Persistent homology

관련된 항목들

• 호몰로지

계산 리소스

• http://comptop.stanford.edu/programs/
• http://www.math.rutgers.edu/~vidit/perseus.html

사전 형태의 자료

• http://en.wikipedia.org/wiki/Topological_data_analysis

리뷰, 에세이, 강의노트

• What is Persistent Homology?

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

• ID : Q17099562

말뭉치

1. A method for the use of persistent homology in the statistical analysis of landmark-based shape data is given.
2. Three-dimensional landmark configurations are used as input for separate filtrations, persistent homology is performed, and persistence diagrams are obtained.
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.
4. Persistent homology (PH), a tool from topological data analysis (TDA), serves as the basis for this work.
5. We use persistent homology, which allows us to study these features at varying scales.
6. 3 is an illustrative example that shows the steps of computing persistent homology on a simple three gland example.
7. Persistent homology tracks the changes in homology (i.e., the topological features that we are interested in) over a range of thresholds.
8. We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks.
9. We show that persistent homology corresponds to tangible features of the networks.
10. To do so we use persistent homology, a recent technique from computational topology.
11. The framework of persistent homology records structural properties and their changes for a whole range of thresholds.
12. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set.
13. The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low.
14. A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A).
15. The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space.
16. We introduce the relative Delaunay-Čech complex DelČ(X, A) whose homology is the relative persistent homology.
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.
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.
19. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates.
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.
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.
22. Persistent homology is a tool that allows multi-scale analysis.
23. Persistent homology follows the rule that the oldest one survives.
24. Computing persistent homology is equivalent to reducing that matrix with the following rules.
25. There are numerous libraries that compute persistent homology and that are aimed at different public.
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.
27. However, few studies have assessed the use of persistent homology for the analysis of gene expression data.
28. Persistent homology introduced by Edelsbrunner et al.
29. In persistent homology, ε varies, which allows the assessment of topological invariants of an object at different scales.
30. Using persistent homology and dynamical distances to analyze protein binding ,” Stat.
31. Persistent homology is a method for computing topological features of a space at different spatial resolutions.
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.
33. Persistent homology is stable in a precise sense, which provides robustness against noise.
34. Persistent homology is a homology theory adapted to a computational context, for instance, in analysis of large data sets.
35. The idea of persistent homology is to look for features that persist for some range of parameter values.
36. The math linking the many uses of persistent homology described here is deep, and not covered in this write-up.
37. This section looks at several dimensions of persistent homology with Euclidean data (e.g. sets of n-dimensional separate points).
38. 0d persistent homology in Euclidean space can best be explained as growing balls simultaneously around each point.
39. 0d persistent homology is tracking when these balls intersect.
40. In this section, we discuss the application of our localized persistent homology and localized weighted persistent homology in the study of DNA structures.
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.
42. In this section, we will give a brief introduction of persistent homology and weighted persistent homology.
43. The persistent homology, a tool from algebraic topology and computational topology, is proposed to characterize data “shape”64.
44. Persistent homology can be understood from three different aspects.
45. In persistent homology, the data is characterized by Betti numbers, including β 0 , β 1 , β 2 and higher order topological invariants93,94.
46. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution.
47. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.
48. Thus, an increasing number of researchers is now approaching to persistent homology as a tool to be used in their research activity.
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.

메타데이터

위키데이터

• ID : Q4460773