In other words, we perform a nonlinear mapping via kernel PCA that transforms the data onto a higher-dimensional space. We then use standard PCA in this higher-dimensional space to project the data back onto a lower-dimensional space where the samples can be separated by a linear classifier (under the condition that the samples can be separated by density in the input space). However, one downside of this approach is that it is computationally very expensive, and this is where we use the kernel trick. Using the kernel trick, we can compute the similarity between two high-dimension feature
...more
