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Probabilistic Tangent Subspace: A Unified View
 PROC. INT’L CONF. MACHINE LEARNING
, 2004
"... Tangent Distance (TD) is one classical method for invariant pattern classification. However, ..."
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Cited by 2 (1 self)
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Tangent Distance (TD) is one classical method for invariant pattern classification. However,
Rights Compositio Mathematica. Copyright © London MathematicalSociety. Characterization of Certain Holomorphic Geodesic Cycles on Quotients of Bounded Symmetric Domains in terms of Tangent Subspaces
, 2000
"... Characterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspaces ..."
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Characterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspaces
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
Angles Between Subspaces and Their Tangents
, 2013
"... Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomp ..."
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decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and nonorthonormal bases for subspaces, as well as projectors. Such a construction has applications, e
Principal Angles Between Subspaces and Their Tangents
, 2012
"... Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced and used via their cosines. The tangents of PABS have attracted relatively less attention, but are im ..."
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Cited by 1 (0 self)
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Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced and used via their cosines. The tangents of PABS have attracted relatively less attention
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
Estimation of tangent planes for neighborhood graph correction
 In: Proceedings of ESANN  European Symposium on Artificial Neural Networks
, 2007
"... [7] use spectral decomposition based on a nearest neighborhood graph. In the presence of shortcuts (union of two points whose distance measure along the submanifold is actually large), the resulting embbeding will be unsatisfactory. This paper proposes an algorithm to correct wrong graph connection ..."
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Cited by 3 (0 self)
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connections based on the tangent subspace of the manifold at each point. This leads to the estimation of the proper and adaptive number of neighbors for each point in the dataset. Experiments show graph construction improvement.
An investigation of the tangent splash of a subplane of PG(2
"... planes AMS code: 51E20 In PG(2, q3), let pi be a subplane of order q that is tangent to `∞. The tangent splash of pi is defined to be the set of q2 + 1 points on ` ∞ that lie on a line of pi. This article investigates properties of the tangent splash. We prove results about sublines contained in a t ..."
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tangent splash, transitivity results, and counting results. We also show that a tangent splash is a Sherk surface. Further, in the BruckBose representation of PG(2, q3) in PG(6, q), we prove the existence of a set of cover planes of a tangent splash, and investigate the tangent subspace of a point of pi
Projective Subspaces in the Variety of Normal Sections and Tangent Spaces to a Symmetric Space
 ZBL 0908.53029
, 1998
"... In the present article we continue the study of the variety X [M ] associated to pointwise planar normal sections of a natural imbedding for a flag manifold M . When M = G=T is the manifold of complete flags of a compact simple Lie group G; we obtain two results about subspaces of the tangent spac ..."
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In the present article we continue the study of the variety X [M ] associated to pointwise planar normal sections of a natural imbedding for a flag manifold M . When M = G=T is the manifold of complete flags of a compact simple Lie group G; we obtain two results about subspaces of the tangent
Results 1  10
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12,464