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5,253
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 semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning al ..."
Abstract
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Cited by 578 (16 self)
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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 semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning
A Geometric Framework for Unsupervised Anomaly Detection: Detecting Intrusions in Unlabeled Data
- Applications of Data Mining in Computer Security
, 2002
"... Abstract Most current intrusion detection systems employ signature-based methods or data mining-based methods which rely on labeled training data. This training data is typically expensive to produce. We present a new geometric framework for unsupervised anomaly detection, which are algorithms that ..."
Abstract
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Cited by 238 (9 self)
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Abstract Most current intrusion detection systems employ signature-based methods or data mining-based methods which rely on labeled training data. This training data is typically expensive to produce. We present a new geometric framework for unsupervised anomaly detection, which are algorithms
New geometrical frameworks for Classical Impulsive
- Mechanics, Rep. Math. Phys
"... A new context is introduced to give a formal geometric environment for the study of Impulsive Mechanics of systems with finite number of degrees of freedom. The new structures embody the usual ones of Analytical Mechanics such as tangent bundles for time independent systems and jet–bundles for time ..."
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Cited by 1 (1 self)
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A new context is introduced to give a formal geometric environment for the study of Impulsive Mechanics of systems with finite number of degrees of freedom. The new structures embody the usual ones of Analytical Mechanics such as tangent bundles for time independent systems and jet–bundles for time
Public Announcement Logic in Geometric Frameworks
"... In this paper we introduce public announcement logic in different geo-metric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the completeness of public announcement logic in those framewo ..."
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In this paper we introduce public announcement logic in different geo-metric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the completeness of public announcement logic in those
An Intrinsic Geometric Framework for the Building Block
- Synthesis of Single Point Compliant Mechanisms,” ASME J. Mech. Rob.,
, 2011
"... ..."
The geometry of algorithms with orthogonality constraints
- SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 640 (1 self)
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processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view
A Geometric Framework to Visualize Fuzzy-clustered Data
"... Fuzzy clustering methods have been widely used in many applications. These methods, including fuzzy k-means and Expectation Maximization, allow an object to be assigned to multi-clusters with different degrees of membership. However, the memberships that result from fuzzy clustering algorithms are d ..."
Abstract
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Cited by 1 (1 self)
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are difficult to analyze and visualize, and usually are converted to 0-1 memberships. In this paper, we propose a geometric framework to visualize fuzzy-clustered data. The scheme provides a geometric visualization by grouping the objects with similar cluster membership, and shows clear advantages over existing
The classical r-matrix in a geometric framework ∗
, 1998
"... We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate the theory of the classical r-matrix for integrable systems. In this picture the r-matrix is related to a fourth rank tensor, named the r-tensor, on the configuration space. The r-matrix itself carries one connection type in ..."
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We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate the theory of the classical r-matrix for integrable systems. In this picture the r-matrix is related to a fourth rank tensor, named the r-tensor, on the configuration space. The r-matrix itself carries one connection type
A Statistical Geometric Framework for Reconstruction of Scene Models
"... This paper addresses the problem of reconstructing surface models of indoor scenes from sparse 3D scene structure captured from N camera views. Sparse 3D measurements of real scenes are readily estimated from image sequences using structure-from-motion techniques. Currently there is no general metho ..."
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of real-scenes in the presence of noise. A statistical geometric framework is described that provides a unified approach to probabilistic scene reconstruction from sparse or even dense 3D scene structure. 1
Results 1 - 10
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