A Latent Anchor Approach to Identifiable Nonnegative Tucker Decomposition

Nonnegative Tucker decomposition is a powerful tool for analyzing multiway data, but its parameters are generally not identifiable. Recent work addresses this problem, establishing identifiability guarantees under certain sparsity assumptions on the factor matrices. This paper proposes a complementary approach that instead assumes a low-rank structure on Tucker's core tensor. We introduce "latent anchors" to construct the core tensor itself as a structured canonical polyadic (CP) decomposition. We draw insights from CP decomposition and separable nonnegative matrix factorization to prove the uniqueness of nonnegative Tucker under our parameterization. We verify the uniqueness result numerically through a correspondence between uniqueness, statistical identifiability, and Fisher information. Synthetic experiments demonstrate that the proposed method bridges the gap between the identifiability of CP and expressivity of Tucker.