"Isomap"의 두 판 사이의 차이

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== 노트 ==
 
== 노트 ==
  
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* The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph.<ref name="ref_5b8b">[https://www.emerald.com/insight/content/doi/10.1108/IJICC-03-2016-0014/full/html An improved Isomap method for manifold learning]</ref>
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* The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths.<ref name="ref_5b8b" />
 +
* The purpose of this paper is to speed up Isomap.<ref name="ref_5b8b" />
 +
* Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.<ref name="ref_9aa2">[https://www.spiedigitallibrary.org/conference-proceedings-of-spie/9399/939904/Adaptive-graph-construction-for-Isomap-manifold-learning/10.1117/12.2082646.full Adaptive graph construction for Isomap manifold learning]</ref>
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* : S-ISOMAP is a manifold learning algorithm, which is a supervised variant of ISOMAP.<ref name="ref_dd7e">[https://www.lamda.nju.edu.cn/code_S-Isomap.ashx S-Isomap]</ref>
 +
* Experiment results show that 3N-Isomap is a more practical and simple algorithm than Isomap.<ref name="ref_36b0">[https://www.scientific.net/AMR.219-220.994 Natural Nearest Neighbor for Isomap Algorithm without Free-Parameter]</ref>
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* A SemiSupervised local multimanifold Isomap by linear embedding is proposed.<ref name="ref_abbd">[https://dl.acm.org/citation.cfm?id=3178636 Semi-supervised local multi-manifold Isomap by linear embedding for feature extraction]</ref>
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* We mainly evaluate SSMM-Isomap for manifold feature learning, data clustering and classification.<ref name="ref_abbd" />
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* It is becoming more and more difficult for MDS and ISOMAP to solve the full eigenvector problem with the increasing sample size.<ref name="ref_3500">[https://scialert.net/fulltextmobile/?doi=itj.2012.380.383 A Fast Manifold Learning Algorithm]</ref>
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* The basic idea: In MDS and ISOMAP, solving the full eigenvector problem leads to higher complexity.<ref name="ref_3500" />
 +
* If MDS and ISOMAP also solve a sparse eigenvector problem, its execution will greatly speed up.<ref name="ref_3500" />
 +
* For ISOMAP, we computed the time of solving the full NxN eigenvector problem.<ref name="ref_3500" />
 +
* the result of ISOMAP is showed below, which indicates the successful extraction of the underlying manifold in original 3D space.<ref name="ref_f35b">[https://sites.google.com/site/machinelearningbybobon/home/dr/isomap Machine Learning]</ref>
 +
* Isomap can be viewed as an extension of Multi-dimensional Scaling (MDS) or Kernel PCA.<ref name="ref_9fb3">[http://semantic-portal.net/base-machine-learning-scikit-learn-unsupervised-manifold-learning Semantic portal — learn smart!]</ref>
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* Isomap seeks a lower-dimensional embedding which maintains geodesic distances between all points.<ref name="ref_9fb3" />
 +
* The algorithm can be selected by the user with the path_method keyword of Isomap .<ref name="ref_9fb3" />
 +
* The eigensolver can be specified by the user with the path_method keyword of Isomap .<ref name="ref_9fb3" />
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* To give you a solution first, you can use eigen_solver='dense' when using Isomap .<ref name="ref_699a">[https://stackoverflow.com/questions/44852406/python-scikit-learn-isomap-results-seem-random-but-no-possibility-to-set-rando Python: scikit-learn isomap results seem random, but no possibility to set random_state]</ref>
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* No, there is currently no way to set a seed for KernelPCA from Isomap .<ref name="ref_699a" />
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* L-Isomap reduces both the time and space complexities of Isomap significantly.<ref name="ref_48fb">[https://www.hindawi.com/journals/mpe/2015/241436/ Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection]</ref>
 +
* So far, we have presented EL-Isomap through comparing with L-Isomap (and Isomap) in various viewpoints.<ref name="ref_48fb" />
 +
* The D embeddings of the data set were calculated by LLE, Laplacian eigenmap, Isomap, L-Isomap, and EL-Isomap.<ref name="ref_48fb" />
 +
* The neighborhood sizes of LLE, Laplacian eigenmap, Isomap, L-Isomap, and EL-Isomap are set as , , , , and , respectively.<ref name="ref_48fb" />
 
* Isomap is distinguished by its use of the geodesic distance induced by a neighborhood graph embedded in the classical scaling.<ref name="ref_cdb3">[https://en.wikipedia.org/wiki/Isomap Wikipedia]</ref>
 
* Isomap is distinguished by its use of the geodesic distance induced by a neighborhood graph embedded in the classical scaling.<ref name="ref_cdb3">[https://en.wikipedia.org/wiki/Isomap Wikipedia]</ref>
 
* In a similar manner, the geodesic distance matrix in Isomap can be viewed as a kernel matrix.<ref name="ref_cdb3" />
 
* In a similar manner, the geodesic distance matrix in Isomap can be viewed as a kernel matrix.<ref name="ref_cdb3" />
−
* Isomap can be viewed as an extension of Multi-dimensional Scaling (MDS) or Kernel PCA.<ref name="ref_9fb3">[http://scikit-learn.org/stable/modules/manifold.html 2.2. Manifold learning — scikit-learn 0.23.2 documentation]</ref>
+
* Isomap can be performed with the object Isomap .<ref name="ref_ef6d">[http://scikit-learn.org/stable/modules/manifold.html 2.2. Manifold learning — scikit-learn 0.23.2 documentation]</ref>
−
* Isomap seeks a lower-dimensional embedding which maintains geodesic distances between all points.<ref name="ref_9fb3" />
+
* The eigensolver can be specified by the user with the eigen_solver keyword of Isomap .<ref name="ref_ef6d" />
−
* Isomap can be performed with the object Isomap .<ref name="ref_9fb3" />
 
−
* The algorithm can be selected by the user with the path_method keyword of Isomap .<ref name="ref_9fb3" />
 
 
* Isomap is viewed as a variant of metric multidimensional scaling (MDS) to model nonlinear data using its geodesic distance.<ref name="ref_c313">[https://link.springer.com/article/10.1007/s42979-020-00179-y An Extended Isomap Approach for Nonlinear Dimension Reduction]</ref>
 
* Isomap is viewed as a variant of metric multidimensional scaling (MDS) to model nonlinear data using its geodesic distance.<ref name="ref_c313">[https://link.springer.com/article/10.1007/s42979-020-00179-y An Extended Isomap Approach for Nonlinear Dimension Reduction]</ref>
 
* No such type of method has been used in recent years from the Isomap perspective.<ref name="ref_c313" />
 
* No such type of method has been used in recent years from the Isomap perspective.<ref name="ref_c313" />
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===소스===
 
===소스===
 
  <references />
 
  <references />
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q6086067 Q6086067]
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===Spacy 패턴 목록===
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* [{'LEMMA': 'Isomap'}]

2021년 2월 17일 (수) 01:55 기준 최신판

노트

  • The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph.[1]
  • The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths.[1]
  • The purpose of this paper is to speed up Isomap.[1]
  • Next, the proposed approach is applied to two image data sets and achieved improved performances over standard Isomap.[2]
  • : S-ISOMAP is a manifold learning algorithm, which is a supervised variant of ISOMAP.[3]
  • Experiment results show that 3N-Isomap is a more practical and simple algorithm than Isomap.[4]
  • A SemiSupervised local multimanifold Isomap by linear embedding is proposed.[5]
  • We mainly evaluate SSMM-Isomap for manifold feature learning, data clustering and classification.[5]
  • It is becoming more and more difficult for MDS and ISOMAP to solve the full eigenvector problem with the increasing sample size.[6]
  • The basic idea: In MDS and ISOMAP, solving the full eigenvector problem leads to higher complexity.[6]
  • If MDS and ISOMAP also solve a sparse eigenvector problem, its execution will greatly speed up.[6]
  • For ISOMAP, we computed the time of solving the full NxN eigenvector problem.[6]
  • the result of ISOMAP is showed below, which indicates the successful extraction of the underlying manifold in original 3D space.[7]
  • Isomap can be viewed as an extension of Multi-dimensional Scaling (MDS) or Kernel PCA.[8]
  • Isomap seeks a lower-dimensional embedding which maintains geodesic distances between all points.[8]
  • The algorithm can be selected by the user with the path_method keyword of Isomap .[8]
  • The eigensolver can be specified by the user with the path_method keyword of Isomap .[8]
  • To give you a solution first, you can use eigen_solver='dense' when using Isomap .[9]
  • No, there is currently no way to set a seed for KernelPCA from Isomap .[9]
  • L-Isomap reduces both the time and space complexities of Isomap significantly.[10]
  • So far, we have presented EL-Isomap through comparing with L-Isomap (and Isomap) in various viewpoints.[10]
  • The D embeddings of the data set were calculated by LLE, Laplacian eigenmap, Isomap, L-Isomap, and EL-Isomap.[10]
  • The neighborhood sizes of LLE, Laplacian eigenmap, Isomap, L-Isomap, and EL-Isomap are set as , , , , and , respectively.[10]
  • Isomap is distinguished by its use of the geodesic distance induced by a neighborhood graph embedded in the classical scaling.[11]
  • In a similar manner, the geodesic distance matrix in Isomap can be viewed as a kernel matrix.[11]
  • Isomap can be performed with the object Isomap .[12]
  • The eigensolver can be specified by the user with the eigen_solver keyword of Isomap .[12]
  • Isomap is viewed as a variant of metric multidimensional scaling (MDS) to model nonlinear data using its geodesic distance.[13]
  • No such type of method has been used in recent years from the Isomap perspective.[13]
  • Second section provides an overview and background work, which is followed by a brief discussion on manifold learning and Isomap.[13]
  • Isomap stands for isometric mapping.[14]
  • Isomap starts by creating a neighborhood network.[14]
  • Isomap uses the above principle to create a similarity matrix for eigenvalue decomposition.[14]
  • Classical MDS uses the euclidean distances as the similarity metric while isomap uses geodesic distances.[14]
  • We will use the neighborhood graph to achieve ISOMAP.[15]
  • kNN(k-Nearest Neighbors), the most common choice for ISOMAP, connects each data point to its k nearest neighbors.[15]
  • It uses ISOMAP and it embeds 4096 pixels and 698 face pictures into 2D space and lines them onto light direction and up-down pose.[15]

소스

  1. ↑ 1.0 1.1 1.2 An improved Isomap method for manifold learning
  2. ↑ Adaptive graph construction for Isomap manifold learning
  3. ↑ S-Isomap
  4. ↑ Natural Nearest Neighbor for Isomap Algorithm without Free-Parameter
  5. ↑ 5.0 5.1 Semi-supervised local multi-manifold Isomap by linear embedding for feature extraction
  6. ↑ 6.0 6.1 6.2 6.3 A Fast Manifold Learning Algorithm
  7. ↑ Machine Learning
  8. ↑ 8.0 8.1 8.2 8.3 Semantic portal — learn smart!
  9. ↑ 9.0 9.1 Python: scikit-learn isomap results seem random, but no possibility to set random_state
  10. ↑ 10.0 10.1 10.2 10.3 Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection
  11. ↑ 11.0 11.1 Wikipedia
  12. ↑ 12.0 12.1 2.2. Manifold learning — scikit-learn 0.23.2 documentation
  13. ↑ 13.0 13.1 13.2 An Extended Isomap Approach for Nonlinear Dimension Reduction
  14. ↑ 14.0 14.1 14.2 14.3 Tutorial: Dimension Reduction
  15. ↑ 15.0 15.1 15.2 VC: ISOMAP, Manifolds Learning

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LEMMA': 'Isomap'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Isomap&oldid=51607"