In the previous chapter, we understood what principal component analysis(PCA) is, how it works, and when we should be deploying it. However, as a dimensionality reduction technique, do you think that you can put this to use in every scenario? Can you recall the roadblock or the underlying assumption behind it that we discussed?
Yes, the most important assumption behind PCA is that it works for datasets that are linearly separable. However, in the real world, you don't get this kind of dataset very often. We need a method to capture non-linear data patterns.
On the left-hand side, we have got a dataset in which there are two classes. We can see that once we arrive at the projections and establish the components, PCA doesn't have an effect on it and that it is not able to separate it by a line in a 2D dimension. That is, PCA can only function well when we have got low-level dimensions and linearly separable data. The following plot shows the dataset of two classes:
This is why we...