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The quantum extension of the Geometric Machine Model ∗
"... extends the Geometric Machine [6] Model to obtain a semantic modelling of quantum algorithms related to the multidimensional Hilbert Space [3], involving possibly infinite synchronous and nondeterministic computations based on the spatial distribution of the memory states. The QGM Model provides ..."
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extends the Geometric Machine [6] Model to obtain a semantic modelling of quantum algorithms related to the multidimensional Hilbert Space [3], involving possibly infinite synchronous and nondeterministic computations based on the spatial distribution of the memory states. The QGM Model
Specifying the geometric machine visual language
 In IEEE Symposium on Visual Languages and Formal Methods
, 2003
"... This paper summarizes an experiment in the formal specification of the visual language for the Geometric Machine model [3], denoted by GMVL. The specification follows the approach proposed in the GENGED project, of the T. U. Berlin [1]. In the GMLV, supported by a visual alphabet and a visual gramma ..."
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Cited by 2 (1 self)
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This paper summarizes an experiment in the formal specification of the visual language for the Geometric Machine model [3], denoted by GMVL. The specification follows the approach proposed in the GENGED project, of the T. U. Berlin [1]. In the GMLV, supported by a visual alphabet and a visual
Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semisupervised framework that incorporates labeled and unlabeled data in a generalpurpose learner. Some transductive graph learning al ..."
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Cited by 578 (16 self)
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algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely
A Programming Language for the Interval Geometric Machine
"... This paper presents an interval version of the Geometric Machine Model (GMM) machine model, based on Girard’s coherence space, capable of modelling sequential, alternative, parallel (synchronous) and nondeterministic computations on a (possibly infinite) shared memory. The processes of the GMM are ..."
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This paper presents an interval version of the Geometric Machine Model (GMM) machine model, based on Girard’s coherence space, capable of modelling sequential, alternative, parallel (synchronous) and nondeterministic computations on a (possibly infinite) shared memory. The processes of the GMM
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing on the correspondenc ..."
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Cited by 1226 (15 self)
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One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing
First steps in the construction of the Geometric Machine, em “Seleta do XXIV
 Tendências em Matemática Aplicada e Computacional
, 2002
"... Abstract. This work introduces the Geometric Machine (GM) – a computational model for the construction and representation of concurrent and nondeterministic processes, preformed in a synchronized way, with infinite memory whose positions are labelled by the points of a geometric space. The ordered ..."
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Cited by 2 (2 self)
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Abstract. This work introduces the Geometric Machine (GM) – a computational model for the construction and representation of concurrent and nondeterministic processes, preformed in a synchronized way, with infinite memory whose positions are labelled by the points of a geometric space
c ○ Uma Publicação da Sociedade Brasileira de Matemática Aplicada e Computacional. The Stochastic Geometric Machine Model 1
"... Abstract. This paper introduces the stochastic version of the Geometric Machine Model for the modelling of sequential, alternative, parallel (synchronous) and nondeterministic computations with stochastic numbers stored in a (possibly infinite) shared memory. The programming language L(D → ∞), induc ..."
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Abstract. This paper introduces the stochastic version of the Geometric Machine Model for the modelling of sequential, alternative, parallel (synchronous) and nondeterministic computations with stochastic numbers stored in a (possibly infinite) shared memory. The programming language L
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
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Cited by 257 (45 self)
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of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace
Support vector machines: Training and applications
 A.I. MEMO 1602, MIT A. I. LAB
, 1997
"... The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Laboratories [3, 6, 8, 24]. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and MultiLayer Perc ..."
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Cited by 223 (3 self)
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of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Since Structural Risk Minimization is an inductive principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing the Mean Square Error over the data set
Results 1  10
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