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Nonlocal estimation of manifold structure
 Neural Computation
, 2006
"... We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality. This observation invites an exploration of nonlocal manifold learning algorithms, ..."
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Cited by 14 (2 self)
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, which attempt to discover shared structure in the tangent planes at different positions. A criterion for such an algorithm is proposed and experiments 1 estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms: it is able
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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on such a manifold and Taylor coefficients of periods of Hodge structures considered as functions on the moduli space of complex structures on a mirror manifold. Recently it has been realized that one can make predictions for numbers of curves of positive genera and also on CalabiYau manifolds of arbitrary
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami 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 ..."
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Cited by 668 (7 self)
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of t he same object is the number of degrees of freedom of the camera in fact the space has the natural structure of a manifold embedded in rn: n2 . While there is a large body of work on dimensionality reduction in general, most existing approaches do not explicitly take into account the structure
On the Manifold Structure of the Space of Brain Images
"... Abstract. This paper investigates an approach to model the space of brain images through a lowdimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approx ..."
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Cited by 15 (1 self)
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the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed
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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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
Robust Multiple Manifolds Structure Learning
"... We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local tangent space by weighted lowrank matrix factorization. In ..."
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Cited by 6 (0 self)
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We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local tangent space by weighted lowrank matrix factorization
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 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 ..."
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Cited by 534 (11 self)
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of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
Querying Heterogeneous Information Sources Using Source Descriptions
, 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 ..."
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Cited by 724 (34 self)
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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
A COMPOSITION FORMULA FOR MANIFOLD STRUCTURES
"... Abstract. The structure set S T OP (M) of an ndimensional topological manifold M for n � 5 has a homotopy invariant functorial abelian group structure, by the algebraic version of the BrowderNovikovSullivanWall surgery theory. An element (N, f) ∈ S T OP (M) is an equivalence class of ndimensio ..."
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Cited by 4 (0 self)
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Abstract. The structure set S T OP (M) of an ndimensional topological manifold M for n � 5 has a homotopy invariant functorial abelian group structure, by the algebraic version of the BrowderNovikovSullivanWall surgery theory. An element (N, f) ∈ S T OP (M) is an equivalence class of n
Results 1  10
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7,767