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I have done a dimensionality reduction of binary labelled data (0,1 labels) from 300 features to 2 features. The plot looks like -

enter image description here

What kind of inferences can I make from this plot? Can I infer -

  1. Linear models probably would not generalize well for this data?
  2. Non linear models would probably be a better fit for this data?
  3. For this feature space (300 features), the data is non-linear?
  4. What inferences can be made using PCA plots?

UPDATE: More context on the question. I am solving a classification problem (a model to predict class membership). I was doing exploratory data analysis to gauge if my data is better fit for linear or non-linear models. I know there are other ways to do this QQ-plots, feature-label scatter plots etc. But can we deduce this using a PCA plot as shown above? The original 300 features have 15 discrete features & 285 continuous features.

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  • $\begingroup$ The questions are vague because you don't give enough details: what do you want to "model" or "fit"? Do you want a model to predict class membership? Apart from that, you seem to have some discrete features. Are all of them discrete? Only some of them? $\endgroup$ – amoeba Jan 27 '16 at 17:33
  • $\begingroup$ @amoeba amended the question to answer your clarifications. $\endgroup$ – Srikar Appalaraju Jan 28 '16 at 3:42
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For your 4th question: I don't think you can conclude much from this plot beyond the fact that a two component reduction of your data doesn't seem to allow a good categorization.

For your 1st and 2nd: It still could be that, on your original 300 variable data set, linear models work well (or not), nonlinear models work well (or not).

For your 3rd: I don't understand. Data can't be linear or nonlinear - that's a characteristic of models, not data - and, since you've shown nothing about the full data set, you can't draw conclusions about it.

If you had found that the two components extracted 90% of the variance, then the above would have to be amended. But you haven't told us how well the PCA worked.

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