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69,184
The space complexity of approximating the frequency moments
- JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 845 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
Optimal approximation by piecewise smooth functions and associated variational problems
- Commun. Pure Applied Mathematics
, 1989
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. ..."
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Cited by 1294 (14 self)
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems
Greedy Function Approximation: A Gradient Boosting Machine
- Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 1000 (13 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
- ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real d-dimensional 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 984 (32 self)
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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
The Concept of a Linguistic Variable and its Application to Approximate Reasoning
- Journal of Information Science
, 1975
"... By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, et ..."
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Cited by 1430 (9 self)
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rule which generates the terms in T(z); and M is a semantic rule which associates with each linguistic value X its meaning, M(X), where M(X) denotes a fuzzy subset of U The meaning of a linguistic value X is characterized by a compatibility function, c: l / + [0, I], which associates with each u in U
Surface deformation due to shear and tensile faults in a half-space
, 1985
"... A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms r ..."
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Cited by 727 (1 self)
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A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms
Representing twentieth century space-time climate variability, part 1: development of a 1961-90 mean monthly terrestrial climatology
- Journal of Climate
, 1999
"... The construction of a 0.58 lat 3 0.58 long surface climatology of global land areas, excluding Antarctica, is described. The climatology represents the period 1961–90 and comprises a suite of nine variables: precipitation, wet-day frequency, mean temperature, diurnal temperature range, vapor pressur ..."
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Cited by 581 (13 self)
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to the period 1961–90, describes an extended suite of surface climate variables, explicitly incorporates elevation as a predictor variable, and contains an evaluation of regional errors associated with this and other commonly used climatologies. The climatology is already being used by researchers in the areas
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. A major theme
View Interpolation for Image Synthesis
"... Image-space simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry t ..."
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Cited by 603 (0 self)
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Image-space simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry
From Few to many: Illumination cone models for face recognition under variable lighting and pose
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a smal ..."
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Cited by 754 (12 self)
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conditions. The pose space is then sampled, and for each pose the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated
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