Rank: 833 based on 92 downloads (last 30 days) and 4 files submitted
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Kye Taylor

E-mail
Company/University
MathWorks
Lat/Long
42.3, -71.35

Personal Profile:

Let's do this, MATLAB

Professional Interests:
math

 

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Files Posted by Kye View all
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18 Jun 2013 Screenshot Draw or add axes to figure Super helpful way to visualize axes in a 2D figure. Author: Kye Taylor demo, visualization, axes, axis, x, y 28 1
02 Apr 2013 Screenshot Color-balance demo with GPU computing Use GPU in MATLAB to perform white-balance operation to input image. Author: Kye Taylor graphical processing ..., gpu, high performance comp..., demo, image processing 26 0
17 Apr 2012 Screenshot Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor diffusion map, spectral clustering, laplacian eigenmap, lowdimensional geomet..., how to add some image... 30 4
  • 5.0
5.0 | 1 rating
01 Sep 2011 Screenshot Color code a scatter plot Color code a scatter plot in one, two, or three dimensions according to scalar function of the data. Author: Kye Taylor data exploration, plot, scatter plot, highdimensional visua... 8 0
Comments and Ratings by Kye View all
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19 Jun 2013 Draw or add axes to figure Super helpful way to visualize axes in a 2D figure. Author: Kye Taylor

t = -1:.1:1;
plot(t,t), drawAxes
13 Dec 2012 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor

First, note that these type of algorithms use the eigenvectors of a diffusion operator to map the data to a new space. The diffusion operator is N-by-N, where N is the number of points in the dataset, so there are N possible eigenvectors to use in this mapping. Typically much fewer than N eigenvectors are used in practice because 1.) reducing dimensionality means you want fewer coordinates to describe each point and 2.) the number of degrees of freedom in a geometrically structured dataset are typically less than the number of points, making dimensionality reduction possible. It turns out that you want the eigenvectors associated with one of the diffusion operators spectrum, depending on how it is defined.

As I've defined it, the diffusion operator (matrix DO) is a sparse matrix (very few nonzero entries) so I use eigs to compute eigenvectors... DO also has eigenvalues that are real and less than or equal to 1. So I ask eigs for the 10 largest algebraic ('la') nvec eigenpairs.

18 Apr 2012 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor

Although the implementation is more in line with Laplacian eigenmaps, I chose to include "diffusion map" in the title since the concept is the same.

Comments and Ratings on Kye's Files View all
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Updated File Comment by Comments Rating
19 Jun 2013 Draw or add axes to figure Super helpful way to visualize axes in a 2D figure. Author: Kye Taylor Taylor, Kye

t = -1:.1:1;
plot(t,t), drawAxes
18 May 2013 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor Shuai

09 Apr 2013 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor PK

how to add some image to this code to check dimensionality reduction

13 Dec 2012 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor Taylor, Kye

First, note that these type of algorithms use the eigenvectors of a diffusion operator to map the data to a new space. The diffusion operator is N-by-N, where N is the number of points in the dataset, so there are N possible eigenvectors to use in this mapping. Typically much fewer than N eigenvectors are used in practice because 1.) reducing dimensionality means you want fewer coordinates to describe each point and 2.) the number of degrees of freedom in a geometrically structured dataset are typically less than the number of points, making dimensionality reduction possible. It turns out that you want the eigenvectors associated with one of the diffusion operators spectrum, depending on how it is defined.

As I've defined it, the diffusion operator (matrix DO) is a sparse matrix (very few nonzero entries) so I use eigs to compute eigenvectors... DO also has eigenvalues that are real and less than or equal to 1. So I ask eigs for the 10 largest algebraic ('la') nvec eigenpairs.

13 Dec 2012 Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor Cat

Hi Kye Taylor,

Can you explain a bit about the reason why you choose to use "eigs" function with "la" option ?

Regards

Cat Le
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demo, axes, axis, data exploration, diffusion map
Files Tagged by Kye View all
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Updated   File Tags Downloads
(last 30 days) 		Comments Rating
18 Jun 2013 Screenshot Draw or add axes to figure Super helpful way to visualize axes in a 2D figure. Author: Kye Taylor demo, visualization, axes, axis, x, y 28 1
02 Apr 2013 Screenshot Color-balance demo with GPU computing Use GPU in MATLAB to perform white-balance operation to input image. Author: Kye Taylor graphical processing ..., gpu, high performance comp..., demo, image processing 26 0
17 Apr 2012 Screenshot Laplacian eigenmap ~ Diffusion map ~ manifold learning Demo techniques of nonlinear eigenmaps for the purpose of recovering low-dimensional geometries. Author: Kye Taylor diffusion map, spectral clustering, laplacian eigenmap, lowdimensional geomet..., how to add some image... 30 4
  • 5.0
5.0 | 1 rating
01 Sep 2011 Screenshot Color code a scatter plot Color code a scatter plot in one, two, or three dimensions according to scalar function of the data. Author: Kye Taylor data exploration, plot, scatter plot, highdimensional visua... 8 0

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