PCA vs.KernelPCA: which one to use for high dimensional data? I have a dataset which contains a lot of features (>>3). For computational reasons, I would like to apply a dimensionality reduction. At this point I could use different techniques:

standard PCA
Kernel PCA
LLE
...
My problem is to choose the right approach since the number of features is so high that I cannot know beforehand what the distribution of points is like. I could do it only if I have 3D data, but in my case I have much more than that.

I know for example that if the set of points was lineary seperable I could use standard PCA; if it was somehow a sort of concentric circles like shape, then KernelPCA would be a better option.

Therefore how can I know beforehand which dimensionality reduction technique I need to use for high dimensional data?
It can be hard to choose - because it's hard to visualize. However, you probably have a specific goal right? Maximizing some kind of score.

Why don't you try a Grid Search applied to your dimensionality reduction decision? See this.

I'm interested in reading other, more theoretical answers to this question, though.