Download presentation

Presentation is loading. Please wait.

Published byDennis Snow Modified over 2 years ago

1
Manifold Learning Dimensionality Reduction

2
Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s algorithm Reference

3
Introduction (dim. reduction) Dimensionality Reduction Linear PCA MDS Non-linear Isomap(2000) LLE(2000) SDE(2005)

4
Introduction (dim. reduction) Principal Component Analysis x ∑

5
Introduction (dim. reduction) Dimensionality Reduction Linear PCA MDS Non-linear Isomap(2000) LLE(2000) SDE(2005)

6
Introduction (dim. reduction) Multidimensional Scaling ChicagoRaleighBostonSeattleS.F.AustinOrlando Chicago0 Raleigh6410 Boston8516080 Seattle1733236324880 S.F.1855240626966840 Austin97211671691176414950 Orlando99452011052565245810150

7
Introduction (dim. reduction)

8
Dimensionality Reduction Linear PCA MDS Non-linear Isomap(2000) LLE(2000) SDE(2005)

9
Introduction (manifold) Linear methods do nothing more than “ globally transform ” (rotate/translate..) data. Sometimes need to “ unwrap ” the data first PCA

10
Introduction (dim. reduction) The task of dimensionality reduction is to find a small number of features to represent a large number of observed dimensions.

11
Introduction (manifold)

13
Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s algorithm Reference

14
Isomap (overall procedure) Compute fully-connected neighborhood of points for each item (k nearest) Calculate pairwise Euclidean distances within each neighborhood Use Dijkstra ’ s Algorithm to compute shortest path from each point to non- neighboring points Run MDS on resulting distance matrix

15
Isomap (Approximating geodesic dist.)

17
is not much bigger than

18
Isomap (Approximating geodesic dist.) is not much bigger than

19
Isomap (Approximating geodesic dist.) is not much bigger than

20
Isomap (Approximating geodesic dist.) is not much bigger than

21
Isomap (Approximating geodesic dist.)

22
Isomap (Dijkstra ’ s Algorithm) Greedy breadth-first algorithm to compute shortest path from one point to all other points

23
Isomap (Dijkstra ’ s Algorithm) Greedy breadth-first algorithm to compute shortest path from one point to all other points

24
Isomap (Dijkstra ’ s Algorithm) Greedy breadth-first algorithm to compute shortest path from one point to all other points

25
Isomap (Dijkstra ’ s Algorithm) Greedy breadth-first algorithm to compute shortest path from one point to all other points

26
Isomap

28
Reference http://www.cs.unc.edu/Courses/comp290-090-s06/ http://www.cse.msu.edu/~lawhiu/manifold/

Similar presentations

OK

Three Algorithms for Nonlinear Dimensionality Reduction Haixuan Yang Group Meeting Jan. 011, 2005.

Three Algorithms for Nonlinear Dimensionality Reduction Haixuan Yang Group Meeting Jan. 011, 2005.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on index numbers Ppt on trial and error supernatural Ppt on sikkim culture Ppt online education Ppt on indian textile industries chicago Ppt on minimum oil circuit breaker Ppt on new york stock exchange Ppt on law and social justice class 8 Download ppt on sound for class 9th Download ppt on pulse code modulation experiment