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875
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 2295 (11 self)
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The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.
A tutorial on support vector regression
, 2004
"... In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing ..."
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Cited by 477 (2 self)
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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.
Bundle adjustment – a modern synthesis
 Vision Algorithms: Theory and Practice, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 388 (10 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than restricting attention to traditional nonlinear least squares.
Snopt: An SQP Algorithm For LargeScale Constrained Optimization
, 1997
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 332 (18 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse.
A scaled conjugate gradient algorithm for fast supervised learning
 NEURAL NETWORKS
, 1993
"... A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural netwo ..."
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Cited by 300 (0 self)
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A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural network but requires only O(N) memory usage, where N is the number of weights in the network. The performance of SCG is benchmarked against the performance of the standard backpropagation algorithm (BP) [13], the conjugate gradient backpropagation (CGB) [6] and the onestep BroydenFletcherGoldfarbShanno memoryless quasiNewton algorithm (BFGS) [1]. SCG yields a speedup of at least an order of magnitude relative to BP. The speedup depends on the convergence criterion, i.e., the bigger demand for reduction in error the bigger the speedup. SCG is fully automated including no user dependent parameters and avoids a time consuming linesearch, which CGB and BFGS uses in each iteration in order to determine an appropriate step size.
Incorporating problem dependent structural information in the architecture of a neural network often lowers the overall complexity. The smaller the complexity of the neural network relative to the problem domain, the bigger the possibility that the weight space contains long ravines characterized by sharp curvature. While BP is inefficient on these ravine phenomena, it is shown that SCG handles them effectively.
RateDistortion Optimized Streaming of Packetized Media
 IEEE Trans. Multimedia
, 2001
"... This paper addresses the problem of streaming packetized media ..."
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Cited by 224 (12 self)
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This paper addresses the problem of streaming packetized media
Support Vector Clustering
, 2001
"... We present a novel clustering method using the approach of support vector machines. Data points are mapped by means of a Gaussian kernel to a high dimensional feature space, where we search for the minimal enclosing sphere. This sphere, when mapped back to data space, can separate into several compo ..."
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Cited by 164 (1 self)
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We present a novel clustering method using the approach of support vector machines. Data points are mapped by means of a Gaussian kernel to a high dimensional feature space, where we search for the minimal enclosing sphere. This sphere, when mapped back to data space, can separate into several components, each enclosing a separate cluster of points. We present a simple algorithm for identifying these clusters. The width of the Gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters. The structure of a dataset is explored by varying the two parameters, maintaining a minimal number of support vectors to assure smooth cluster boundaries. We demonstrate the performance of our algorithm on several datasets.
On the Learnability and Design of Output Codes for Multiclass Problems
 In Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
, 2000
"... . Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problem ..."
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Cited by 163 (5 self)
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. Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problems. For the design problem of discrete codes, which have been used extensively in previous works, we present mostly negative results. We then introduce the notion of continuous codes and cast the design problem of continuous codes as a constrained optimization problem. We describe three optimization problems corresponding to three different norms of the code matrix. Interestingly, for the l 2 norm our formalism results in a quadratic program whose dual does not depend on the length of the code. A special case of our formalism provides a multiclass scheme for building support vector machines which can be solved efficiently. We give a time and space efficient algorithm for solving the quadratic program. We describe preliminary experiments with synthetic data show that our algorithm is often two orders of magnitude faster than standard quadratic programming packages. We conclude with the generalization properties of the algorithm. Keywords: Multiclass categorization,output coding, SVM 1.
On sparse representations in arbitrary redundant bases
 IEEE Trans. Inf. Th
, 2004
"... Abstract—The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases. The question that is considered is the following: given a matrix of dimension ( ) with and a vector = , find a sufficient condition for to have a unique sparsest re ..."
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Cited by 158 (0 self)
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Abstract—The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases. The question that is considered is the following: given a matrix of dimension ( ) with and a vector = , find a sufficient condition for to have a unique sparsest representation as a linear combination of columns of. Answers to this question are known when is the concatenation of two unitary matrices and either an extensive combinatorial search is performed or a linear program is solved. We consider arbitrary matrices and give a sufficient condition for the unique sparsest solution to be the unique solution to both a linear program or a parametrized quadratic program. The proof is elementary and the possibility of using a quadratic program opens perspectives to the case where = + with a vector of noise or modeling errors. Index Terms—Basis pursuit, global matched filter, linear program, quadratic program, redundant dictionaries, sparse representations. I.
Adapting Multimedia Internet Content for Universal Access
 IEEE Transactions on Multimedia
, 1999
"... Content delivery over the Internet needs to address both the multimedia nature of the content and the capabilities of the diverse client platforms the content is being delivered to. We present a system that adapts multimedia Web documents to optimally match the capabilities of the client device requ ..."
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Cited by 147 (2 self)
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Content delivery over the Internet needs to address both the multimedia nature of the content and the capabilities of the diverse client platforms the content is being delivered to. We present a system that adapts multimedia Web documents to optimally match the capabilities of the client device requesting it. This system has two key components: (1) A representation scheme called the InfoPyramid that provides a multimodal, multiresolution representation hierarchy for multimedia. (2) A customizer that selects the best content representation to meet the client capabilities while delivering the most value. We model the selection process as a resource allocation problem in a generalized ratedistortion framework. In this framework, we address the issue of both multiple media types in a Web document and multiple resource types at the client. We extend this framework to allow prioritization on the content items in a Web document. We illustrate our content adaptation technique with a web ...