PCA == Principal component analysis. If one models the pieces as being linear combinations of orthogonal vectors, the eigenvalues corresponding to the different modes will follow some distribution. A mostly-monotonous image (e.g., blue sky above a field of snow) might have high eigenvalues for a few modes and low values for the rest, hinting that the puzzle has relatively few kinds of pieces which poses a challenge to puzzle solvers. And an extremely detailed image might have a near-uniform set of eigenvalues across a very large number of modes, hinting that the puzzle may have relatively little piece-to-piece structure or clustering of similar pieces which poses a challenge to puzzle solvers.
Do puzzle buyers pay more for "hard puzzles" versus "easy puzzles" of a given piece count? And are there algorithmic indicators for difficulty?