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52
Generalization Performance of Regularization Networks and Support . . .
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2001
"... We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the field of statistical learning theory. The hy ..."
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Cited by 73 (20 self)
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We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinitedimensional unit ball in feature space into a finitedimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator, can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence, we are able to theoretically explain the effect of the choice of kernel function on the generalization performance of support vector machines.
A coinductive calculus of streams
, 2005
"... We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analo ..."
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Cited by 27 (9 self)
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We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analogy to classical analysis, the latter are presented as behavioural differential equations. A number of applications of the calculus are presented, including difference equations, analytical differential equations, continued fractions, and some problems from discrete mathematics and combinatorics.
Generalized Digital Trees and their Differencedifferential Equations
, 1992
"... . Consider a tree partitioning process in which n elements are split into b at the root of a tree (b a design parameter), the rest going recursively into two subtrees with a binomial probability distribution. This extends some familiar tree data structures of computer science like the digital trie ..."
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Cited by 24 (5 self)
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. Consider a tree partitioning process in which n elements are split into b at the root of a tree (b a design parameter), the rest going recursively into two subtrees with a binomial probability distribution. This extends some familiar tree data structures of computer science like the digital trie and the digital search tree. The exponential generating function for the expected size of the tree satisfies a difference differential equation of order b, d b dz b f(z) = e z + 2e z=2 f( z 2 ): The solution involves going to ordinary (rather than exponential) generating functions, analyzing singularities by means of Mellin transforms and contour integration. The method is of some general interest since a large number of related problems on digital structures can be treated in this way via singularity analysis of ordinary generating functions. Work of this author was supported in part by the Basic Research Action of the E.C. under contract No. 3075 (Project ALCOM). y The resea...
Channel Sharing by RateAdaptive Streaming Applications
, 2002
"... There are various techniques for adapting the transmission rate of an application while maintaining the perceived quality at the receiver at acceptable levels. Shared channel systems can use this rate adaptation capability to increase the number of concurrent applications in the system. This can be ..."
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Cited by 14 (3 self)
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There are various techniques for adapting the transmission rate of an application while maintaining the perceived quality at the receiver at acceptable levels. Shared channel systems can use this rate adaptation capability to increase the number of concurrent applications in the system. This can be achieved by appropriately modifying the rate of the already running applications when a new connection arrives in the system. In this paper we present an analytical model for a class of algorithms for channel sharing by rate adaptive applications. We provide means for calculating performance measures related to the quality of reception of an application. We also present the design of algorithms that ensure fair channel sharing while keeping the application performance within acceptable levels.
Discrete simulation models for multidimensional systems based on functional transformations
 In J.G. McWhirter and I.K. Proudler, editors, Mathematics in Signal Processing IV
, 1998
"... A method for the discrete simulation of continuous multidimensional systems is presented. It is based on a transfer function description of the continuous system, which is obtained by application of appropriate functional transformations for each independent variable. Digital signal processing analo ..."
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Cited by 11 (11 self)
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A method for the discrete simulation of continuous multidimensional systems is presented. It is based on a transfer function description of the continuous system, which is obtained by application of appropriate functional transformations for each independent variable. Digital signal processing analogtodiscrete transformations turn the transfer function into a discrete simulation model. It is suitable for computer implementation and provides simulation algorithms, which are competitive with customary numerical methods. A comparison with a commercial software package demonstrates the advantage of the proposed simulation models. 1
Generalized minimumerror thresholding for unsupervised change detection from SAR amplitude imagery
 IEEE Transactions on Geoscience and Remote Sensing
, 2006
"... Abstract—The availability of synthetic aperture radar (SAR) data offers great potential for environmental monitoring due to the insensitiveness of SAR imagery to atmospheric and sunlightillumination conditions. In addition, the short revisit time provided by future SARbased missions will allow a h ..."
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Cited by 11 (0 self)
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Abstract—The availability of synthetic aperture radar (SAR) data offers great potential for environmental monitoring due to the insensitiveness of SAR imagery to atmospheric and sunlightillumination conditions. In addition, the short revisit time provided by future SARbased missions will allow a huge amount of multitemporal SAR data to become systematically available for monitoring applications. In this paper, the problem of detecting the changes that occurred on the ground by analyzing SAR imagery is addressed by a completely unsupervised approach, i.e., by developing an automatic thresholding technique. The imageratioing approach to SAR change detection is adopted, and the Kittler and Illingworth minimumerror thresholding algorithm is generalized to take into account the nonGaussian distribution of the amplitude values of SAR images. In particular, a SARspecific parametric modeling approach for the ratio image is proposed and integrated into the thresholding process. Experimental results, which confirm the accuracy of the method for real Xband SAR and spaceborne imaging radar Cband images, are presented. Index Terms—Change detection, Kittler and Illingworth method, method of logcumulants (MoLC), parametric density estimation, synthetic aperture radar (SAR), thresholding. I.
SAR Amplitude Probability Density Function Estimation Based on a Generalized Gaussian Model
, 2011
"... Abstract—In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or ..."
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Cited by 9 (6 self)
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Abstract—In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closedform expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “methodoflogcumulants ” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GGbased amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS1, XSAR, ESAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena. Index Terms—Generalized Gaussian (GG), parametric estimation, probability density function (PDF), synthetic aperture radar (SAR). I.
Dictionarybased stochastic expectation maximization for SAR amplitude probability density function estimation
 IEEE Trans. Geosci. Remote Sens
, 2006
"... Abstract—In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitud ..."
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Cited by 7 (5 self)
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Abstract—In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different landcover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SARspecific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation–maximization iterative methodology with the recently developed “methodoflogcumulants ” for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data. Index Terms—Finite mixture models (FMMs), parametric estimation, probability density function (pdf) estimation, stochastic expectation maximization (SEM), synthetic aperture radar (SAR) images. I.