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Manifold regularization: A geometric framework for learning from labeled and unlabeled examples

by Mikhail Belkin, Partha Niyogi, Vikas Sindhwani - 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 - Cited by 578 (16 self) - Add to MetaCart
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

by Eleazar Eskin, Andrew Arnold, Michael Prerau, Leonid Portnoy, Sal Stolfo - 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 - Cited by 238 (9 self) - Add to MetaCart
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

✪ Geometric Framework for Duality and Penalty

by Asu Ozdaglar , 2007
"... minimize f0(x) ..."
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minimize f0(x)

New geometrical frameworks for Classical Impulsive

by Stefano Pasquero - 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 ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
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

by unknown authors
"... 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

by Girish Krishnan , Assistant Professor Charles Kim , Professor Sridhar Kota - Synthesis of Single Point Compliant Mechanisms,” ASME J. Mech. Rob., , 2011
"... ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
Abstract not found

The geometry of algorithms with orthogonality constraints

by Alan Edelman, Tomás A. Arias, Steven T. Smith - 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 ..."
Abstract - Cited by 640 (1 self) - Add to MetaCart
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

by Yuanquan Zhang, Luis Rueda
"... 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 - Cited by 1 (1 self) - Add to MetaCart
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 ∗

by Kjell Rosquist , 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

by Anastasios Manessis, Adrian Hilton, Phil Mclauchlan, Phil Palmer
"... 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
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