What is the difference between PCA and Factor Analysis in dimensionality reduction?

PCA focuses on variance maximization, while Factor Analysis models latent variables causing observed correlations.

PCA is a deterministic linear transformation that projects data onto orthogonal axes maximizing variance, treating all variance as signal. Factor Analysis assumes observed variables are generated from a smaller number of latent factors plus noise. It explicitly separates shared variance (common factors) from unique variance (noise), making it probabilistic and more interpretable in statistical modeling contexts.