Fitting MPCA: HOSVD, then alternate

Initialize with HOSVD — the leading left singular vectors of the three feature-mode unfoldings. Then update one factor at a time with the other two fixed, maximizing total score energy; each update is one matrix SVD.

The joint problem is nonconvex. HOSVD alone need not maximize retained energy, and refinement seeks a stationary point: a finite budget guarantees neither convergence nor a global optimum.

At an equal 12 scores, unrestricted PCA must win on training reconstruction error. Held-out classification may disagree: dense PCA-12 gives about 0.788 balanced accuracy, multilinear about 0.774 — less accuracy for 18 times less basis storage.