Machine Learning Algorithms - Second Edition

Kernel PCA

We're going to discuss kernel methods in Chapter 7, Support Vector Machines, however, it's useful to mention the KernelPCA class, which performs a PCA with non-linearly separable datasets. This approach is analogous to a standard PCA with a particular preprocessing step. Contrary to what many people can expect, a non-linear low-dimensional dataset can often become linearly separable when projected onto special higher-dimensional spaces. On the other hand, we prefer not to introduce a major complexity that could even result in an unsolvable problem. The kernel trick can help us in achieving this goal without the burden of hard, non-linear operations. The complete mathematical proofs are beyond the scope of this book, however, we ...