"Persistent homology"의 두 판 사이의 차이

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==관련된 항목들==
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==리뷰논문, 에세이, 강의노트==
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==리뷰, 에세이, 강의노트==
 
* [http://www.ams.org/notices/201101/rtx110100036p.pdf What is Persistent Homology?]
 
* [http://www.ams.org/notices/201101/rtx110100036p.pdf What is Persistent Homology?]
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==관련논문==
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* Otter, Nina, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, and Heather A. Harrington. ‘A Roadmap for the Computation of Persistent Homology’. arXiv:1506.08903 [cs, Math], 29 June 2015. http://arxiv.org/abs/1506.08903.
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* Lampret, Leon. ‘Tensor, Symmetric, Exterior, and Other Powers of Persistence Modules’. arXiv:1503.08266 [math], 28 March 2015. http://arxiv.org/abs/1503.08266.
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* Jaquette, Jonathan, and Miroslav Kramár. “Rigorous Computation of Persistent Homology.” arXiv:1412.1805 [math], December 4, 2014. http://arxiv.org/abs/1412.1805.
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q17099562 Q17099562]
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===말뭉치===
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# A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given.<ref name="ref_e0b00e35">[https://www.sciencedirect.com/science/article/pii/S0047259X1000117X Exploring uses of persistent homology for statistical analysis of landmark-based shape data]</ref>
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# Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained.<ref name="ref_e0b00e35" />
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# A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects.<ref name="ref_e0b00e35" />
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# Persistent homology (PH), a tool from topological data analysis (TDA), serves as the basis for this work.<ref name="ref_5e0f74ac">[https://www.nature.com/articles/s41598-018-36798-y Persistent Homology for the Quantitative Evaluation of Architectural Features in Prostate Cancer Histology]</ref>
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# We use persistent homology, which allows us to study these features at varying scales.<ref name="ref_5e0f74ac" />
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# 3 is an illustrative example that shows the steps of computing persistent homology on a simple three gland example.<ref name="ref_5e0f74ac" />
 +
# Persistent homology tracks the changes in homology (i.e., the topological features that we are interested in) over a range of thresholds.<ref name="ref_5e0f74ac" />
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# We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks.<ref name="ref_0b990242">[https://www.hindawi.com/journals/mpe/2013/815035/ Persistent Homology of Collaboration Networks]</ref>
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# We show that persistent homology corresponds to tangible features of the networks.<ref name="ref_0b990242" />
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# To do so we use persistent homology, a recent technique from computational topology.<ref name="ref_0b990242" />
 +
# The framework of persistent homology records structural properties and their changes for a whole range of thresholds.<ref name="ref_0b990242" />
 +
# One such tool is persistent homology, which provides a multiscale description of the homological features within a data set.<ref name="ref_f1074bfb">[https://jmlr.org/papers/v18/16-337.html Persistence Images: A Stable Vector Representation of Persistent Homology]</ref>
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# The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low.<ref name="ref_d8e950cc">[https://drops.dagstuhl.de/opus/volltexte/2020/12176/ Relative Persistent Homology]</ref>
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# A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A).<ref name="ref_d8e950cc" />
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# The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space.<ref name="ref_d8e950cc" />
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# We introduce the relative Delaunay-Čech complex DelČ(X, A) whose homology is the relative persistent homology.<ref name="ref_d8e950cc" />
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# Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.<ref name="ref_44c41551">[http://proceedings.mlr.press/v37/chazal15.html Subsampling Methods for Persistent Homology]</ref>
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# When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms.<ref name="ref_44c41551" />
 +
# We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates.<ref name="ref_44c41551" />
 +
# %V 37 %W PMLR %X Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.<ref name="ref_44c41551" />
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# In this paper, we propose to use the persistent homology to systematically study the osmolytes’ molecular aggregation and their hydrogen-bonding network from a global topological perspective.<ref name="ref_b42e2c02">[https://pubs.rsc.org/en/content/articlelanding/2019/cp/c9cp03009c Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks]</ref>
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# Persistent homology is a tool that allows multi-scale analysis.<ref name="ref_8e55f46f">[https://link.springer.com/chapter/10.1007/978-981-10-7617-6_5 Persistent Homology and Materials Informatics]</ref>
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# Persistent homology follows the rule that the oldest one survives.<ref name="ref_8e55f46f" />
 +
# Computing persistent homology is equivalent to reducing that matrix with the following rules.<ref name="ref_8e55f46f" />
 +
# There are numerous libraries that compute persistent homology and that are aimed at different public.<ref name="ref_8e55f46f" />
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# Persistent homology methods have found applications in the analysis of multiple types of biological data, particularly imaging data or data with a spatial and/or temporal component.<ref name="ref_603c428a">[https://royalsocietypublishing.org/doi/10.1098/rsif.2019.0531 Persistent homology analysis of brain transcriptome data in autism]</ref>
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# However, few studies have assessed the use of persistent homology for the analysis of gene expression data.<ref name="ref_603c428a" />
 +
# Persistent homology introduced by Edelsbrunner et al.<ref name="ref_603c428a" />
 +
# In persistent homology, ε varies, which allows the assessment of topological invariants of an object at different scales.<ref name="ref_603c428a" />
 +
# Using persistent homology and dynamical distances to analyze protein binding ,” Stat.<ref name="ref_05844cd3">[https://www.x-mol.com/paperRedirect/1212915512059437056 Persistent homology of time-dependent functional networks constructed from coupled time series: Chaos: An Interdisciplinary Journal of Nonlinear Science: Vol 27, No 4]</ref>
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# Persistent homology is a method for computing topological features of a space at different spatial resolutions.<ref name="ref_ce02f960">[https://en.wikipedia.org/wiki/Persistent_homology Persistent homology]</ref>
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# Each of these two theorems allows us to uniquely represent the persistent homology of a filtered simplicial complex with a barcode or persistence diagram.<ref name="ref_ce02f960" />
 +
# Persistent homology is stable in a precise sense, which provides robustness against noise.<ref name="ref_ce02f960" />
 +
# Persistent homology is a homology theory adapted to a computational context, for instance, in analysis of large data sets.<ref name="ref_46625e57">[https://ncatlab.org/nlab/show/persistent+homology persistent homology in nLab]</ref>
 +
# The idea of persistent homology is to look for features that persist for some range of parameter values.<ref name="ref_46625e57" />
 +
# The math linking the many uses of persistent homology described here is deep, and not covered in this write-up.<ref name="ref_c255475d">[https://towardsdatascience.com/persistent-homology-with-examples-1974d4b9c3d0 Persistent Homology: A Non-Mathy Introduction with Examples]</ref>
 +
# This section looks at several dimensions of persistent homology with Euclidean data (e.g. sets of n-dimensional separate points).<ref name="ref_c255475d" />
 +
# 0d persistent homology in Euclidean space can best be explained as growing balls simultaneously around each point.<ref name="ref_c255475d" />
 +
# 0d persistent homology is tracking when these balls intersect.<ref name="ref_c255475d" />
 +
# In this section, we discuss the application of our localized persistent homology and localized weighted persistent homology in the study of DNA structures.<ref name="ref_aee10f48">[https://www.nature.com/articles/s41598-019-55660-3 Weighted persistent homology for biomolecular data analysis]</ref>
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# We study the barcodes for both LPH and LWPH models, i.e., one with traditional persistent homology and the other with the weighted persistent homology as in Eq.<ref name="ref_aee10f48" />
 +
# In this section, we will give a brief introduction of persistent homology and weighted persistent homology.<ref name="ref_1737d1cc">[https://www.nature.com/articles/s41598-020-66710-6 Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis]</ref>
 +
# The persistent homology, a tool from algebraic topology and computational topology, is proposed to characterize data “shape”64.<ref name="ref_1737d1cc" />
 +
# Persistent homology can be understood from three different aspects.<ref name="ref_1737d1cc" />
 +
# In persistent homology, the data is characterized by Betti numbers, including β 0 , β 1 , β 2 and higher order topological invariants93,94.<ref name="ref_1737d1cc" />
 +
# We define two filtered complexes with which we can calculate the persistent homology of a probability distribution.<ref name="ref_905c8423">[https://projecteuclid.org/euclid.hha/1201127341 Bubenik , Kim : A statistical approach to persistent homology]</ref>
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# Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.<ref name="ref_905c8423" />
 +
# Thus, an increasing number of researchers is now approaching to persistent homology as a tool to be used in their research activity.<ref name="ref_2cfbc961">[https://diglib.eg.org/handle/10.2312/stag20161358 Persistent Homology: a Step-by-step Introduction for Newcomers]</ref>
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# The first one is a web-based user-guide equipped with interactive examples to facilitate the comprehension of the notions at the basis of persistent homology.<ref name="ref_2cfbc961" />
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===소스===
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<references />
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q17099562 Q17099562]
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===Spacy 패턴 목록===
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* [{'LOWER': 'persistent'}, {'LEMMA': 'homology'}]

2021년 2월 17일 (수) 02:27 기준 최신판

관련된 항목들


계산 리소스


사전 형태의 자료


리뷰, 에세이, 강의노트


관련논문

  • Otter, Nina, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, and Heather A. Harrington. ‘A Roadmap for the Computation of Persistent Homology’. arXiv:1506.08903 [cs, Math], 29 June 2015. http://arxiv.org/abs/1506.08903.
  • Lampret, Leon. ‘Tensor, Symmetric, Exterior, and Other Powers of Persistence Modules’. arXiv:1503.08266 [math], 28 March 2015. http://arxiv.org/abs/1503.08266.
  • Jaquette, Jonathan, and Miroslav Kramár. “Rigorous Computation of Persistent Homology.” arXiv:1412.1805 [math], December 4, 2014. http://arxiv.org/abs/1412.1805.

노트

위키데이터

말뭉치

  1. A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given.[1]
  2. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained.[1]
  3. A three-dimensional landmark-based data set is used from a longitudinal orthodontic study, and the persistent homology method is able to distinguish clinically relevant treatment effects.[1]
  4. Persistent homology (PH), a tool from topological data analysis (TDA), serves as the basis for this work.[2]
  5. We use persistent homology, which allows us to study these features at varying scales.[2]
  6. 3 is an illustrative example that shows the steps of computing persistent homology on a simple three gland example.[2]
  7. Persistent homology tracks the changes in homology (i.e., the topological features that we are interested in) over a range of thresholds.[2]
  8. We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks.[3]
  9. We show that persistent homology corresponds to tangible features of the networks.[3]
  10. To do so we use persistent homology, a recent technique from computational topology.[3]
  11. The framework of persistent homology records structural properties and their changes for a whole range of thresholds.[3]
  12. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set.[4]
  13. The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low.[5]
  14. A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A).[5]
  15. The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space.[5]
  16. We introduce the relative Delaunay-Čech complex DelČ(X, A) whose homology is the relative persistent homology.[5]
  17. Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.[6]
  18. When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms.[6]
  19. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates.[6]
  20. %V 37 %W PMLR %X Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.[6]
  21. In this paper, we propose to use the persistent homology to systematically study the osmolytes’ molecular aggregation and their hydrogen-bonding network from a global topological perspective.[7]
  22. Persistent homology is a tool that allows multi-scale analysis.[8]
  23. Persistent homology follows the rule that the oldest one survives.[8]
  24. Computing persistent homology is equivalent to reducing that matrix with the following rules.[8]
  25. There are numerous libraries that compute persistent homology and that are aimed at different public.[8]
  26. Persistent homology methods have found applications in the analysis of multiple types of biological data, particularly imaging data or data with a spatial and/or temporal component.[9]
  27. However, few studies have assessed the use of persistent homology for the analysis of gene expression data.[9]
  28. Persistent homology introduced by Edelsbrunner et al.[9]
  29. In persistent homology, ε varies, which allows the assessment of topological invariants of an object at different scales.[9]
  30. Using persistent homology and dynamical distances to analyze protein binding ,” Stat.[10]
  31. Persistent homology is a method for computing topological features of a space at different spatial resolutions.[11]
  32. Each of these two theorems allows us to uniquely represent the persistent homology of a filtered simplicial complex with a barcode or persistence diagram.[11]
  33. Persistent homology is stable in a precise sense, which provides robustness against noise.[11]
  34. Persistent homology is a homology theory adapted to a computational context, for instance, in analysis of large data sets.[12]
  35. The idea of persistent homology is to look for features that persist for some range of parameter values.[12]
  36. The math linking the many uses of persistent homology described here is deep, and not covered in this write-up.[13]
  37. This section looks at several dimensions of persistent homology with Euclidean data (e.g. sets of n-dimensional separate points).[13]
  38. 0d persistent homology in Euclidean space can best be explained as growing balls simultaneously around each point.[13]
  39. 0d persistent homology is tracking when these balls intersect.[13]
  40. In this section, we discuss the application of our localized persistent homology and localized weighted persistent homology in the study of DNA structures.[14]
  41. We study the barcodes for both LPH and LWPH models, i.e., one with traditional persistent homology and the other with the weighted persistent homology as in Eq.[14]
  42. In this section, we will give a brief introduction of persistent homology and weighted persistent homology.[15]
  43. The persistent homology, a tool from algebraic topology and computational topology, is proposed to characterize data “shape”64.[15]
  44. Persistent homology can be understood from three different aspects.[15]
  45. In persistent homology, the data is characterized by Betti numbers, including β 0 , β 1 , β 2 and higher order topological invariants93,94.[15]
  46. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution.[16]
  47. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.[16]
  48. Thus, an increasing number of researchers is now approaching to persistent homology as a tool to be used in their research activity.[17]
  49. The first one is a web-based user-guide equipped with interactive examples to facilitate the comprehension of the notions at the basis of persistent homology.[17]

소스

  1. ↑ 1.0 1.1 1.2 Exploring uses of persistent homology for statistical analysis of landmark-based shape data
  2. ↑ 2.0 2.1 2.2 2.3 Persistent Homology for the Quantitative Evaluation of Architectural Features in Prostate Cancer Histology
  3. ↑ 3.0 3.1 3.2 3.3 Persistent Homology of Collaboration Networks
  4. ↑ Persistence Images: A Stable Vector Representation of Persistent Homology
  5. ↑ 5.0 5.1 5.2 5.3 Relative Persistent Homology
  6. ↑ 6.0 6.1 6.2 6.3 Subsampling Methods for Persistent Homology
  7. ↑ Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks
  8. ↑ 8.0 8.1 8.2 8.3 Persistent Homology and Materials Informatics
  9. ↑ 9.0 9.1 9.2 9.3 Persistent homology analysis of brain transcriptome data in autism
  10. ↑ Persistent homology of time-dependent functional networks constructed from coupled time series: Chaos: An Interdisciplinary Journal of Nonlinear Science: Vol 27, No 4
  11. ↑ 11.0 11.1 11.2 Persistent homology
  12. ↑ 12.0 12.1 persistent homology in nLab
  13. ↑ 13.0 13.1 13.2 13.3 Persistent Homology: A Non-Mathy Introduction with Examples
  14. ↑ 14.0 14.1 Weighted persistent homology for biomolecular data analysis
  15. ↑ 15.0 15.1 15.2 15.3 Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis
  16. ↑ 16.0 16.1 Bubenik , Kim : A statistical approach to persistent homology
  17. ↑ 17.0 17.1 Persistent Homology: a Step-by-step Introduction for Newcomers

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'persistent'}, {'LEMMA': 'homology'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Persistent_homology&oldid=52041"