Results 1 - 10 of 3,428

Ranking on Data Manifolds

by Dengyong Zhou, Jason Weston, Arthur Gretton, Olivier Bousquet, Bernhard Schölkopf - Advances in Neural Information Processing Systems 16 , 2004
"... The Google search engine has enjoyed huge success with its web page ranking algorithm, which exploits global, rather than local, hyperlink structure of the web using random walks. Here we propose a simple universal ranking algorithm for data lying in the Euclidean space, such as text or image data. ..."
Abstract - Cited by 144 (1 self) - Add to MetaCart
. The core idea of our method is to rank the data with respect to the intrinsic manifold structure collectively revealed by a great amount of data. Encouraging experimental results from synthetic, image, and text data illustrate the validity of our method.

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

Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

by Mikhail Belkin, Partha Niyogi , 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 low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondenc ..."
Abstract - Cited by 1226 (15 self) - Add to MetaCart
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

Laplacian eigenmaps and spectral techniques for embedding and clustering.

by Mikhail Belkin , Partha Niyogi - Proceeding of Neural Information Processing Systems, , 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator 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 ..."
Abstract - Cited by 668 (7 self) - Add to MetaCart
Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator 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

Surface reconstruction from unorganized points

by Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, Werner Stuetzle - COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS) , 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
Abstract - Cited by 815 (8 self) - Add to MetaCart
We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed

Reconstruction and Representation of 3D Objects with Radial Basis Functions

by J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, T. R. Evans - Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH , 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
Abstract - Cited by 505 (1 self) - Add to MetaCart
We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs

Querying Heterogeneous Information Sources Using Source Descriptions

by Alon Levy, Anand Rajaraman, Joann Ordille , 1996
"... We witness a rapid increase in the number of structured information sources that are available online, especially on the WWW. These sources include commercial databases on product information, stock market information, real estate, automobiles, and entertainment. We would like to use the data stored ..."
Abstract - Cited by 724 (34 self) - Add to MetaCart
We witness a rapid increase in the number of structured information sources that are available online, especially on the WWW. These sources include commercial databases on product information, stock market information, real estate, automobiles, and entertainment. We would like to use the data

Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams

by Leonidas Guibas, Jorge Stolfi - ACM Tmns. Graph , 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract - Cited by 534 (11 self) - Add to MetaCart
to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings

A volumetric method for building complex models from range images,”

by Brian Curless , Marc Levoy - in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM, , 1996
"... Abstract A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, ..."
Abstract - Cited by 1020 (17 self) - Add to MetaCart
with one range image at a time, we first scan-convert it to a distance function, then combine this with the data already acquired using a simple additive scheme. To achieve space efficiency, we employ a run-length encoding of the volume. To achieve time efficiency, we resample the range image to align

Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds

by Lawrence K. Saul, Sam T. Roweis, Yoram Singer - Journal of Machine Learning Research , 2003
"... The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. ..."
Abstract - Cited by 385 (10 self) - Add to MetaCart
The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.
Results 1 - 10 of 3,428