Edit topic "Topological data analysis" Accepted
The requested resource couldn't be found.
Changes: 8
-
Add Topological data analysis
- Title
-
- Unchanged
- Topological data analysis
- Type
-
- Unchanged
- Course
- Created
-
- Unchanged
- no value
- Description
-
- Unchanged
- Basic topological concepts and models and their use in data analysis will be introduced. Course contents 1. Topological models: triangulations and simplicial complexes, cell complexes 2. Finding holes and tunels: homology groups 3. Distinguishing between the details and the big picture: persistent homology
- Link
-
- Unchanged
- https://ucilnica.fri.uni-lj.si/course/view.php?id=111
- Identifier
-
- Unchanged
- 63542
Resource | v1 | current (v1) -
Update Topological data analysis (TDA)
- Title
-
- Unchanged
- Topological data analysis (TDA)
- At edit time
- Topological data analysis
- Description
-
- Unchanged
- 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 chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools. The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields.
- At edit time
- 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 chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools. The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields.
- Link
-
- Unchanged
- https://en.wikipedia.org/?curid=17740009
- At edit time
- https://en.wikipedia.org/?curid=17740009
-
Add Žiga Virk
- Name
-
- Unchanged
- Žiga Virk
- Bio
-
- Unchanged
- My research interests are in topology and geometry. I am particularly interested in geometric interpretation of persistent homology. I did my undergraduate and graduate studies at University of Ljubljana and University of Tennessee in Knoxville, the later under supervision of Jerzy Dydak. I was a postdoctoral researcher at IST Austria under supervision of Herbert Edelsbrunner.
- Link
-
- Unchanged
- https://zigavirk.gitlab.io/
Author | v1 | current (v1) -
Add Neža Mramor Kosta
- Name
-
- Unchanged
- Neža Mramor Kosta
- Bio
-
- Unchanged
- I am a mathematician teaching computer science students math. My research interests are connected to topology and its applications to computer science. Lately I have been working mostly in computational topology. Computational topoogy is an exciting growing field on the border between mathematics and computer science, the central topic of the European Science Foundation networking programme Algebraic and Computational Topology. I am also a member of the Institute for Mathematics, Physics and Mechanics of Slovenia.
- Link
-
- Unchanged
- https://www.fri.uni-lj.si/en/employees/nezka-mramor-kosta
Author | v1 | current (v1) -
Add Topological data analysis (TDA) treated in Topological data analysis
- Current
- treated in
Topic to resource relation | v1 -
Add University of Ljubljana published Topological data analysis
- Current
- published
Author to resource relation | v1 -
Add Neža Mramor Kosta created Topological data analysis
- Current
- created
Author to resource relation | v1 -
Add Žiga Virk created Topological data analysis
- Current
- created
Author to resource relation | v1