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Topological data analysis: Applications & Art

In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric…

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Topological data analysis topic overview

The analysis highlights Applications and Art as prominent areas in the source structure around Topological data analysis.

Related topics
86
Source areas
13
Connected nodes
99
Extracted relationships
37
Concept neighborhoods
43
Bridge connections
99

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Basic theory · 20 topics
Statistics · 15 topics
Overview · 11 topics
Categorification and cosheaves · 9 topics
Computation · 7 topics
Visualization · 6 topics
Applications · 5 topics
Multidimensional persistence · 4 topics
Other persistences · 4 topics
Structure theorem · 2 topics
Monograph · 1 topics
Other Resources of TDA · 1 topics
Stability · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Basic theory

Computation

Visualization

Multidimensional persistence

Other persistences

Categorification and cosheaves

Stability

Structure theorem

Statistics

Applications

Monograph

  • ISBN ISBN (identifier)

Other Resources of TDA

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Topological data analysis connects Entity context

The extracted context around Topological data analysis shows recurring relationship patterns in the source. For example, Topological data analysis → American Mathematical Society, Barbara Giunti, Bastian Rieck, DONUT, Janis Lazovskis, Non-Theoretical Uses, Notices, November, October, Original, The Database, Topology Another extracted example is Topological data analysis → Deheuvels, MAPPER, Morse, One, Reeb, Some, TDA, The, This, Topological. Use these groups to spot repeated connection types before inspecting the individual relationships.

Topological data analysis

Top relations

has application · 12
Topological data analysis → American Mathematical Society, Barbara Giunti, Bastian Rieck, DONUT, Janis Lazovskis, Non-Theoretical Uses, Notices, November, October, Original, The Database, Topology
has impact · 10
Topological data analysis → Deheuvels, MAPPER, Morse, One, Reeb, Some, TDA, The, This, Topological
related to Brief Introductions · 9
Topological data analysis → Advanced Study, Data Using Topology, Institute, Lesnick, Michael, Mikael Vejdemo-Johansson, Shape, Source Material, Studying
related to Statistics · 6
Topological data analysis → Katharine Turner, One, Persistent, Real, Statistical, The

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

persistence displaystyle tda data homology theory persistent mathbb topology theorem et al topological complex one space module analysis many study

Topological data analysis relationships Subject–Predicate–Object triples

TTTA extracted 37 structured relationships around Topological data analysis. Examples in this analysis include Topological data analysis → has application → The Database and Topological data analysis → has application → Original. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Topological data analysishas applicationThe Database0.60section
Topological data analysishas applicationOriginal0.60section
Topological data analysishas applicationNon-Theoretical Uses0.60section
Topological data analysishas applicationTopology0.60section
Topological data analysishas applicationDONUT0.60section
Topological data analysishas applicationBarbara Giunti0.60section
Topological data analysishas applicationJanis Lazovskis0.60section
Topological data analysishas applicationBastian Rieck0.60section
Topological data analysishas applicationOctober0.60section
Topological data analysishas applicationNovember0.60section
Topological data analysishas applicationNotices0.60section
Topological data analysishas applicationAmerican Mathematical Society0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Topological data analysis bring nearby vocabulary together. In this analysis, examples include Analysis, Data and Topological. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Topological data analysis
    • Analysis
    • Data
    • Topological
    • Features
    • Topology
    • Structure
    • Morse
    • Point
    • Stability
    • Study
    • Tda
    • Space
  • topological data analysis
    • Analysis
    • Data
    • Topological
    • Topology
    • Statistical
    • Features
    • Persistent
    • Study
    • Theory
    • Homology
    • Set
    • Structure
  • persistent homology
    • Persistent
    • Persistence
    • Morse
    • Theorem
    • Topology
    • Complex
    • Theory
    • First
    • Defined
    • Displaystyle
    • Module
    • Al
  • homology
    • Persistent
    • Persistence
    • Morse
    • Theorem
    • Topology
    • Complex
    • Theory
    • Displaystyle
    • Module
    • Topological
    • Al
    • Et
  • homology group
    • Persistent
    • Persistence
    • Morse
    • Theorem
    • Topology
    • Complex
    • Theory
    • Displaystyle
    • Module
    • Topological
    • Al
    • Et
  • persistence barcodes
    • Module
    • Displaystyle
    • Mathbb
    • Theorem
    • Modules
    • Leq
    • Space
    • Set
    • Structure
    • Defined
    • Category
    • Theory
  • čech complex
    • Complexes
    • Point
    • Displaystyle
    • Homology
    • Finite
    • Structure
    • Theory
    • Module
    • One
    • Space
    • Theorem
    • Persistence
  • persistence module
    • Displaystyle
    • Module
    • Persistence
    • Mathbb
    • Theorem
    • Modules
    • Leq
    • Space
    • Set
    • Structure
    • Defined
    • Point

Connections between topic areas Semantic bridges

For Topological data analysis, one of the stronger structural bridges in this analysis connects Topological data analysis with Basic theory. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Topological data analysis — Basic theory · splits 79 ⟂ 21
Topological data analysis — Statistics · splits 84 ⟂ 16
Topological data analysis — Overview · splits 88 ⟂ 12
Topological data analysis — Categorification and cosheaves · splits 90 ⟂ 10
Topological data analysis — Computation · splits 92 ⟂ 8
Topological data analysis — Visualization · splits 93 ⟂ 7
Topological data analysis — Applications · splits 94 ⟂ 6
Topological data analysis — Multidimensional persistence · splits 95 ⟂ 5
Topological data analysis — Other persistences · splits 95 ⟂ 5
Topological data analysis — Structure theorem · splits 97 ⟂ 3

Map overview Semantic statistics

Topological data analysis

Nodes100
Edges99
Triples37
Avg. degree1.98
Density0.02
Components1

Source & methodology

TTTA analyzes the structure around Topological data analysis to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications & Art, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Topological data analysis · EN edition · Analysis: TopicsToTalkAbout

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