PPT-Nonlinear Dimensionality

Reduction by Locally Linear Embedding Sam T Roweis and Lawrence K Saul Reference Nonlinear dimensionality reduction by locally linear embedding Roweis amp Saul Science 2000. Nonlinear Model Problem Let us consider the nonlinear model problem 87228711 f in 8486 1a 0 on 8486 1b where is a given positive function depending on the unknown solution As usual is a given source function which we for simplicity assume not to Di64256erentiating 8706S 8706f Setting the partial derivatives to 0 produces estimating equations for the regression coe64259cients Because these equations are in general nonlinear they require solution by numerical optimization As in a linear model dimensionalityreduction dimensionality Nuno Vasconcelos ECE De p artment , UCSD p, Note this course requires a it is responsibility to define it (although we can talk) If you are too far from this, Framework in . Py. . A. . Da. . Ronch. University of. L. iverpool. , . UK. Liverpool, . 16. March 2012. Target. . Nonlinear models . for flexible aircraft (hierarchy). Nonlinear . model reduction. Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. Dimensionality Reduction. Author: . Christoph. . Eick. The material is mostly based on the . Shlens. PCA. Tutorial . http://www2.cs.uh.edu/~. ceick/ML/pca.pdf. . and . to a lesser extend based on material . Computer Graphics Course. June 2013. What is high dimensional data?. Images. Videos. Documents. Most data, actually!. What is high dimensional data?. Images – dimension 3·X·Y. Videos – dimension of image * number of frames. Identifying functions . on tables, graphs, and equations.. Irma Crespo 2010. Warm Up. Graph y = 2x + 1. Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.. What is the linear equation for this graph?. Bishwajyoti Dey. Department of Physics,. University of Pune, Pune. With Galal Alakhaly. GA, BD Phys. Rev. E 84, 036607 (1-9) 2011. Nonlinear localised excitations – solitons, breathers, compactons.. Principle Component Analysis. Why Dimensionality Reduction?. It becomes more difficult to extract meaningful conclusions from a data set as data dimensionality increases--------D. L. . Donoho. Curse of dimensionality. Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. John A. Lee, Michel Verleysen. 1. Dimensionality Reduction. By: . sadatnejad. دانشگاه صنعتي اميرکبير. (. پلي تکنيک تهران). Dim. Reduction- . Practical Motivations . 2. Third order nonlinear optics offers a wide range of interesting phenomena which are very . different. from . what is expected from linear optics. The most important are due to changes in the . properties. John A. Lee, Michel Verleysen, . Chapter4 . 1. Distance Preservation. دانشگاه صنعتي اميرکبير. (. پلي تکنيک تهران). 2. The motivation behind distance preservation is that any .