標(biāo)題: Titlebook: Geometric Structure of High-Dimensional Data and Dimensionality Reduction; Jianzhong Wang Book 2012 Higher Education Press, Beijing and Sp [打印本頁] 作者: MASS 時間: 2025-3-21 17:58
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書目名稱Geometric Structure of High-Dimensional Data and Dimensionality Reduction影響因子(影響力)學(xué)科排名
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書目名稱Geometric Structure of High-Dimensional Data and Dimensionality Reduction讀者反饋
書目名稱Geometric Structure of High-Dimensional Data and Dimensionality Reduction讀者反饋學(xué)科排名
作者: 刺穿 時間: 2025-3-21 23:20
Geometric Structure of High-Dimensional Data and Dimensionality Reduction作者: 摘要記錄 時間: 2025-3-22 03:42 作者: 發(fā)微光 時間: 2025-3-22 07:58 作者: octogenarian 時間: 2025-3-22 10:56
Geometric Structure of High-Dimensional Data system on a data set defines a data graph, which can be considered as a discrete form of a manifold. In Section 2, we introduce the basic concepts of graphs. In Section 3, the spectral graph analysis is introduced as a tool for analyzing the data geometry. Particularly, the Laplacian on a graph is 作者: 終點(diǎn) 時間: 2025-3-22 16:54 作者: 終點(diǎn) 時間: 2025-3-22 18:33 作者: Licentious 時間: 2025-3-22 23:03 作者: ironic 時間: 2025-3-23 04:38
Local Tangent Space Alignmentensional representation of the patch. An alignment technique is introduced in LTSA to align the local representation to a global one. The chapter is organized as follows. In Section 11.1, we describe the method, paying more attention to the global alignment technique. In Section 11.2, the LTSA algor作者: 耕種 時間: 2025-3-23 08:17 作者: Sputum 時間: 2025-3-23 09:43 作者: 寬大 時間: 2025-3-23 16:03
Fast Algorithms for DR Approximation. In Section 15.2, we present the randomized low rank approximation algorithms. In Section 15.3, greedy lank-revealing algorithms (GAT) and randomized anisotropic transformation algorithms (RAT), which approximate leading eigenvalues and eigenvectors of DR kernels, are introduced. Numerical experime作者: 植物學(xué) 時間: 2025-3-23 18:53 作者: OVERT 時間: 2025-3-23 22:12 作者: PRO 時間: 2025-3-24 02:37
https://doi.org/10.1057/978-1-137-53792-8 efficient, yet produces sufficient accuracy with a high probability. In Section 7.1, we give a review of Lipschitz embedding. In Section 7.2, we introduce random matrices and random projection algorithms. In Section 7.3, the justification of the validity of random projection is presented in detail.作者: CHAFE 時間: 2025-3-24 08:00
Jozef Lacko,Ladislav Kusňír,Ivan Slameňn 9.1, we describe the MVU method and the corresponding maximization model. In Section 9.2, we give a brief review of SDP and introduce several popular SDP software packages. The experiments and applications of MVU are included in Section 9.3. The LMVU is discussed in Section 9.4.作者: 貧困 時間: 2025-3-24 12:38
https://doi.org/10.1007/978-1-4615-9813-8ensional representation of the patch. An alignment technique is introduced in LTSA to align the local representation to a global one. The chapter is organized as follows. In Section 11.1, we describe the method, paying more attention to the global alignment technique. In Section 11.2, the LTSA algor作者: 小溪 時間: 2025-3-24 15:24 作者: 預(yù)定 時間: 2025-3-24 22:39 作者: Adjourn 時間: 2025-3-25 00:53
Eating Characteristics and Temperament. In Section 15.2, we present the randomized low rank approximation algorithms. In Section 15.3, greedy lank-revealing algorithms (GAT) and randomized anisotropic transformation algorithms (RAT), which approximate leading eigenvalues and eigenvectors of DR kernels, are introduced. Numerical experime作者: 冰雹 時間: 2025-3-25 06:23 作者: giggle 時間: 2025-3-25 09:33 作者: 用肘 時間: 2025-3-25 12:46
Geometric Structure of High-Dimensional Datahe data geometry is inherited from the manifold. Since the underlying manifold is hidden, it is hard to know its geometry by the classical manifold calculus. The data graph is a useful tool to reveal the data geometry. To construct a data graph, we first find the neighborhood system on the data, whi作者: PHAG 時間: 2025-3-25 16:36
Data Models and Structures of Kernels of DRrs, which represent the objects of interest. In the second type, the data describe the similarities (or dissimilarities) of objects that cannot be digitized or hidden. The output of a DR processing with an input of the first type is a low-dimensional data set, having the same cardinality as the inpu作者: Climate 時間: 2025-3-25 23:09 作者: admission 時間: 2025-3-26 03:47 作者: Prostatism 時間: 2025-3-26 05:53
Random Projectionus norm of the matrix of data difference. The reduced data of PCA consists of several leading eigenvectors of the covariance matrix of the data set. Hence, PCA may not preserve the local separation of the original data. To respect local properties of data in dimensionality reduction (DR), we employ 作者: 暫時別動 時間: 2025-3-26 11:24 作者: 課程 時間: 2025-3-26 14:50 作者: 生銹 時間: 2025-3-26 17:52 作者: 長矛 時間: 2025-3-26 23:42
Local Tangent Space Alignmentame geometric intuitions as LLE: If a data set is sampled from a smooth manifold, then the neighbors of each point remain nearby and similarly co-located in the low dimensional space. LTSA uses a different approach to the embedded space compared with LLE. In LLE, each point in the data set is linear作者: HATCH 時間: 2025-3-27 02:22 作者: Silent-Ischemia 時間: 2025-3-27 06:25 作者: Monolithic 時間: 2025-3-27 12:56
Diffusion Mapsbserved data resides. In Chapter 12, it was pointed out that Laplace-Beltrami operator directly links up with the heat diffusion operator by the exponential formula for positive self-adjoint operators. Therefore, they have the same eigenvector set, and the corresponding eigenvalues are linked by the作者: 廚房里面 時間: 2025-3-27 17:36
Fast Algorithms for DR Approximationta vectors is very large. The spectral decomposition of a large dimensioanl kernel encounters difficulties in at least three aspects: large memory usage, high computational complexity, and computational instability. Although the kernels in some nonlinear DR methods are sparse matrices, which enable 作者: 六邊形 時間: 2025-3-27 18:59 作者: PANT 時間: 2025-3-28 00:14
https://doi.org/10.1007/978-3-642-27497-8HEP; dimensionality reduction; geometric diffusion; intrinsic dimensionality of data; manifolds; neighbor作者: 步兵 時間: 2025-3-28 05:59
St Ephrem and the Pursuit of Wisdom2 discusses the acquisition of high-dimensional data. When dimensions of the data are very high, we shall meet the so-called curse of dimensionality, which is discussed in Section 3. The concepts of extrinsic and intrinsic dimensions of data are discussed in Section 4. It is pointed out that most hi作者: 吸引人的花招 時間: 2025-3-28 09:28 作者: Adulterate 時間: 2025-3-28 11:43
https://doi.org/10.1007/978-1-349-22299-5he data geometry is inherited from the manifold. Since the underlying manifold is hidden, it is hard to know its geometry by the classical manifold calculus. The data graph is a useful tool to reveal the data geometry. To construct a data graph, we first find the neighborhood system on the data, whi作者: FAWN 時間: 2025-3-28 16:18
Kevin McDermott,Vítězslav Sommerrs, which represent the objects of interest. In the second type, the data describe the similarities (or dissimilarities) of objects that cannot be digitized or hidden. The output of a DR processing with an input of the first type is a low-dimensional data set, having the same cardinality as the inpu作者: 討人喜歡 時間: 2025-3-28 22:45 作者: Kinetic 時間: 2025-3-29 02:59 作者: painkillers 時間: 2025-3-29 04:32 作者: 使更活躍 時間: 2025-3-29 09:24 作者: 迷住 時間: 2025-3-29 13:27
Jozef Lacko,Ladislav Kusňír,Ivan Slameňetween the pairs of all neighbors of each point in the data set. Since the method keeps the local maximum variance in dimensionality reduction processing, it is called maximum variance unfolding (MVU). Like multidimensional scaling (MDS), MVU can be applied to the cases that only the local similarit作者: 儲備 時間: 2025-3-29 18:25 作者: flaggy 時間: 2025-3-29 20:02 作者: geriatrician 時間: 2025-3-30 00:05
https://doi.org/10.1007/978-3-322-82834-7n a low-dimentional manifold .. Let . be the coordinate mapping on . so that . = .(.)is a DR of .. Each component of the coordinate mapping . is a linear function on .. Hence, all components of . nearly reside on the numerically null space of the Laplace-Beltrsmi operator on .. In Leigs method, a La作者: 領(lǐng)袖氣質(zhì) 時間: 2025-3-30 07:07
https://doi.org/10.1007/978-1-4612-0553-1 conceptual framework of HLLE may be viewed as a modification of the Laplacian Eigenmaps framework. Let . be the observed high-dimensional data which reside on a low-dimentional manifold . and . be the coordinate mapping on . so that . = .(.)is a DR of .. In Laplacian eigenmaps method, . is found in作者: 避開 時間: 2025-3-30 11:10
