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48,821
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1-norm Solution is also the Sparsest Solution
- Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract
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Cited by 568 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
A density-based algorithm for discovering clusters in large spatial databases with noise
, 1996
"... Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clu ..."
Abstract
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Cited by 1786 (70 self)
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of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover
Range-Free Localization Schemes for Large Scale Sensor Networks
, 2003
"... Wireless Sensor Networks have been proposed for a multitude of location-dependent applications. For such systems, the cost and limitations of hardware on sensing nodes prevent the use of range-based localization schemes that depend on absolute point-to-point distance estimates. Because coarse accura ..."
Abstract
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Cited by 525 (8 self)
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accuracy is sufficient for most sensor network applications, solutions in range-free localization are being pursued as a cost-effective alternative to more expensive range-based approaches. In this paper, we present APIT, a novel localization algorithm that is range-free. We show that our APIT scheme
FastSLAM: A Factored Solution to the Simultaneous Localization and Mapping Problem
- In Proceedings of the AAAI National Conference on Artificial Intelligence
, 2002
"... The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filter-base ..."
Abstract
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Cited by 599 (10 self)
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The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filter
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
- PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
Abstract
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Cited by 1816 (10 self)
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(LSA), is presented and used to successfully simulate such learning and several other psycholinguistic phenomena. By inducing global knowledge indirectly from local co-occurrence data in a large body of representative text, LSA acquired knowledge about the full vocabulary of English at a comparable
The Digital Michelangelo Project: 3D Scanning of Large Statues
, 2000
"... We describe a hardware and software system for digitizing the shape and color of large fragile objects under non-laboratory conditions. Our system employs laser triangulation rangefinders, laser time-of-flight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merg ..."
Abstract
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Cited by 488 (8 self)
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We describe a hardware and software system for digitizing the shape and color of large fragile objects under non-laboratory conditions. Our system employs laser triangulation rangefinders, laser time-of-flight rangefinders, digital still cameras, and a suite of software for acquiring, aligning
An affine invariant interest point detector
- In Proceedings of the 7th European Conference on Computer Vision
, 2002
"... Abstract. This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of ..."
Abstract
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Cited by 1467 (55 self)
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Abstract. This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
Abstract
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Cited by 757 (102 self)
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Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more
Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
Abstract
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Cited by 715 (33 self)
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Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory
Knowledge-based Analysis of Microarray Gene Expression Data By Using Support Vector Machines
, 2000
"... We introduce a method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments. The method is based on the theory of support vector machines (SVMs). SVMs are considered a supervised computer learning method because they exploit prior knowledge of ..."
Abstract
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Cited by 520 (8 self)
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analysis, including their exibility in choosing a similarity function, sparseness of solution when dealing with large data sets, the ability t...
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