Results 1  10
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73
Gaussian Networks for Direct Adaptive Control
 IEEE Transactions on Neural Networks
, 1991
"... A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial ..."
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Cited by 132 (8 self)
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A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example syst...
Stratified exponential families: Graphical models and model selection
 ANNALS OF STATISTICS
, 2001
"... ..."
From RankNet to LambdaRank to LambdaMART: An Overview
"... LambdaMART is the boosted tree version of LambdaRank, which is based on RankNet. RankNet, LambdaRank, and LambdaMART have proven to be very successful algorithms for solving real world ranking problems: for example an ensemble of LambdaMART rankers won Track 1 of the 2010 Yahoo! Learning To Rank Cha ..."
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Cited by 35 (1 self)
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LambdaMART is the boosted tree version of LambdaRank, which is based on RankNet. RankNet, LambdaRank, and LambdaMART have proven to be very successful algorithms for solving real world ranking problems: for example an ensemble of LambdaMART rankers won Track 1 of the 2010 Yahoo! Learning To Rank Challenge. The details of these algorithms are spread across several papers and reports, and so here we give a selfcontained, detailed and complete description of them. 1
Bounds on packings of spheres in the Grassmann manifolds
, 2000
"... We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal ..."
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Cited by 29 (1 self)
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We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal angles between $p$ and $q$.
Generalized polar varieties: Geometry and algorithms
, 2004
"... Let V be a closed algebraic subvariety of the n–dimensional projective space over the complex or real numbers and suppose that V is non–empty and equidimensional. The classic notion of a polar variety of V associated with a given linear subvariety of the ambient space of V was generalized and motiva ..."
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Cited by 26 (8 self)
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Let V be a closed algebraic subvariety of the n–dimensional projective space over the complex or real numbers and suppose that V is non–empty and equidimensional. The classic notion of a polar variety of V associated with a given linear subvariety of the ambient space of V was generalized and motivated in [2]. As particular instances of this notion of a generalized polar variety one reobtains the classic one and an alternative type of a polar varietiy, called dual. As main result of the present paper we show that for a generic choice of their parameters the generalized polar varieties of V are empty or equidimensional and smooth in any regular point of V. In the case that the variety V is affine and smooth and has a complete intersection ideal of definition, we are able, for a generic parameter choice, to describe locally the generalized polar varieties of V by explicit equations. Finally, we indicate how this description may be used in order to design in
Programming graphics processors functionally
 In Haskell workshop
, 2004
"... Graphics cards for personal computers have recently undergone a radical transformation from fixedfunction graphics pipelines to multiprocessor, programmable architectures. Multiprocessor architectures are clearly advantageous for graphics for the simple reason that graphics computations are natur ..."
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Cited by 23 (0 self)
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Graphics cards for personal computers have recently undergone a radical transformation from fixedfunction graphics pipelines to multiprocessor, programmable architectures. Multiprocessor architectures are clearly advantageous for graphics for the simple reason that graphics computations are naturally concurrent, mapping well to stateless stream processing. They therefore parallelize easily and need no random access to memory with its problematic latencies. This paper presents Vertigo, a purely functional, Haskellembedded language for 3D graphics and an optimizing compiler that generates graphics processor code. The language integrates procedural surface modeling, shading, and texture generation, and the compiler exploits the unusual processor architecture. The shading sublanguage is based on a simple and precise semantic model, in contrast to previous shading languages. Geometry and textures are also defined via a very simple denotational semantics. The formal semantics yields not only programs that are easy to understand and reason about, but also very efficient implementation, thanks to a compiler based on partial evaluation and symbolic optimization, much in the style of Pan [2]. Haskell’s overloading facility is extremely useful throughout Vertigo. For instance, math operators are used not just for floating point numbers, but also expressions (for differentiation and compilation), tuples, and functions. Typically, these overloadings cascade, as in the case of surfaces, which may be combined via math operators, though they are really functions over tuples of expressions on floating point numbers. Shaders may be composed with the same notational convenience. Functional dependencies are exploited for vector spaces, cross products, and derivatives.
Visualizing Quaternion Rotation
, 1993
"... Quaternions play a vital role in the representation of rotations in computer graphics, primarily for animation and user interfaces. Unfortunately, quaternion rotation is often left as an advanced topic in computer graphics education due to difficulties in portraying the fourdimensional space of the ..."
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Cited by 21 (1 self)
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Quaternions play a vital role in the representation of rotations in computer graphics, primarily for animation and user interfaces. Unfortunately, quaternion rotation is often left as an advanced topic in computer graphics education due to difficulties in portraying the fourdimensional space of the quaternions. One tool for overcoming these obstacles is the quaternion demonstrator, a physical visual aid consisting primarily of a belt. Every quaternion used to specify a rotation can be represented by fixing one end of the belt and rotating the other. Multiplication of quaternions is demonstrated by the composition of rotations, and the resulting twists in the belt visually depict how quaternions interpolate rotation. This paper introduces to computer graphics the exponential notation that mathematicians have used to represent unit quaternions. Exponential notation combines the angle and axis of the rotation into a concise quaternion expression. This notation allows the paper to more cl...
Graphical models and exponential families
 In Proceedings of the 14th Annual Conference on Uncertainty in Arti cial Intelligence (UAI98
, 1998
"... We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, includin ..."
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Cited by 20 (1 self)
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We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families (CEFs) and graphical models with hidden variables are stratified exponential families (SEFs). An SEF is a finite union of CEFs satisfying a frontier condition. In addition, we illustrate how one can automatically generate independence and nonindependence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables. The relevance of these results for model selection is examined. 1
Isometric Embedding and Continuum ISOMAP
 In Proceedings of the Twentieth International Conference on Machine Learning
, 2003
"... Recently, the Isomap algorithm has been proposed for learning a nonlinear manifold from a set of unorganized highdimensional data points. It is based on extending the classical multidimensional scaling method for dimension reduction. In this paper, we present a continuous version of Isomap wh ..."
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Cited by 18 (1 self)
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Recently, the Isomap algorithm has been proposed for learning a nonlinear manifold from a set of unorganized highdimensional data points. It is based on extending the classical multidimensional scaling method for dimension reduction. In this paper, we present a continuous version of Isomap which we call continuum isomap and show that manifold learning in the continuous framework is reduced to an eigenvalue problem of an integral operator. We also show that the continuum isomap can perfectly recover the underlying natural parametrization if the nonlinear manifold can be isometrically embedded onto an Euclidean space. Several numerical examples are given to illustrate the algorithm.
Topics In Harmonic Analysis With Applications To Radar And Sonar
 in RADAR and SONAR, Part 1, IMA Volumes in Mathematics and its Applications
, 1991
"... This minicourse is an introduction to basic concepts and tools in group representation theory, both commutative and noncommutative, that are fundamental for the analysis of radar and sonar imaging. Several symmetry groups of physical interest will be studied (circle, line, rotation, ax + b, Heisenbe ..."
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Cited by 12 (1 self)
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This minicourse is an introduction to basic concepts and tools in group representation theory, both commutative and noncommutative, that are fundamental for the analysis of radar and sonar imaging. Several symmetry groups of physical interest will be studied (circle, line, rotation, ax + b, Heisenberg, etc.) together with their associated transforms and representation theories (DFT, Fourier transform, expansions in spherical harmonics, wavelets, etc.). Through the unifying concepts of group representation theory, familiar tools for commutative groups, such as the Fourier transform on the line, extend to transforms for the noncommutative groups which arise in radarsonar. The insight and results obtained will be related directly to objects of interest in radarsonar, such as the ambiguity function. The material will be presented with many examples and should be easily comprehensible by engineers and physicists, as well as mathematicians. *School of Mathematics and IMA, University of Minnesota. The research contribution of this paper was supported in part by the National Science Foundation under grant DMS 8823054 Typeset by A M ST E X 1 2 WILLARD MILLER JR.* TABLE OF CONTENTS 1.