High dimensional reverse nearest neighbor queries

The VLDB Journal, 2007

Given a multi-dimensional point q, a reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k nearest neighbors. Existing methods for processing such queries have at least one of the following deficiencies: they (i) do not support arbitrary values of k, (ii) cannot deal efficiently with database updates, (iii) are applicable only to 2D data but not to higher dimensionality, and (iv) retrieve only approximate results. Motivated by these shortcomings, we develop algorithms for exact RkNN processing with arbitrary values of k on dynamic, multi-dimensional datasets. Our methods utilize a conventional data-partitioning index on the dataset and do not require any pre-computation. As a second step, we extend the proposed techniques to continuous RkNN search, which returns the RkNN results for every point on a line segment. We evaluate the effectiveness of our algorithms with extensive experiments using both real and synthetic datasets.

Proceedings 2004 VLDB Conference, 2004

Given a point q, a reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k nearest neighbors. Existing methods for processing such queries have at least one of the following deficiencies: (i) they do not support arbitrary values of k (ii) they cannot deal efficiently with database updates, (iii) they are applicable only to 2D data (but not to higher dimensionality), and (iv) they retrieve only approximate results. Motivated by these shortcomings, we develop algorithms for exact processing of RkNN with arbitrary values of k on dynamic multidimensional datasets. Our methods utilize a conventional data-partitioning index on the dataset and do not require any pre-computation. In addition to their flexibility, we experimentally verify that the proposed algorithms outperform the existing ones even in their restricted focus.

2009 Second International Workshop on Similarity Search and Applications, 2009

Retrieving the k-nearest neighbors of a query object is a basic primitive in similarity searching. A related, far less explored primitive is to obtain the dataset elements which would have the query object within their own k-nearest neighbors, known as the reverse k-nearest neighbor query. We already have indices and algorithms to solve k-nearest neighbors queries in general metric spaces; yet, in many cases of practical interest they degenerate to sequential scanning. The naive algorithm for reverse k-nearest neighbor queries has quadratic complexity, because the k-nearest neighbors of all the dataset objects must be found; this is too expensive. Hence, when solving these primitives we can tolerate trading correctness in the solution for searching time. In this paper we propose an efficient approximate approach to solve these similarity queries with high retrieval rate. Then, we show how to use our approximate k-nearest neighbor queries to construct (an approximation of) the k-nearest neighbor graph when we have a fixed dataset. Finally, combining both primitives we show how to dynamically maintain the approximate k-nearest neighbor graph of the objects currently stored within the metric dataset, that is, considering both object insertions and deletions.

2011

Given a set of objects and a query q, a point p is called the reverse k nearest neighbor (RkNN) of q if q is one of the k closest objects of p. In this paper, we introduce the concept of influence zone which is the area such that every point inside this area is the RkNN of q and every point outside this area is not the RkNN. The influence zone has several applications in location based services, marketing and decision support systems. It can also be used to efficiently process RkNN queries. First, we present efficient algorithm to compute the influence zone. Then, based on the influence zone, we present efficient algorithms to process RkNN queries that significantly outperform existing best known techniques for both the snapshot and continuous RkNN queries. We also present a detailed theoretical analysis to analyse the area of the influence zone and IO costs of our RkNN processing algorithms. Our experiments demonstrate the accuracy of our theoretical analysis.

Proceedings of the 35th SIGMOD international conference on Management of data - SIGMOD '09, 2009

Nearest neighbor (NN) search in high dimensional space is an important problem in many applications. Ideally, a practical solution (i) should be implementable in a relational database, and (ii) its query cost should grow sub-linearly with the dataset size, regardless of the data and query distributions. Despite the bulk of NN literature, no solution fulfills both requirements, except locality sensitive hashing (LSH). The existing LSH implementations are either rigorous or adhoc. Rigorous-LSH ensures good quality of query results, but requires expensive space and query cost. Although adhoc-LSH is more efficient, it abandons quality control, i.e., the neighbor it outputs can be arbitrarily bad. As a result, currently no method is able to ensure both quality and efficiency simultaneously in practice.

The VLDB Journal, 2012

Given a set of objects and a query , a point is called the reverse nearest neighbor (R NN) of if is one of the closest objects of. In this paper, we introduce the concept of influence zone which is the area such that every point inside this area is the R NN of and every point outside this area is not the R NN. The influence zone has several applications in location based services, marketing and decision support systems. It can also be used to efficiently process R NN queries. First, we present efficient algorithm to compute the influence zone. Then, based on the influence zone, we present efficient algorithms to process R NN queries that significantly outperform existing best known techniques for both the snapshot and continuous R NN queries. We also present a detailed theoretical analysis to analyse the area of the influence zone and IO costs of our R NN processing algorithms. Our experiments demonstrate the accuracy of our theoretical analysis. This paper is an extended version of our previous work [9]. We make the following new contributions in this extended version: 1) we conduct a rigorous complexity analysis and show that the complexity of one of our proposed algorithms in [9] can be reduced from (2) to () where > is the number of objects used to compute the influence zone ; 2) we show that our techniques can

SIAM Journal on Computing, 2013

We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved efficiently despite the high dimensionality of the data.

2010

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.

Reverse nearest neighbor (RNN) queries are useful in identifying objects that are of significant influence or importance. Existing methods reply on pre-computation of nearest neighbor distances, do not scale well with high dimensionality, or do not produce exact solutions. In this work we motivate and investigate the problem of reverse nearest neighbor search on high dimensional, multimedia data. We propose several heuristic algorithms to approximate the optimal solution and reduce the computation complexity. We propose exact and approximate algorithms that do not require precomputation of nearest neighbor distances, and can potentially prune off most of the search space. We demonstrate the utility of reverse nearest neighbor search by showing how it can help improve the classification accuracy.

1998

Similarity search in multimedia databases requires an efficient support of nearest-neighbor search on a large set of high-dimensional points as a basic operation for query processing. As recent theoretical results show, state of the art approaches to nearest-neighbor search are not efficient in higher dimensions. In our new approach, we therefore precompute the result of any nearest-neighbor search which corresponds to a computation of the voronoi cell of each data point. In a second step, we store the voronoi cells in an index structure efficient for high-dimensional data spaces. As a result, nearest neighbor search corresponds to a simple point query on the index structure. Although our technique is based on a precomputation of the solution space, it is dynamic, i.e. it supports insertions of new data points. An extensive experimental evaluation of our technique demonstrates the high efficiency for uniformly distributed as well as real data. We obtained a significant reduction of the search time compared to nearest neighbor search in the X-tree (up to a factor of 4).