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An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 776 (31 self)
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Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any positive real ffl, a data point p is a (1 + ffl)approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a query point q 2 R d , and ffl ? 0, a (1 + ffl)approximate nearest neighbor of q can be computed in O(c d;ffl log n) time, where c d;ffl d d1 + 6d=ffle d is a factor depending only on dimension and ffl. In general, we show that given an integer k 1, (1 + ffl)approximations to the k nearest neighbors of q can be computed in additional O(kd log n) time.
NeTra: A toolbox for navigating large image databases
 Multimedia Systems
, 1999
"... . We present here an implementation of NeTra, a prototype image retrieval system that uses color, texture, shape and spatial location information in segmented image regions to search and retrieve similar regions from the database. A distinguishing aspect of this system is its incorporation of a robu ..."
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Cited by 314 (16 self)
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. We present here an implementation of NeTra, a prototype image retrieval system that uses color, texture, shape and spatial location information in segmented image regions to search and retrieve similar regions from the database. A distinguishing aspect of this system is its incorporation of a robust automated image segmentation algorithm that allows object or regionbased search. Image segmentation significantly improves the quality of image retrieval when images contain multiple complex objects. Images are segmented into homogeneous regions at the time of ingest into the database, and image attributes that represent each of these regions are computed. In addition to image segmentation, other important components of the system include an efficient color representation, and indexing of color, texture, and shape features for fast search and retrieval. This representation allows the user to compose interesting queries such as "retrieve all images that contain regions that have the colo...
Blobworld: A System for RegionBased Image Indexing and Retrieval
 In Third International Conference on Visual Information Systems
, 1999
"... . Blobworld is a system for image retrieval based on finding coherent image regions which roughly correspond to objects. Each image is automatically segmented into regions ("blobs") with associated color and texture descriptors. Querying is based on the attributes of one or two regions of interest, ..."
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Cited by 305 (4 self)
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. Blobworld is a system for image retrieval based on finding coherent image regions which roughly correspond to objects. Each image is automatically segmented into regions ("blobs") with associated color and texture descriptors. Querying is based on the attributes of one or two regions of interest, rather than a description of the entire image. In order to make largescale retrieval feasible, we index the blob descriptions using a tree. Because indexing in the highdimensional feature space is computationally prohibitive, we use a lowerrank approximation to the highdimensional distance. Experiments show encouraging results for both querying and indexing. 1 Introduction From a user's point of view, the performance of an information retrieval system can be measured by the quality and speed with which it answers the user's information need. Several factors contribute to overall performance:  the time required to run each individual query,  the quality (precision/recall) of each i...
Distance Browsing in Spatial Databases
, 1999
"... Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is kn ..."
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Cited by 291 (19 self)
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Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the knearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the Rtree and its performance is compared to an existing knearest neighbor algorithm for Rtrees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the knearest neighbor algorithm for distance browsing queries in a spatial database that uses the Rtree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the knearest neighbor algorithm when applied to the knearest neighbor problem for the Rtree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...
When Is "Nearest Neighbor" Meaningful?
 In Int. Conf. on Database Theory
, 1999
"... . We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the fa ..."
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Cited by 291 (1 self)
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. We explore the effect of dimensionality on the "nearest neighbor " problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 1015 dimensions. These results should not be interpreted to mean that highdimensional indexing is never meaningful; we illustrate this point by identifying some highdimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate highdimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple...
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 245 (21 self)
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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...
Optimal MultiStep kNearest Neighbor Search
, 1998
"... For an increasing number of modern database applications, efficient support of similarity search becomes an important task. Along with the complexity of the objects such as images, molecules and mechanical parts, also the complexity of the similarity models increases more and more. Whereas algorithm ..."
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Cited by 166 (19 self)
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For an increasing number of modern database applications, efficient support of similarity search becomes an important task. Along with the complexity of the objects such as images, molecules and mechanical parts, also the complexity of the similarity models increases more and more. Whereas algorithms that are directly based on indexes work well for simple mediumdimensional similarity distance functions, they do not meet the efficiency requirements of complex highdimensional and adaptable distance functions. The use of a multistep query processing strategy is recommended in these cases, and our investigations substantiate that the number of candidates which are produced in the filter step and exactly evaluated in the refinement step is a fundamental efficiency parameter. After revealing the strong performance shortcomings of the stateoftheart algorithm for knearest neighbor search [Korn et al. 1996], we present a novel multistep algorithm which is guaranteed to produce the minim...
Indexdriven similarity search in metric spaces
 ACM Transactions on Database Systems
, 2003
"... Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some similarity measure. In this article, we focus on methods for similarity search th ..."
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Cited by 132 (6 self)
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Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query object q, based on some similarity measure. In this article, we focus on methods for similarity search that make the general assumption that similarity is represented with a distance metric d. Existing methods for handling similarity search in this setting typically fall into one of two classes. The first directly indexes the objects based on distances (distancebased indexing), while the second is based on mapping to a vector space (mappingbased approach). The main part of this article is dedicated to a survey of distancebased indexing methods, but we also briefly outline how search occurs in mappingbased methods. We also present a general framework for performing search based on distances, and present algorithms for common types of queries that operate on an arbitrary “search hierarchy. ” These algorithms can be applied on each of the methods presented, provided a suitable search hierarchy is defined.
Efficient Similarity Search and Classification Via Rank Aggregation
 In Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data
, 2003
"... We propose a novel approach to performing efficient similarity search and classification in high dimensional data. In this framework, the database elements are vectors in a Euclidean space. Given a query vector in the same space, the goal is to find elements of the database that are similar to the ..."
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Cited by 122 (5 self)
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We propose a novel approach to performing efficient similarity search and classification in high dimensional data. In this framework, the database elements are vectors in a Euclidean space. Given a query vector in the same space, the goal is to find elements of the database that are similar to the query. In our approach, a small number of independent "voters" rank the database elements based on similarity to the query. These rankings are then combined by a highly efficient aggregation algorithm. Our methodology leads both to techniques for computing approximate nearest neighbors and to a conceptually rich alternative to nearest neighbors.