# How do I know whether to use linear or nonlinear dimension reduction method given a high dimensional data set

I want to use dimension reduction method for a high dimensional data set Is there any possible way to assess the "non-linearity" of the data first to give me the insight of whether I should use linear method (e.g. PCA) or nonlinear method (e.g. NLPCA)? I read several literatures and neither of them could provide a justification of when should I use linear of nonlinear method. They always use examples of "swiss roll" to indicate a data set which I should use nonlinear method. But for practical case, I cannot visualize a high dimensional data set first before I choose the method. To put it more straightforward, I want to have a test of the data set first and the result will tell me whether the nonlinear method is more suitable for this data set or vice versus.

Thank you!

• "But for practical case, I cannot visualize a high dimensional data set first before I choose the method." - I don't get this part. What do you mean you can't visualize the data first? For visualization purposes 2 or 3-dimensional reduction is used, so if you can't run this, you won't be able to run anything using more dimensions. Sep 6, 2017 at 20:01
• @JakubBartczuk Hi Jakub, in my opinion, using dimension reduction will change the original form of the data. Some data will look linearly after dimension reduction but it is nonlinear in the original space, thats what I am saying here. Sep 6, 2017 at 23:37
• The problem with this question is that there is no such single thing as 'nonlinear structure'. Different manifold learning algorithms optimize for different things, and it seems like there is no single one to outperform the others. Sep 9, 2017 at 10:10
• I've had this question for years and still cannot find a clear answer which is general. I always get over simplified examples which do not reflect most real world cases... May 28, 2020 at 9:44
• I often do both and make a comparison between the two. Jun 23, 2021 at 21:26