Spiked tensor PCA

A different “tensor PCA” — recover one planted direction from a single noisy symmetric order-3 tensor, Y = β v⊗v⊗v + E, with ‖v‖₂ = 1. Spanish: PCA tensorial con señal plantada.

The objective is cubic, not quadratic like uᵀCu, and a power-style step contracts two indices: u ← Y(I, u, u), normalized. The notebook tries several starts and keeps the best visited point — which does not certify a global optimum.

This is the problem of Montanari and Richard (2014). Statistical recoverability and an algorithm’s ability to find the signal are separate questions — and it is a different problem from multilinear PCA.