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Tangent space
, 2014
"... nsid disc ratel we employ a greedy technique that partitions manifold samples into groups, which are approximated by low dimensional subspaces. We start by considering each manifold sample as a different group and we use the difference of local tangents to determine e of to fac ensio a smaller dimen ..."
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nsid disc ratel we employ a greedy technique that partitions manifold samples into groups, which are approximated by low dimensional subspaces. We start by considering each manifold sample as a different group and we use the difference of local tangents to determine e of to fac ensio a smaller
1Tangent spaces to metric spaces
"... Abstract. We introduce a tangent space at an arbitrary point of a general metric space. It is proved that all tangent spaces are complete. The conditions under which these spaces have a finite cardinality are found. ..."
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Abstract. We introduce a tangent space at an arbitrary point of a general metric space. It is proved that all tangent spaces are complete. The conditions under which these spaces have a finite cardinality are found.
4. Tangent Spaces 8
"... Abstract. This paper will provide some simple explanation about matrix Lie groups. I intend for the reader to have a background in calculus, pointset topology, group theory, and linear algebra, particularly the Spectral Theorem. ..."
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Abstract. This paper will provide some simple explanation about matrix Lie groups. I intend for the reader to have a background in calculus, pointset topology, group theory, and linear algebra, particularly the Spectral Theorem.
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2004
"... Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized ..."
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Cited by 261 (15 self)
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data points sampled with noise from the manifold, we represent the local geometry of the manifold using tangent spaces learned by fitting an affine subspace in a neighborhood of each data point. Those tangent spaces are aligned to give the internal global coordinates of the data points with respect
Tangent Spaces of Rational Matrix Functions*
"... We consider the task of determining tangent spaces for classes of rational matrix valued functions. Our analysis is based on methods from control theory, and in particular the theory of polynomial models. Explicit descriptions of tangent spaces of rational transfer functions, stable rational transfe ..."
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Cited by 1 (0 self)
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We consider the task of determining tangent spaces for classes of rational matrix valued functions. Our analysis is based on methods from control theory, and in particular the theory of polynomial models. Explicit descriptions of tangent spaces of rational transfer functions, stable rational
On the Tangent Space to the Universal Teichmüller Space
, 1992
"... We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space: (1) The realanalytic model consisting of Zygmund class vector fields on the unit circle; (2) The complexanalytic model comprising 1parameter families of schlicht func ..."
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Cited by 6 (1 self)
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We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space: (1) The realanalytic model consisting of Zygmund class vector fields on the unit circle; (2) The complexanalytic model comprising 1parameter families of schlicht
Image tangent space for image retrieval
 18th IEEE International Conference on Pattern Recognition Vol
, 2006
"... Image tangent space is actually highlevel semantic space learned from lowlevel feature space by modified local tangent space alignment which was originally proposed for nonlinear manifold learning. Under the assumption that a data point in image space can be linearly approximated by some nearest ..."
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Cited by 1 (0 self)
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Image tangent space is actually highlevel semantic space learned from lowlevel feature space by modified local tangent space alignment which was originally proposed for nonlinear manifold learning. Under the assumption that a data point in image space can be linearly approximated by some nearest
TANGENT SPACES OF MULTIPLY SYMPLECTIC GRASSMANNIANS
"... Abstract. In this note, we give a new proof of a technical result in [Ossa] related to proving expected dimension for rank 2 BrillNoether loci with special determinant such that h1(det) = 2. Moreover, we give a necessary and sufficient condition for the tangent space of the multiply symplectic G ..."
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Abstract. In this note, we give a new proof of a technical result in [Ossa] related to proving expected dimension for rank 2 BrillNoether loci with special determinant such that h1(det) = 2. Moreover, we give a necessary and sufficient condition for the tangent space of the multiply symplectic
Results 1  10
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