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Information Sciences, ISSN 0020-0255, 01/2020, Volume 508, pp. 1 - 21
Subspace techniques have gained much attention for their remarkable efficiency in representing high-dimensional data, in which sparse subspace clustering (SSC)... 
Subspace clustering | Low-rank representation | Local tangent space | Manifold learning | Locally linear embedding | REGRESSION | ALGORITHM | REPRESENTATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | MODEL | FEATURE-SELECTION | ALTERNATING DIRECTION METHOD | NORM
Journal Article
Journal of Neural Engineering, ISSN 1741-2560, 06/2018, Volume 15, Issue 4, p. 046021
Journal Article
Neurocomputing, ISSN 0925-2312, 2007, Volume 70, Issue 7, pp. 1547 - 1553
In this paper, linear local tangent space alignment (LLTSA), as a novel linear dimensionality reduction algorithm, is proposed. It uses the tangent space in... 
Dimensionality reduction | Linear local tangent space alignment (LLTSA) | Manifold learning | Face recognition | face recognition | dimensionality reduction | linear local tangent space alignment (LLTSA) | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | manifold learning | Biometry | Algorithms
Journal Article
Annals of statistics, ISSN 0090-5364, 10/2017, Volume 45, Issue 5, pp. 1951 - 1987
We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are... 
Primary 62G05 | U-statistic | nonparametric estimation | 62G20 | tangent space | 62F25 | influence function | Nonlinear functional
Journal Article
Annals of Statistics, ISSN 0090-5364, 10/2017, Volume 45, Issue 5, pp. 1951 - 1987
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method employs U-statistics that are based on... 
Nonparametric estimation | Influence function | U-statistic | Tangent space | Nonlinear functional | DENSITY | INTEGRAL FUNCTIONALS | ORDER | SCORE | nonparametric estimation | STATISTICS & PROBABILITY | tangent space | influence function | ADAPTIVE ESTIMATION | EFFICIENCY
Journal Article
by Cai, HQ and Cai, JF and Wei, K
JOURNAL OF MACHINE LEARNING RESEARCH, ISSN 1532-4435, 2019, Volume 20
We study robust PCA for the fully observed setting, which is about separating a low rank matrix L and a sparse matrix S from their sum D = L + S. In this... 
Robust PCA | Matrix Manifold | Subspace Projection | MINIMIZATION ALGORITHM | Alternating Projections | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Tangent Space | RANK MATRIX COMPLETION
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 10040, pp. 541 - 552
Journal Article
Journal of Algebra, ISSN 0021-8693, 2019
A rational map ϕ:P ⇢P is defined by homogeneous polynomials of a common degree d. We establish a linear bound in terms of d for the number of (m−1)-dimensional... 
Jacobian matrices | Rational maps | Blow-up algebras | Fibers of rational maps | Tangent space
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 2255 - 2270
weakly filtered and diffeological spaces, whose tangent spaces are easier to understand. These are the diffeological spaces whose categories of pointed plots... 
Tangent space | Tangent bundle | Diffeological bundle | MATHEMATICS | MATHEMATICS, APPLIED | diffeological bundle | tangent bundle | Mathematics - Differential Geometry
Journal Article
Pattern Recognition, ISSN 0031-3203, 2009, Volume 42, Issue 9, pp. 2054 - 2066
Dimensionality reduction is a big challenge in many areas. A large number of local approaches, stemming from statistics or geometry, have been developed.... 
Dimensionality reduction | Laplacian eigenmaps | Manifold learning | Local tangent space alignment | Locally linear embedding | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2008, Volume 39, Issue 1, pp. 419 - 441
Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high-dimensional spaces. We consider the case where data... 
Computational Mathematics and Numerical Analysis | Fundamental Form | Condition Number | Mathematics | Discrete Comput Geom | Combinatorics | Simplicial Complex | Tangent Space | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Computer science | Information management | Geometry | Probability | Data analysis | Theory
Journal Article
Neurocomputing, ISSN 0925-2312, 01/2013, Volume 99, pp. 423 - 438
In recent times the dimensionality reduction technique has been widely exploited in pattern recognition and data mining. The global linear algorithms... 
Local tangent space | Principal Component Analysis | Similarity embedding | Cosine metric | TANGENT-SPACE ALIGNMENT | NONLINEAR DIMENSIONALITY REDUCTION | FACE REPRESENTATION | EIGENMAPS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Computer science | Algorithms | Universities and colleges | Data mining | Analysis
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 08/2018, Volume 116, pp. 40 - 51
For an n-dimensional real hyperbolic manifold M, we calculate the Zariski tangent space of a character variety χ(π1(M),SL(n+1,R)), n>2 at Fuchsian locus to... 
Weil's local rigidity | Zariski tangent space | Real projective structure | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | LIE-GROUPS | SURFACES | lie-groups | surfaces | Mathematics | Matematik | space
Journal Article
Journal Article
by Ren, HH and Yu, XL and Wang, XG
JOURNAL OF APPLIED REMOTE SENSING, ISSN 1931-3195, 11/2019, Volume 13, Issue 4
We present a modified local tangent space alignment (LTSA) algorithm, called supervised kernel discriminant local tangent space alignment (SKDLTSA), for radar... 
ENVIRONMENTAL SCIENCES | REMOTE SENSING | feature extraction | local tangent space alignment | radar target recognition | FACE RECOGNITION | DICTIONARY | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | high-resolution range profile
Journal Article
Measurement Science and Technology, ISSN 0957-0233, 03/2017, Volume 28, Issue 5, p. 55009
Extraction of sensitive features is a challenging but key task in data-driven machinery running state identification. Aimed at solving this problem, a method... 
feature fusion and extraction | vibration signal | running state identification | local tangent space alignment | manifold learning | DIMENSIONALITY REDUCTION | ENERGY | CLASSIFICATION | VIBRATION SIGNALS | COMPONENT ANALYSIS | GEARBOX | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | FAULT-DIAGNOSIS | ENTROPY
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2017, Volume 47, Issue 4, pp. 1169 - 1225
Let K be an algebraically closed field of characteristic 0, and let H-AK(n mu) denote the Hilbert scheme of mu points of A(K)(n). An elementary component E of... 
Hilbert scheme of points | Small tangent space | Generic algebra | Elementary component | MATHEMATICS | small tangent space | elementary component
Journal Article
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