Results 1  10
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17,891
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
 Advances in Neural Information Processing Systems 14
, 2001
"... Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
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Cited by 664 (8 self)
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Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
 Neural Computation
, 2003
"... Abstract 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 low dimensional manifold embedded in a high dimensional space. Drawing on the corr ..."
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Cited by 1205 (16 self)
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on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality
Laplacian Eigenmap for Image Retrieval
, 2002
"... Dimensionality reduction has received much attention in image retrieval. Even though the dimension of image feature vectors is normally very high, the embedded dimension is much lower. Before we utilize any image retrieval technique, it is beneficial to first perform dimensionality reduction. Princi ..."
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Cited by 1 (0 self)
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Dimensionality reduction has received much attention in image retrieval. Even though the dimension of image feature vectors is normally very high, the embedded dimension is much lower. Before we utilize any image retrieval technique, it is beneficial to first perform dimensionality reduction
Convergence of laplacian eigenmaps
 In NIPS
, 2006
"... Geometrically based methods for various tasks of machine learning have attracted considerable attention over the last few years. In this paper we show convergence of eigenvectors of the point cloud Laplacian to the eigenfunctions of the LaplaceBeltrami operator on the underlying manifold, thus esta ..."
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Cited by 46 (3 self)
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Geometrically based methods for various tasks of machine learning have attracted considerable attention over the last few years. In this paper we show convergence of eigenvectors of the point cloud Laplacian to the eigenfunctions of the LaplaceBeltrami operator on the underlying manifold, thus
SemiSupervised Learning Literature Survey
, 2006
"... We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter ..."
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Cited by 757 (8 self)
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We review the literature on semisupervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole
spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semisupervised learning. This document is a chapter excerpt from the author’s
doctoral thesis (Zhu, 2005). However the author plans to update the online version frequently to incorporate the latest development in the field. Please obtain the latest
version at http://www.cs.wisc.edu/~jerryzhu/pub/ssl_survey.pdf
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Shape modeling with front propagation: A level set approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods ..."
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Cited by 804 (20 self)
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Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and overcomes some of their limitations. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object’s topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solidhiquid interfaces with curvaturedependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropysatisfying upwind finite difference schemes. We present a variety of ways of computing evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. Index Terms Shape modeling, shape recovery, interface motion, level sets, hyperbolic conservation laws, HamiltonJacobi
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Detecting faces in images: A survey
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... Images containing faces are essential to intelligent visionbased human computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation, and expression recognition. However, many reported methods assume that the faces in an image or an image se ..."
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Cited by 831 (4 self)
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Images containing faces are essential to intelligent visionbased human computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation, and expression recognition. However, many reported methods assume that the faces in an image or an image sequence have been identified and localized. To build fully automated systems that analyze the information contained in face images, robust and efficient face detection algorithms are required. Given a single image, the goal of face detection is to identify all image regions which contain a face regardless of its threedimensional position, orientation, and the lighting conditions. Such a problem is challenging because faces are nonrigid and have a high degree of variability in size, shape, color, and texture. Numerous techniques have been developed to detect faces in a single image, and the purpose of this paper is to categorize and evaluate these algorithms. We also discuss relevant issues such as data collection, evaluation metrics, and benchmarking. After analyzing these algorithms and identifying their limitations, we conclude with several promising directions for future research.
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instantons'. The same equations may be
Results 1  10
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17,891