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Kernel PCA and Pre-Image Reconstruction

version 1.4 (6.9 MB) by

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

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13 Ratings

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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.

Comments and Ratings (22)

Hi Wang, I have a small doubt. How do we define our own kernel here? I want to use an rbf kernel.

chen

chen (view profile)

kumud arora

Why the test data kernel is not centralized??

Anamika jain

which type of data should be used to execute this code?

danhe

danhe (view profile)

what is the form of the database to use

phil

phil (view profile)

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.

Phil

Yan wang

mania

mania (view profile)

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

Quan Wang

Quan Wang (view profile)

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.

如果用||a-b||,就需要是用MATLAB循环,而MATLAB循环非常慢。我的distanceMatrix就是一个巧妙避免使用循环的方法,因此很快。

Cheung

Cheung (view profile)

您好,请问在distanceMatrix函数中D=XX1+XX2-2*(X*X')起什么作用?如果使用gaussian的话,distance不应该直接就是||a-b||吗?请赐教,非常感谢!

Quan Wang

Quan Wang (view profile)

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.

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

Yan Ou

Yan Ou (view profile)

Siqi

Siqi (view profile)

So Good!

Siqi

Siqi (view profile)

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.

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!

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,
Kris

Updates

1.4

Fixed a fatal bug in pre-image reconstruction.

1.3

addpath('../code') in demo2

1.2

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.

1.1

The efficiency is optimized.

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