数据科学的拓扑方法的各个方面。
ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.
作者信息
Grbić Jelena, Wu Jie, Xia Kelin, Wei Guo-Wei
机构信息
School of Mathematical Sciences, University of Southampton, Southampton, UK.
School of Mathematical Sciences, Center of Topology and Geometry based Technology, Hebei Normal University, Yuhua District, Shijiazhuang, Hebei, 050024 China.
出版信息
Found Data Sci. 2022 Jun;4(2):165-216. doi: 10.3934/fods.2022002.
Abstract
We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.
摘要
我们建立了一种新理论，该理论统一了数据科学拓扑方法的各个方面，既适用于点云数据，也适用于图数据，包括超越成对相互作用的网络。我们将单纯复形和超图推广到超超图，并建立超超图同调作为单纯同调的扩展。受应用驱动，我们还引入了超持久同调。
相似文献
1
ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.数据科学的拓扑方法的各个方面。
Found Data Sci. 2022 Jun;4(2):165-216. doi: 10.3934/fods.2022002.
2
Eigenvector centrality in simplicial complexes of hypergraphs.超图单纯复形中的特征向量中心性。
Chaos. 2023 Sep 1;33(9). doi: 10.1063/5.0144871.
3
Persistent Homology for RNA Data Analysis.RNA 数据分析中的持久同调。
Methods Mol Biol. 2023;2627:211-229. doi: 10.1007/978-1-0716-2974-1_12.
4
Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes.高阶相互作用在超图和单纯复形中以不同的方式塑造集体动力学。
Nat Commun. 2023 Mar 23;14(1):1605. doi: 10.1038/s41467-023-37190-9.
5
(Hyper)graph Kernels over Simplicial Complexes.单纯复形上的（超）图核
Entropy (Basel). 2020 Oct 14;22(10):1155. doi: 10.3390/e22101155.
6
Hypergraph partitioning using tensor eigenvalue decomposition.张量特征值分解的超图划分。
PLoS One. 2023 Jul 21;18(7):e0288457. doi: 10.1371/journal.pone.0288457. eCollection 2023.
7
Topological Simplifications of Hypergraphs.超图的拓扑简化。
IEEE Trans Vis Comput Graph. 2023 Jul;29(7):3209-3225. doi: 10.1109/TVCG.2022.3153895. Epub 2023 May 26.
8
Distances in Higher-Order Networks and the Metric Structure of Hypergraphs.高阶网络中的距离与超图的度量结构
Entropy (Basel). 2023 Jun 12;25(6):923. doi: 10.3390/e25060923.
9
Computing degree based topological indices of algebraic hypergraphs.计算代数超图的基于度的拓扑指标。
Heliyon. 2024 Jul 22;10(15):e34696. doi: 10.1016/j.heliyon.2024.e34696. eCollection 2024 Aug 15.
10
Spectral detection of simplicial communities via Hodge Laplacians.通过霍奇拉普拉斯算子对单纯复形群落进行光谱检测。
Phys Rev E. 2021 Dec;104(6-1):064303. doi: 10.1103/PhysRevE.104.064303.
引用本文的文献
1
PERSISTENT DIRAC OF PATHS ON DIGRAPHS AND HYPERGRAPHS.图和超图上路径的持久狄拉克（指标）
Found Data Sci. 2024 Jun;6(2):124-153. doi: 10.3934/fods.2024001.
2
Persistent Mayer Dirac.持续的迈耶·狄拉克。
J Phys Complex. 2024 Dec 1;5(4):045005. doi: 10.1088/2632-072X/ad83a5. Epub 2024 Oct 17.
3
PERSISTENT HYPERDIGRAPH HOMOLOGY AND PERSISTENT HYPERDIGRAPH LAPLACIANS.持久超图同调与持久超图拉普拉斯算子
Found Data Sci. 2023 Dec;5(4):558-588. doi: 10.3934/fods.2023010.
4
Identification of Autism Spectrum Disorder Using Topological Data Analysis.使用拓扑数据分析识别自闭症谱系障碍。
J Imaging Inform Med. 2024 Jun;37(3):1023-1037. doi: 10.1007/s10278-024-01002-3. Epub 2024 Feb 13.
5
PERSISTENT PATH LAPLACIAN.持久路径拉普拉斯算子
Found Data Sci. 2023 Mar;5(1):26-55. doi: 10.3934/fods.2022015.
6
Persistent topological Laplacian analysis of SARS-CoV-2 variants.严重急性呼吸综合征冠状病毒2（SARS-CoV-2）变体的持久拓扑拉普拉斯分析
J Comput Biophys Chem. 2023 Aug;22(5):569-587. doi: 10.1142/s2737416523500278. Epub 2023 Jun 8.
7
Mitochondrial networks through the lens of mathematics.通过数学的视角看线粒体网络。
Phys Biol. 2023 Jul 14;20(5):051001. doi: 10.1088/1478-3975/acdcdb.
8
Persistent topological Laplacian analysis of SARS-CoV-2 variants.严重急性呼吸综合征冠状病毒2（SARS-CoV-2）变体的持久拓扑拉普拉斯分析
ArXiv. 2023 Apr 6:arXiv:2301.10865v2.
本文引用的文献
1
An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists.《拓扑数据分析导论：数据科学家的基础与实践》
Front Artif Intell. 2021 Sep 29;4:667963. doi: 10.3389/frai.2021.667963. eCollection 2021.
2
A topology-based network tree for the prediction of protein-protein binding affinity changes following mutation.一种基于拓扑结构的网络树，用于预测突变后蛋白质-蛋白质结合亲和力的变化。
Nat Mach Intell. 2020;2(2):116-123. doi: 10.1038/s42256-020-0149-6. Epub 2020 Feb 14.
3
Persistent spectral-based machine learning (PerSpect ML) for protein-ligand binding affinity prediction.用于蛋白质-配体结合亲和力预测的基于持久光谱的机器学习（PerSpect ML）。
Sci Adv. 2021 May 7;7(19). doi: 10.1126/sciadv.abc5329. Print 2021 May.
4
Forman persistent Ricci curvature (FPRC)-based machine learning models for protein-ligand binding affinity prediction.基于 Forman 持续 Ricci 曲率 (FPRC) 的蛋白质-配体结合亲和力预测机器学习模型。
Brief Bioinform. 2021 Nov 5;22(6). doi: 10.1093/bib/bbab136.
5
Ollivier Persistent Ricci Curvature-Based Machine Learning for the Protein-Ligand Binding Affinity Prediction.基于奥利维尔持续 Ricci 曲率的机器学习在蛋白质-配体结合亲和力预测中的应用。
J Chem Inf Model. 2021 Apr 26;61(4):1617-1626. doi: 10.1021/acs.jcim.0c01415. Epub 2021 Mar 16.
6
Hypergraph-based persistent cohomology (HPC) for molecular representations in drug design.基于超图的持久同调（HPC）在药物设计中的分子表示。
Brief Bioinform. 2021 Sep 2;22(5). doi: 10.1093/bib/bbaa411.
7
Persistent spectral graph.持续谱图。
Int J Numer Method Biomed Eng. 2020 Sep;36(9):e3376. doi: 10.1002/cnm.3376. Epub 2020 Aug 17.
8
A review of mathematical representations of biomolecular data.生物分子数据的数学表示方法综述。
Phys Chem Chem Phys. 2020 Feb 26;22(8):4343-4367. doi: 10.1039/c9cp06554g.
9
MathDL: mathematical deep learning for D3R Grand Challenge 4.MathDL：用于 D3R 大挑战 4 的数学深度学习。
J Comput Aided Mol Des. 2020 Feb;34(2):131-147. doi: 10.1007/s10822-019-00237-5. Epub 2019 Nov 16.
10
Fast and accurate tumor segmentation of histology images using persistent homology and deep convolutional features.利用持久同调与深度卷积特征实现快速准确的组织学图像肿瘤分割。
Med Image Anal. 2019 Jul;55:1-14. doi: 10.1016/j.media.2019.03.014. Epub 2019 Apr 4.
Zotero 插件