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Seaching in HighDimensional Spaces  . . .
, 2001
"... During the last decade, multimedia databases have become increasingly important in many application areas such as medicine, CAD, geography, and molecular biology. An important research issue in the field of multimedia databases is the contentbased retrieval of similar multimedia objects such as im ..."
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that transforms important properties of the multimedia objects into highdimensional points (feature vectors). Thus, the similarity search is transformed into a search of points in the feature space that are close to a given query point in the highdimensional feature space. Query processing in highdimensional
EM in HighDimensional Spaces
"... Abstract—This paper considers fitting a mixture of Gaussians model to highdimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside ExpectationMaximization (EM ..."
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Cited by 1 (1 self)
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Abstract—This paper considers fitting a mixture of Gaussians model to highdimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation
Nearest Neighbors In HighDimensional Spaces
, 2004
"... In this chapter we consider the following problem: given a set P of points in a highdimensional space, construct a data structure which given any query point q nds the point in P closest to q. This problem, called nearest neighbor search is of significant importance to several areas of computer sci ..."
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Cited by 95 (3 self)
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In this chapter we consider the following problem: given a set P of points in a highdimensional space, construct a data structure which given any query point q nds the point in P closest to q. This problem, called nearest neighbor search is of significant importance to several areas of computer
Indexing Methods in HighDimensional Spaces
"... Introduction The indexing problem in highdimensional spaces in connection with image databases is an active area of research. The databases are quite large and images are usually described (abstracted) into a vector of components which are usually considered useful for recognition purposes (those ..."
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Introduction The indexing problem in highdimensional spaces in connection with image databases is an active area of research. The databases are quite large and images are usually described (abstracted) into a vector of components which are usually considered useful for recognition purposes (those
Resolving Bridging Descriptions in HighDimensional Space
, 1998
"... Contents 1 Introduction 1 2 Background 1 2.1 Bridging Descriptions . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 The System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 HighDimensional Space . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Creating highdimensional space . ..."
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Cited by 7 (2 self)
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Contents 1 Introduction 1 2 Background 1 2.1 Bridging Descriptions . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 The System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 HighDimensional Space . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Creating highdimensional space
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
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
On the Surprising Behavior of Distance Metrics in High Dimensional Space
 Lecture Notes in Computer Science
, 2001
"... In recent years, the effect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a efficienc ..."
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Cited by 197 (2 self)
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In recent years, the effect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a
Chromatic Clustering in High Dimensional Space
"... Abstract. In this paper, we study a new type of clustering problem, called Chromatic Clustering, in high dimensional space. Chromatic clustering seeks to partition a set of colored points into groups (or clusters) so that no group contains points with the same color and a certain objective function ..."
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Abstract. In this paper, we study a new type of clustering problem, called Chromatic Clustering, in high dimensional space. Chromatic clustering seeks to partition a set of colored points into groups (or clusters) so that no group contains points with the same color and a certain objective function
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
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