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Kernel PCA and Pre-Image Reconstruction


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Kernel PCA and Pre-Image Reconstruction



04 Jan 2013 (Updated )

standard PCA, Gaussian kernel PCA, polynomial kernel PCA, pre-image reconstruction

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In this package, we implement standard PCA, kernel PCA, and pre-image reconstruction of Gaussian kernel PCA. We also provide three demos: (1) Two concentric spheres embedding; (2) Face classification with PCA/kPCA; (3) Active shape models with kPCA.
Standard PCA is not optimized for very high dimensional data. But our kernel PCA implementation is very efficient, and has been used in many research projects.

Required Products MATLAB
MATLAB release MATLAB 8.0 (R2012b)
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Comments and Ratings (13)
08 Dec 2014 phil

Hi, Wang!
For several reasons, I need to do the KNN classifier after reducing the dimension of training and sampling data. When the type is guassian, it seems that the eigenvector will be complex number so that KNN is invaild. How can I solve this problem? Thanks so much.


23 Nov 2014 Yan wang  
16 Jul 2014 mania

please help us to do fault detection in nonlinear systems with kernel pca. because i'm a starter in this field.

18 Jun 2014 Quan Wang

Hi Cheung,

If you compute ||a-b||, you will have to use loops. MATLAB loops are slow, and distanceMatrix avoids using loops, thus is very fast.


17 Jun 2014 Cheung


24 Apr 2014 Quan Wang

Dear all,

We have updated the code and the document. The code now generates exactly the same results as shown in the document. I am sorry for the confusion in previous versions of this package. The current version has lots of significant improvements.

08 Mar 2014 Pradeesh

When running demo file why the 3rd fig is in 2d but not in 3d as plot3() is used to plot variable in 3d

03 Mar 2014 Yan Ou  
03 Mar 2014 Siqi

So Good!

03 Mar 2014 Siqi  
05 Apr 2013 Quan Wang

Beside, I myself am using this code package (v2.0) for a number of research projects. I am pretty sure the code works well and has been well optimized.

05 Apr 2013 Quan Wang

Hi Kris. The "paper" (actually a course project report) was using unordered eigenvalues, while in the updated code I have decreasingly ordered eigenvalues. So the code is more "correct" in a scientific sense. If you want to generate the same results as the report, you can uncomment
"% eigValue=eigValue(1:min(size(X)));"
in kPCA.m.

Hope this helps!

04 Apr 2013 Kris Villez

Dear Quan Wang,

Thanks for sharing your code. However, I am not able to reproduce the results displayed in Figure 3 and 4 of your paper.

For Figure 3, it is not clear what the order of the applied polynomial is.

For Figure 4, the two features are highly correlated while the should in fact be uncorrelated. I wondered if this is a mistake in the paper or in the code.

Thanks for your comments,

25 Feb 2013

The efficiency is optimized.

24 Apr 2014

We replaces all demos, and the data used for the demo. We also updated the document to provide better illustration and better experiments. Now the code generates exactly the same results as shown in the paper.

24 Apr 2014

addpath('../code') in demo2

02 Sep 2014

Fixed a fatal bug in pre-image reconstruction.

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