PCA is extended to feature space by nonlinearity function for feature study like image denoising applications. Why do we need nonlinear PCA?
Dear Regan,
Currently I am working on application of PCA in Manufacturing Processes.I have no idea about your question.But I will try to study the nonlinear PCA.
Thank you.
Dear Dhaksnamurthy,
Your question seems not very clear to me. To my knowledge non-linear PCA means applying PCA not directly on extracted features, but on some non-linear transformation (or mapping) of them. Like in Kernel based methods or in Support vector machines, performing PCA on non-linear transformed features will have more desirable properties, such as linear separability in classification tasks etc. What ever you menctioned on image denoising is not clear to me. Please let me know why and how do you use PCA for denoising and what non-linear function and where do you use in denoising?
Hi there,
good introduction in kernel PCA is given in Scholkopf et al., "Nonlinear Component Analysis as a Kernel
Eigenvalue Problem", 1996. It's also worth trying software implementation of the technique from http://accord-net.origo.ethz.ch/ (being transferred to Google code repository).
Why? Maybe it works better than linear PCA. You simply have to try.
Kernel based methods work better for non-linear applications. The same can be said for PCA and kernel PCA. In image denoising, where usually there are nonlinearities Linear PCA would perform poorly, I think. In the web you will find several works for the denoising problem with kernel PCA. However, I do not think that this is the best method to perform denoising in kernel spaces.
thanks for your valuable comment.Actually my idea is image denoising using Non linear PCA. i intend to apply different nonlinear functions.Then compare them in performance wise.But my basic break is why we need nonlinear PCA. How it outperforms linear PCA?. i'll refer above said links,works for clarification..
Kernel based Nonlinear PCA reduces the dimensionality of the data set. It's a great way to extract a feature set for further processing. Interpreting those features in terms of the original data set is problematic. For linear PCA the original data can be described as a linear combination of the components. In general with this isn't possible with Nonlinear PCA. Unlike regular PCA projection from the high dimensional space back to the original space is ill defined.
Hi.
We need non linear PCA when we want to find(or represent) data in little informative features. These informative features are more complicated than PCA features but less than it in counts(some times has more information).
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