PCA is a deterministic algorithm which doesn't have parameters to initialize and it doesn't have local minima problem like most of the machine learning algorithms has.

What is local PCA?

The local PCA defines local coordinate patches for the data, with the orientation of the local patches determined by the PCA within each region Ri.

Is PCA optimal?

PCA is often used in this manner for dimensionality reduction. PCA has the distinction of being the optimal orthogonal transformation for keeping the subspace that has largest "variance" (as defined above).