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Finding kdominant skylines in high dimensional space
 SIGMOD
"... Given a ddimensional data set, a point p dominates another point q if it is better than or equal to q in all dimensions and better than q in at least one dimension. A point is a skyline point if there does not exists any point that can dominate it. Skyline queries, which return skyline points, are ..."
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Cited by 73 (9 self)
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points in high dimensional space, we propose a new concept, called kdominant skyline which relaxes the idea of dominance to kdominance. A point p is said to kdominate another point q if there are k ( ≤ d) dimensions in which p is better than or equal to q and is better in at least one of these k
UNCERTAINTY QUANTIFICATION IN HIGHDIMENSIONAL SPACES
"... Abstract. Polynomial chaos expansions have proven powerful for emulating responses of computational models with random input in a wide range of applications. However, they suffer from the curse of dimensionality, meaning the exponential growth of the number of unknown coefficients with the input d ..."
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dimension. By exploiting the tensor product form of the polynomial basis, lowrank approximations drastically reduce the number of unknown coefficients, thus providing a promising tool for effectively dealing with highdimensional problems. In this paper, first, we investigate the construction of low
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
, 1998
"... We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a spaceefficient data structure that would allow us to ..."
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Cited by 220 (9 self)
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We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a spaceefficient data structure that would allow us
Exponential grids in highdimensional space
, 2011
"... We consider the approximation of functions that are localized in space. We show that it is possible to define meshes to approximate such functions with the property that the number of vertices grows only linearly in dimension. In one dimension, we discuss the optimal mesh for approximating exponenti ..."
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We consider the approximation of functions that are localized in space. We show that it is possible to define meshes to approximate such functions with the property that the number of vertices grows only linearly in dimension. In one dimension, we discuss the optimal mesh for approximating
Indexing Regional Objects in HighDimensional Spaces
 CHAPTER XVIII IN "ADVANCED TOPICS IN DATABASE RESEARCH"
, 2006
"... Many spatial access methods, such as the Rtree, have been designed to support spatial search operators (e.g., overlap, containment, and enclosure) over both points and regional objects in multidimensional spaces. Unfortunately, contemporary spatial access methods are limited by many problems that ..."
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that significantly degrade the query performance in highdimensional spaces. This chapter reviews the problems of contemporary spatial access methods in spaces with many dimensions and presents an efficient approach to building advanced spatial access methods that effectively attack these problems. It also discusses
Is Nonparametric Learning Practical in Very High Dimensional Spaces?
 In Proc. 15th Intern. Joint Conf. on AI (IJCAI97
, 1997
"... Many of the challenges faced by the field of Computational Intelligence in building intelligent agents, involve determining mappings between numerous and varied sensor inputs and complex and flexible action sequences. In applying nonparametric learning techniques to such problems we must therefore a ..."
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Cited by 7 (6 self)
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ask: "Is nonparametric learning practical in very high dimensional spaces?" Contemporary wisdom states that variable selection and a "greedy" choice of appropriate functional structures are essential ingredients for nonparametric learning algorithms. However, neither
Robust multiobjective optimization in high dimensional spaces
 Lecture Notes in Computer Science 4403: Evolutionary MultiCriterion Optimization  EMO 2007
, 2007
"... Abstract. 1 In most real world optimization problems several optimization goals have to be considered in parallel. For this reason, there has been a growing interest in MultiObjective Optimization (MOO) in the past years. Several alternative approaches have been proposed to cope with the occurring ..."
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Cited by 8 (1 self)
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problems, e.g. how to compare and rank the different elements. The available techniques produce very good results, but they have mainly been studied for problems of “low dimension”, i.e. with less than 10 optimization objectives. In this paper we study MOO for high dimensional spaces. We first review
OPCluster: Clustering by Tendency in High Dimensional Space
, 2003
"... Clustering is the process of grouping a set of objects into classes of similar objects. Because of unknownness of the hidden patterns in the data sets, the definition of similarity is very subtle. Until recently, similarity measures are typically based on distances, e.g Euclidean distance and cosine ..."
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Cited by 60 (5 self)
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Clustering is the process of grouping a set of objects into classes of similar objects. Because of unknownness of the hidden patterns in the data sets, the definition of similarity is very subtle. Until recently, similarity measures are typically based on distances, e.g Euclidean distance and cosine distance. In this paper, we propose a flexible yet powerful clustering model, namely OPCluster (Order Preserving Cluster). Under this new model, two objects are similar on a subset of dimensions if the values of these two objects induce the same relative order of those dimensions. Such a cluster might arise when the expression levels of (coregulated) genes can rise or fall synchronously in response to a sequence of environment stimuli. Hence, discovery of OPCluster is essential in revealing significant gene regulatory networks. A deterministic algorithm is designed and implemented to discover all the significant OPClusters. A set of extensive experiments has been done on several real biological data sets to demonstrate its effectiveness and efficiency in detecting coregulated patterns.
1Mining Projected Clusters in HighDimensional Spaces
, 2008
"... Clustering highdimensional data has been a major challenge due to the inherent sparsity of the points. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the fulldimensional space. To address this problem, a nu ..."
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Clustering highdimensional data has been a major challenge due to the inherent sparsity of the points. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the fulldimensional space. To address this problem, a
Clustering for approximate similarity search in highdimensional spaces
 IEEE Transactions on Knowledge and Data Engineering
, 2002
"... AbstractÐIn this paper, we present a clustering and indexing paradigm (called Clindex) for highdimensional search spaces. The scheme is designed for approximate similarity searches, where one would like to find many of the data points near a target point, but where one can tolerate missing a few ne ..."
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Cited by 52 (0 self)
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AbstractÐIn this paper, we present a clustering and indexing paradigm (called Clindex) for highdimensional search spaces. The scheme is designed for approximate similarity searches, where one would like to find many of the data points near a target point, but where one can tolerate missing a few
Results 11  20
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