Data science from a topological viewpoint 曹越琦( Yueqi cao Beijing institute of technology
Data science from a topological viewpoint 曹越琦（Yueqi Cao） Beijing institute of technology
05 Unrolled manifold 0.5 公∷ -1.0 1.5-1.0-0.50.00.5101.5-1.5-10-0.50.00.5101.5 Recovery by LLE Recovery by HLLe 0.10 PCA 0.04 神一 43. 008100010 LLE/Hessian LLE Sourcehttps://en.wikipedia.org/wiki/nonli near dimensionality reduction#Hessian L ocally-Linear Embedding( Hessian LLE Isomap
PCA Isomap LLE/Hessian LLE Source:https://en.wikipedia.org/wiki/Nonli near_dimensionality_reduction#Hessian_L ocally-Linear_Embedding_(Hessian_LLE)
opology Connected components Holes Tunnels
Topology Connected components Holes Tunnels
Topological data analysis Subcritical Critical Supercritical nrd→>0 nr2→入∈(0,∞) Source: Hamid R. Eghbalnia, the practice of topological estimation
Topological data analysis • …… Source: Hamid R. Eghbalnia, the practice of topological estimation
Chaos topology nosehoover y=-x+ yz
Chaos & Topology 2 x y y x yz z c y = = − + = −