Hands-On Unsupervised Learning with Python

PCA with Singular Value Decomposition

Even though we are going to employ complete PCA implementations, it will be helpful to understand how such a process can be carried out efficiently. Of course, the most obvious way to proceed is based on the calculation of the sample covariance matrix, its eigendecomposition (which will output the eigenvalues and the corresponding eigenvectors), and then finally, it's possible to build the transformation matrix. This method is straightforward, but unfortunately, it's also inefficient. The main reason is that we need to compute the sample covariance matrix, which can be a very long task for large datasets.

A much more efficient way is provided by Singular Value Decomposition (SVD), which is a linear algebra ...