![Case study: Demographics
Data shape:
[220:45]](https://image.slidesharecdn.com/topologicaldataanalysis-131113075600-phpapp02/85/Topological-Data-Analysis-visual-presentation-of-multidimensional-data-sets-9-320.jpg)
![Case study: YT channel stats
Data shape:
[1500:12]](https://image.slidesharecdn.com/topologicaldataanalysis-131113075600-phpapp02/85/Topological-Data-Analysis-visual-presentation-of-multidimensional-data-sets-10-320.jpg)
![Case study: Netflix dataset
Data shape:
[17770:480189]
8.5 billions of elements](https://image.slidesharecdn.com/topologicaldataanalysis-131113075600-phpapp02/85/Topological-Data-Analysis-visual-presentation-of-multidimensional-data-sets-11-320.jpg)
Topological Data Analysis: visual presentation of multidimensional data sets
- 1. Topological Data Analysis Visual presentation of multidimensional data sets
- 2. Current vs New SQL Topological Data Analysis
- 3. Topology The Seven Bridges of Königsberg, a problem solved by Leonard Euler (1736). The study of qualitative properties of certain objects (topological spaces) that are invariant under a certain kind of transformation (continuous map), especially those properties that are invariant under a certain kind of equivalence (homeomorphism).
- 4. Topology Data Analysis Pipeline a b a. First approximate the unknown space X in a combinatorial structure K b. Then compute topological invariants of K
- 5. Combinatorial Representations The Čech Complex
- 6. Combinatorial Representations Alpha Complex Vietoris-‐‑Rips Complex Witness Complex Cubical Complex
- 7. Topological Invariants A topological invariant is a map f that assigns the same object to homeomorphic spaces, that is: Homology: is a machine that converts local data about a space into global algebraic structure Reference: Wikipedia, 2010.
- 8. Morse Theory and Reeb Graph Theorem: Suppose h : X g is a discrete Morse function. Then X is homotopy equivalent to a CW-‐‑complex with exactly one cell of dimension p for each critical simplex of dimension p. Reference: Teng Ma ; Zhuangzhi Wu ; Pei Luo ; Lu Feng. Reeb graph computation through spectral clustering, 2011.
- 9. Case study: Demographics Data shape: [220:45]
- 10. Case study: YT channel stats Data shape: [1500:12]
- 11. Case study: Netflix dataset Data shape: [17770:480189] 8.5 billions of elements
- 12. Case study: Netflix dataset Indian Honk Kong French Music US Retro Ger man US Cartoons Anime Kids Movie Horror
- 13. Case study: Netflix comparison PCA Isomap LLE LTSA Spectral Embedding Hessian LLE
- 14. Case study: Netflix (music)
- 15. Case study: Netflix (kids movie)
- 16. Case study: Netflix (horror)
- 17. Please sign up for free beta access: www.datarefiner.com info@datarefiner.com
- 18. Questions?