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An introduction to Kolmogorov Complexity and its Applications: Preface to the First Edition
, 1997
"... This document has been prepared using the L a T E X system. We thank Donald Knuth for T E X, Leslie Lamport for L a T E X, and Jan van der Steen at CWI for online help. Some figures were prepared by John Tromp using the xpic program. The London Mathematical Society kindly gave permission to reproduc ..."
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Cited by 2143 (120 self)
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to reproduce a long extract by A.M. Turing. The Indian Statistical Institute, through the editor of Sankhy¯a, kindly gave permission to quote A.N. Kolmogorov. We gratefully acknowledge the financial support by NSF Grant DCR8606366, ONR Grant N0001485k0445, ARO Grant DAAL0386K0171, the Natural Sciences
ReadOnce Threshold Formulas, Justifying Assignments, and Generic Tranformations
, 1992
"... We present a membership query (i.e. interpolation) algorithm for exactly identifying the class of readonce formulas over the basis of boolean threshold functions. Using a generic transformation from [Angluin, Hellerstein, Karpinski 89], this gives an algorithm using membership and equivalence queri ..."
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Cited by 3 (3 self)
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of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N 1N4. This research was supported in Part by the NSERC of Canada. 2 Aiken Computation Laboratory, Harvard University, Cambridge, MA 02138. Supported by ONR grant N0001485K0445. 3 Department of EECS, Northwestern University
Computational Complexity of Learning ReadOnce Formulas over Different Bases
, 1991
"... We study computational complexity of learning readonce formulas over different boolean bases. In particular we design a polynomial time algorithm for learning readonce formulas over a threshold basis. The algorithm works in time O(n 3 ) using O(n 3 ) membership queries. By the result of [An ..."
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Cited by 4 (2 self)
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the Siemens Corporation and ONR grant N0001485K0445. A portion of this research wa...
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
 Journal of Computational Physics
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (64 self)
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We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble HamiltonJacobi equations with parabolic righthandsides, by using techniques from the hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general HamiltonJacobitype problems. We demonstrate our algorithms by computing the solution to a variety of surface motion problems. 1
On Spectral Clustering: Analysis and an algorithm
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
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Cited by 1697 (13 self)
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Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
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Cited by 2263 (18 self)
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We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images of a particular face, under varying illumination but fixed pose, lie in a 3D linear subspace of the high dimensional image space  if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce selfshadowing, images will deviate from this linear subspace. Rather than explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation. Our projection method is based on Fisher's Linear Discriminant and produces well separated classes in a lowdimensional subspace even under severe variation in lighting and facial expressions. The Eigenface
Texture Synthesis by Nonparametric Sampling
 In International Conference on Computer Vision
, 1999
"... A nonparametric method for texture synthesis is proposed. The texture synthesis process grows a new image outward from an initial seed, one pixel at a time. A Markov random field model is assumed, and the conditional distribution of a pixel given all its neighbors synthesized so far is estimated by ..."
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Cited by 1014 (7 self)
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A nonparametric method for texture synthesis is proposed. The texture synthesis process grows a new image outward from an initial seed, one pixel at a time. A Markov random field model is assumed, and the conditional distribution of a pixel given all its neighbors synthesized so far is estimated by querying the sample image and finding all similar neighborhoods. The degree of randomness is controlled by a single perceptually intuitive parameter. The method aims at preserving as much local structure as possible and produces good results for a wide variety of synthetic and realworld textures. 1. Introduction Texture synthesis has been an active research topic in computer vision both as a way to verify texture analysis methods, as well as in its own right. Potential applications of a successful texture synthesis algorithm are broad, including occlusion fillin, lossy image and video compression, foreground removal, etc. The problem of texture synthesis can be formulated as follows: let...
Generation and Synchronous TreeAdjoining Grammars
, 1990
"... Treeadjoining grammars (TAG) have been proposed as a formalism for generation based on the intuition that the extended domain of syntactic locality that TAGs provide should aid in localizing semantic dependencies as well, in turn serving as an aid to generation from semantic representations. We dem ..."
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Cited by 772 (43 self)
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Treeadjoining grammars (TAG) have been proposed as a formalism for generation based on the intuition that the extended domain of syntactic locality that TAGs provide should aid in localizing semantic dependencies as well, in turn serving as an aid to generation from semantic representations. We demonstrate that this intuition can be made concrete by using the formalism of synchronous treeadjoining grammars. The use of synchronous TAGs for generation provides solutions to several problems with previous approaches to TAG generation. Furthermore, the semantic monotonicity requirement previously advocated for generation gram mars as a computational aid is seen to be an inherent property of synchronous TAGs.
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