1 / 20

Dogs and Cats

Dogs and Cats. Dogs. Cats. Low-Dimensional Dogs and Cats: “Eigen-Dogs/Cats”. Linear Discrimination Analysis. Find a projection that maximizes the statistical distance between two random data sets . Histogram of the Data. 95% Accurate. Misclassified Dogs. It’s the ears!!!!.

yoland
Download Presentation

Dogs and Cats

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dogs and Cats Dogs Cats

  2. Low-Dimensional Dogs and Cats: “Eigen-Dogs/Cats”

  3. Linear Discrimination Analysis Find a projection that maximizes the statistical distance between two random data sets

  4. Histogram of the Data 95% Accurate

  5. Misclassified Dogs It’s the ears!!!!

  6. PDEsA backbone of AMATH (fluids) • Getting the right basis • - POD modes • Minimal dynamics • dynamical systems of the cheap

  7. How to solve a PDE: 3 easy steps 1 2 PDE ODE Algebra* 3 Undo • Eigenfunction expansion (separation of variables) • u(x,t) = Σan(t)ϕn(x)

  8. Two SolitonSolution of a nonlinear PDE

  9. SVD on Data

  10. Galerkin Expansion

  11. Nonlinear SchroedingerEquation

  12. Water Waves: Governing Equations V. E. Zakharov. “Stability of periodic waves of finite amplitude on the surface of a deep fluid.” Zh. Prikl. Mekh. Tekh. Fiz. (1968).

  13. Low Amplitude Waves

  14. High Amplitude Waves

  15. Mode Structure

  16. PCA (POD) Convergence The n mode POD basis of a set of data captures more of the L2normof that data than any other linear set of n modes: P. Holmes, J. Lumley, and G. Berkooz. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge U. Press (1996)

  17. www.mathworks/moler/eigs.pdf See also http://people.maths.ox.ac.uk/trefethen/text.html

More Related