Rank: 1077 based on 84 downloads (last 30 days) and 3 files submitted
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Kye Taylor

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MathWorks
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42.3, -71.35

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Let's do this, MATLAB

Professional Interests:
math

 

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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 53 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... 25 4
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... 6 0
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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.

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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
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 Taylor, Kye

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.

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data exploration, demo, diffusion map, gpu, graphical processing unit
Files Tagged by Kye View all
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Updated   File Tags Downloads
(last 30 days) 		Comments Rating
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 53 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... 25 4
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... 6 0

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