data are drawn from a doubling measure; when the data and query distributions are identical and are supported on a set of bounded doubling dimension; and when the data are documents from a topic model.

The nearest neighbor search algorithm is one of the major factors that influence the efficiency of grid interpolation. This paper introduces a KD-tree that is a two-dimensional index structure for use in grid interpolation. It also proposes an improved J-nearest neighbor search strategy based on “priority queue” and “neighbor lag” concepts. In the strategy, two types of J-nearest neighbor search algorithms can be used; these algorithms correspond to the consideration of a fixed number of points and a fixed radius. By using the KD-tree and proposed strategy, interpolation can be performed with methods such as Inverse Distance Weighting and Kriging. Experimental results show that the proposed algorithms has high operating efficiency, especially when the data amount is enormous, and high practical value for increasing the efficiency of grid interpolation.

To reduce the access latencies of end hosts, latency-sensitive applications need to choose suitably close service machines to answer the access requests from end hosts. Distributed K nearest neighbor search locates K service machines closest to end hosts, which can efficiently optimize the access latencies for end hosts. Existing work has weakness in terms of the accuracy and scalability. According to the scalable and accurate K nearest neighbor search problem, we propose a distributed K nearest neighbor search method called DKNNS in this paper. Service machines are organized into a locality-aware multilevel ring. DKNNS first locates a service machine that starts the search process based on a farthest neighbor search scheme, then discovers K nearest service machines based on a backtracking approach within the proximity region containing the target in the latency space. Theoretical analysis, simulation results and deployment experiments on the PlanetLab show that, DKNNS can determine K approximately optimal service machines, with modest completion time and query loads. Finally, DKNNS is also quite stable that can be used for reducing frequent searches by caching found nearest neighbors.

We introduce a GPU grid-based data structure for massively parallel nearest neighbor searches for dynamic point clouds. The implementation provides real-time performance and it is executed on GPU, both grid construction and nearest neighbors (approximate or exact) searches. This minimizes the memory transfer between device and system memories, improving overall performance. The proposed algorithm may be used across different applications with static and dynamic scenarios. Moreover, our data structure supports three-dimensional point clouds and given its dynamic nature, the user can change the data structure’s parameters at runtime. The same applies to the number of neighbors to be found. Performance comparisons were made against previous works, endorsing the benefits of our solution. Finally, we were able to develop a real-time Point-Based Rendering application for validation of the data structure. Its drawbacks and data distribution’s impact on performance were analysed and some directions for further investigation are given.

The paper proposes a novel symmetrical encoding-based index structure, which is called EDD-tree (for encoding-based dual distance tree), to support fast k-nearest neighbor (k-NN) search in high-dimensional spaces. In the EDD-tree, all data points are first grouped into clusters by a k-means clustering algorithm. Then the uniform ID number of each data point is obtained by a dual-distance-driven encoding scheme, in which each cluster sphere is partitioned twice according to the dual distances of start-and centroid-distance. Finally, the uniform ID number and the centroid-distance of each data point are combined to get a uniform index key, the latter is then indexed through a partition-based B+-tree. Thus, given a query point, its k-NN search in high-dimensional spaces can be transformed into search in a single dimensional space with the aid of the EDD-tree index. Extensive performance studies are conducted to evaluate the effectiveness and efficiency of our proposed scheme, and the results demonstrate that this method outperforms the state-of-the-art high-dimensional search techniques such as the X-tree, VA-file, iDistance and NB-tree, especially when the query radius is not very large.

The feature selection problem is an interesting and important topic which is relevant for a variety of database applications. This paper utilizes the Tabu Search metaheuristic algorithm to implement a feature subset selection procedure while the nearest neighbor classification method is used for the classification task. Tabu Search is a general metaheuristic procedure that is used in order to guide the search to obtain good solutions in complex solution spaces. Several metrics are used in the nearest neighbor classification method, such as the euclidean distance, the Standardized Euclidean distance, the Mahalanobis distance, the City block metric, the Cosine distance and the Correlation distance, in order to identify the most significant metric for the nearest neighbor classifier. The performance of the proposed algorithms is tested using various benchmark datasets from UCI Machine Learning Repository.

Nearest Neighbor search is an important and widely used technique in a number of important application domains. In many of these domains, the dimensionality of the data representation is often very high. Recent theoretical results have shown that the concept of proximity or nearest neighbors may not be very meaningful for the high dimensional case. Therefore, it is often a complex problem to find good quality nearest neighbors in such data sets. Furthermore, it is also difficult to judge the value and relevance of the returned results. In fact, it is hard for any fully automated system to satisfy a user about the quality of the nearest neighbors found unless he is directly involved in the process. This is especially the case for high dimensional data in which the meaningfulness of the nearest neighbors found is questionable. In this paper, we address the complex problem of high dimensional nearest neighbor search from the user perspective by designing a system which uses effective cooperation between the human and the computer. The system provides the user with visual representations of carefully chosen subspaces of the data in order to repeatedly elicit his preferences about the data patterns which are most closely related to the query point. These preferences are used in order to determine and quantify the meaningfulness of the nearest neighbors. Our system is not only able to find and quantify the meaningfulness of the nearest neighbors, but is also able to diagnose situations in which the nearest neighbors found are truly not meaningful.

In order to speedup retrieval in large collections of data, index structures partition the data into subsets so that query requests can be evaluated without examining the entire collection. As the complexity of modern data types grows, metric spaces have become a popular paradigm for similarity retrieval. We propose a new index structure, called D-Index, that combines a novel clustering technique and the pivot-based distance searching strategy to speed up execution of similarity range and nearest neighbor queries for large files with objects stored in disk memories. We have qualitatively analyzed D-Index and verified its properties on actual implementation. We have also compared D-Index with other index structures and demonstrated its superiority on several real-life data sets. Contrary to tree organizations, the D-Index structure is suitable for dynamic environments with a high rate of delete/insert operations.

In multimedia databases, k-nearest neighbor queries are popular and frequently contain non-spatial predicates. Among the available techniques for such queries, the incremental nearest neighbor algorithm proposed by Hjaltason and Samet is known as the most useful algorithm [16]. The reason is that if k′ > k neighbors are needed, it can provide the next neighbor for the upper operator without restarting the query from scratch. However, the R-tree in their algorithm has no facility capable of partially pruning tuple candidates that will turn out not to satisfy the remaining predicates, leading their algorithm to inefficiency. In this paper, we propose an RS-tree-based incremental nearest neighbor algorithm complementary to their algorithm. The RS-tree used in our algorithm is a hybrid of the R-tree and the S-tree, as its buddy tree, based on the hierarchical signature file. Experimental results show that our RS-tree enhances the performance of Hjaltason and Samet's algorithm.

Many data centers have archived a tremendous amount of data and begun to publish them on the Web. Due to limited resources and large amount of service requests, data centers usually do not directly support high-cost queries. On the other hand, users are often overwhelmed by the huge data volume and cannot afford to download the whole data sets and search them locally. To support high-dimensional nearest neighbor searches in this environment, the paper develops a multi-level approximation scheme. The coarsest-level approximations are stored locally and searched first. The result is then refined gradually via accesses to remote data centers. Data centers need only to deliver data items or their precomputed finer level approximations by their identifiers.The searching process is usually long in this environment, since it involves remote sites. This paper describes an online search process: the system periodically reports a data item and a positive integer M. The reported item is guaranteed to be one of the M nearest neighbors of the query one. The paper proposes two algorithms to minimize M in each period. Experiments show that one of them performs similarly as a theoretical a posteriori algorithm and significantly outperforms the online extensions of two state-of-the-art nearest neighbor search methods.

Let x denote a given nonempty string of length n = |x| . A proper substring u of x is a proper cover of x if and only if every position of x lies within an occurrence of u within x . This paper introduces an array γ = γ[1..n] called the cover array in which each element γ[i] , 1 ≤ i ≤ n , is the length of the longest proper cover of x[1..i] or zero if no such cover exists. In fact it turns out that γ describes all the covers of every prefix of x . Several interesting properties of γ are established, and a simple algorithm is presented that computes γ on-line in Θ(n) time using Θ(n) additional space. Thus the new algorithm computes for all prefixes of x information that previous cover algorithms could compute only for x itself, and does so with no increase in space or time complexity.

In this paper, we propose an efficient solution to the problem of nearest neighbor query processing in declustered spatial databases. Recently a branch-and-bound nearest neighbor finding (BB-NNF) algorithm has been designed to process nearest neighbor queries in R-trees. However, this algorithm is strictly serial (branch-and-bound oriented) and its performance degrades, during processing of a nearest neighbor query, if applied to a parallel environment, since it does not exploit any kind of parallelization. We develop an efficient query processing strategy for parallel nearest neighbor finding (P-NNF), assuming a shared nothing multi-processor architecture, where the processors communicate via a network. In our method, the relevant sites are activated simultaneously. In order to achieve this goal, statistical information is used. The efficiency measure is the response time of a given query. Experimental results, based on real-life and synthetic datasets, show that the proposed method outperforms the branch-and-bound method by factors.

This note presents a simplification and generalization of an algorithm for searchingk-dimensional trees for nearest neighbors reported by Friedmanet al [3]. If the distance between records is measured usingL2, the Euclidean norm, the data structure used by the algorithm to determine the bounds of the search space can be simplified to a single number. Moreover, because distance measurements inL2 are rotationally invariant, the algorithm can be generalized to allow a partition plane to have an arbitrary orientation, rather than insisting that it be perpendicular to a coordinate axis, as in the original algorithm. When ak-dimensional tree is built, this plane can be found from the principal eigenvector of the covariance matrix of the records to be partitioned. These techniques and others yield variants ofk-dimensional trees customized for specific applications. It is wrong to assume thatk-dimensional trees guarantee that a nearest-neighbor query completes in logarithmic expected time. For smallk, logarithmic behavior is observed on all but tiny trees. However, for largerk, logarithmic behavior is achievable only with extremely large numbers of records. Fork = 16, a search of ak-dimensional tree of 76,000 records examines almost every record.

One of the most important problems in classification is that of quantitative comparison of hierarchical trees. In this note we answer an open problem of Culik and Wood (1982) concerning the nearest neighbor interchange metric by proving that its underlying decision problem is NP-complete.