Kernel PCA and Pre-Image Reconstruction

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

Description

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which is promising in exposing the more complicated correlation between original high-dimensional features. In this paper, we first talk about the basic ideas of PCA and kernel PCA, and then focus on the reconstruction of pre-images for kernel PCA. We also give an introduction on how PCA is used in active shape models (ASMs), and discuss how kernel PCA can be applied to improve traditional ASMs. Then we show some experiment results to compare the performance of kernel PCA and traditional PCA for pattern classification. We also implement the kernel PCA-based ASMs, and use it to construct human face models.

• Required Products: MATLAB
• MATLAB release: MATLAB 7.7 (R2008b)

[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