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132
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 78 (17 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.
Hermeneutics: Interpretation Theory
 in Schleiermacher, Dilthey, Heidegger and Gadamer, Northwestern University Studies in Phenomenology & Existential Philosophy
, 1969
"... Report on proposed doctoral thesis: ..."
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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 38 (13 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 25 (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...
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 19 (13 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.
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 19 (1 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.
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 16 (13 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.
Enhanced dictionarybased SAR amplitude distribution estimation and its validation with very highresolution data
 IEEE Geosci. Remote Sens. Lett
, 2011
"... Abstract—In this letter, we address the problem of estimating the amplitude probability density function (pdf) of singlechannel synthetic aperture radar (SAR) images. A novel flexible method is developed to solve this problem, extending the recently proposed dictionarybased stochastic expectation ..."
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Cited by 15 (12 self)
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Abstract—In this letter, we address the problem of estimating the amplitude probability density function (pdf) of singlechannel synthetic aperture radar (SAR) images. A novel flexible method is developed to solve this problem, extending the recently proposed dictionarybased stochastic expectation maximization approach (developed for a mediumresolution SAR) to very highresolution (VHR) satellite imagery, and enhanced by introduction of a novel procedure for estimating the number of mixture components, that permits to reduce appreciably its computational complexity. The specific interest is the estimation of heterogeneous statistics, and the developed method is validated in the case of the VHR SAR imagery, acquired by the lastgeneration satellite SAR systems, TerraSARX and COSMOSkyMed. This VHR imagery allows the appreciation of various ground materials resulting in highly mixed distributions, thus posing a difficult estimation problem that has not been addressed so far. We also conduct an experimental study of the extended dictionary of stateoftheart SARspecific pdf models and consider the dictionary refinements. Index Terms—Finite mixture models, parametric estimation, probability density function estimation, stochastic expectation maximization (SEM), synthetic aperture radar (SAR) images. I.